AN EXPERIMENTAL FACILITY FOR STUDYING
CONVECTIVE HEAT TRANSFER
IN BUILDINGS
By
SCOTT HOWARD SANDERS
Bachelor of Science
Oklahoma State University
Stillwater, Oklahoma
1992
Submitted to the Faculty of the
Graduate College of
Oklahoma State University
in partial fulfillment of
the requirements for
the degree of
MASTER OF SCIENCE
July, 1995
AN EXPERIMENTAL FACILITY FOR STUDYING
CONVECTIVE HEAT TRANSFER
IN BUILDINGS
By
SCOTT HOWARD SANDERS
Bachelor of Science
Oklahoma State University
Stillwater, Oklahoma
1992
Submitted to the Faculty of the
Graduate College of
Oklahoma State University
in partial fulfillment of
the requirements for
the degree of
MASTER OF SCIENCE
July, 1995
OKLAHOMA STATE U~Tf\TERSITY
AN EXPERIMENTAL FACILITY FOR STUDYING
CONVECTIVE HEAT TRANSFER
IN BUILDINGS
Thesis Approved:
~#tviser
If·
Dean of the Graduate College
11
ACKNOWLEDGMENTS
A thesis could probably be written on all the people that have had some kind of
influence on this research project. These people have all provided valuable knowledge
and even more importantly, priceless friendship.
First of all, I would like to thank the University Center for Energy Research for
providing the funding necessary for the construction of the Building Heat Transfer
Laboratory and for recognize the need for such a facility at Oklahoma State University.
In the same regards, I would like to thank Dr. Lowery for providing the perfect place to
build the facility and allowing us to "ruin a perfectly good reverberation chamber".
A special thank you goes to my advisor Dr. Spitler. His patience on this research
project was deeply appreciated and admired. He allowed me to collaborate with him on
this project and provided the necessary guidance when it was needed. Most importantly,
he believed in my abilities to get the job done.
My office mates: Mike Ramey, who allowed me to search through hundreds of
articles that he had obtained for my literature search which saved me a lot of time in
trying to find those articles for myself, and for teaching me all I ever wanted to know
about UNIX and Jeff Ferguson for his cooperation in the design, construction and testing
of this facility.
Three people who, if it was not for them, this project would still be on the ground
Darrell Daugherty for designing the room supports. Tony Timko for designing the flow
measurement box for the air conditioning system. And lastly Richard Paige for bringing
his construction knowledge to this project.
111
I am also deeply in debt to the MAE Electronics Shop. Without Robert Taylor,
Tom Crowell, and Don Lucas I would have been lost when it came to the electronic
aspect of this project. They provided valuable assistance and allowed me to scavenge
what ever I could find from the shop
The two people who had the most influence on this project do not even attend
Oklahoma State. They are my parents, Ed and Pat Sanders. Mom always saw to it that I
received the very best out of life and dad taught me the most important thing a person can
have is common sense. If it wasn't for their weekend projects around the house, I would
have never learned the skills that I did in order to construct this facility. I love you both.
Lastly, but will always be number one on my list, my wife Valerie and her
daughter Tiara. Their love, smiles and patience always lifts me during hard times. If not
for Valerie's valuable input to the drafts and proofreading of the drafts, it would easily be
another year before graduation. I will always love you both.
There are several people that also have played a valuable importance in my life. I
will not go on to name these people, (if I did, this section would be the longest part of
this dissertation) but they know who they are and what positive affects they have had on
my life.
iv
TABLE OF CONTENTS
Chapter Page
1. INTRODUCTION 1
Overview 1
Literat'ure Review 1
Scale Models 2
Discussion of Scale Model Research 8
Full Scale Enclosures 8
Objectives 15
2. EXPERIMENTAL FACILITY 17
The Experimental Room 17
The Floor of the Experimental Room 18
The Walls of the Experimental Room 21
The Ceiling of the Experimental Room 26
The Guard Space 28
Surface Heat Balance 29
Panel Surface Temperature 30
Unit Resistance for the Elements of the Experimental Room 31
Panel Heating 32
Control of the Heated Panels 37
Experimental Configuration 38
3. ANALYSIS OF EXPERIMENTAL DATA 43
Data Analysis 43
Determining the Heated Panel Fluxes 43
Power Input to a Panel 43
Backlosses from a Panel 44
Radiative Flux from a Panel 45
Convective Flux for a Panel 47
Determination of the Convection Coefficient 47
Characteristic Parameters 47
Volumetric Flow Rate 47
Inlet Velocity 48
Air Changes per Hour 48
v
Archimedes Number 48
GrashofNumber 49
Prandtl Number 50
Rayleigh Number 50
Nusselt Number 51
Jet Momentum 51
Experimental Uncertainties 52
Uncertainties in Fluke Datalogger Temperature Measurements 52
Uncertainties in Panel Power Measurement 52
Uncertainties in Volumetric Flow Rate Measurement 53
Uncertainties in Derived Quantities 54
Uncertainties in the Calculation of the Air Heat Gain 54
Uncertainties in the Calculation of the Film Coefficients 55
4. EXPERIMENTAL RESULTS AND DISCUSSION 59
Overview 59
Experimental Results 59
Panel Control Results 61
Transient Response of the Room 64
Energy Balance on the Room 66
Previously Published Correlations 67
Natural Convection Correlations 67
Forced Convection Correlations 68
Comparison 69
5. CONCLUSIONS AND RECOMMENDATIONS 73
6. REFERENCES 77
APPENDICIES 79
Appendix A: Conduction Program for Predicting
the Panel Surface Temperature 80
Appendix B: Calculation of Unit Resistance for the Floor, Ceiling
and Walls of the Experimental Room 81
Appendix C: Control of Heated Panels and Temperature
Recording Program 85
Appendix D: Interchange Area Factors Calculation Program for
Radiation Analysis 102
vi
Appendix E: Data Reduction and Analysis Program 116
Appendix F: 15 ACH Experimental Averages 123
Appendix G: 20 ACH Experimental Averages 124
Appendix H: 25 ACH Experimental Averages 125
vii
LIST OF TABLES
Table Page
2.1: Panel Surface Temperatures(OF) at Different Wire Temperatures(OF) 35
2.2: Wire Resistance and Current for the Different Surfaces 36
2.3: Wire Diameter for the Different Surfaces 36
4.1: Experimental Results and Derived Quantities 60
4.2: Comparison of Experimental Film Coefficient to the Correlation
Determined Film Coefficient 70
viii
LIST OF FIGURES
Figure Page
2.1: The experimental facility 18
2.2: Leg supports for the floor (typical) 19
2.3: Plan view of the floor 20
2.4: Profile view offloor 20
2.5: Floor joint detail 21
2.6: View of north and south walls 22
2.7: View of west wall 23
2.8: View of east wall 24
2.9: Typical wall cross section looking from side of from top ofwall 25
2.10: Wall joints detail 25
2.11: Corner details of the experimental room 26
2.12: Ceiling plan view 27
2.13: Ceiling profile view 28
2.14: Surface heat balance for a typical surface 29
2.15: Electrical resistance equivalent of the floor's unit resistance 31
2.16: Electrical resistance equivalent of the wall's unit resistance 32
2.17: Typical cross section for a panel 33
2.18: Boundary conditions for calculating the panel surface temperature 34
2.19: Temperature profile for a panel 34
ix
2.20: Panel plan view 37
2.21: Air inlet location in south wall of experimental room 39
2.22: Air outlet location in north wall of experimental room 40
2.23: Floor passive panel cross section 41
2.24: Wall passive panel cross section 41
2.25: West wall configuration for the experiments 42
4.1: Panel number 1 temperature during 15 ach experiment 62
4.2: Panel number 8 temperature during 25 ach experiment 63
4.3: Panel number 12 temperature during 15 ach experiment 64
4.4a: Air inlet and outlet temperatures during the 25 ach experiment 65
4.4b: Air inlet and outlet temperatures during the last 25 minutes of the
25 ach experiment 66
4.5: Energy balance for the three experiments performed showing the
uncertainty in panel power and air heat gain 67
4.6: Film coefficients determined experimentally and by correlations
at each flow rate 71
4.7: h versus bulk air velocity for floor with east wall inlet, 22 tests
(size is proportional to Archimedes number) 71
x
NOMENCLATURE
inlet  the point at which the working fluid enters the enclosure
outlet  the point at which the working fluid exits the enclosure
Nu  The Nusselt number
Ap or A  The aperture ratio
Ra  The Rayleigh number
h  the convective heat transfer coefficient or film coefficient (BTU/ft2  OF)
hmix  the convective heat transfer coefficient or film coefficient for mixed convective
heat transfer (BTU/ft2  OF)
hnatural  the convective heat transfer coefficient or film coefficient for natural
convective heat transfer (BTU/ft2  OF)
hforced  the convective heat transfer coefficient or film coefficient for forced convective
heat transfer (BTU/ft2  OF)
o.c. on center
Q Heat Flux(Btu/hr)
A  Area (ft2)
T  Temperature (OF)
F  The grey interchange factor
cr  The Stefan  Boltzmann constant
Ro  Wire resistance (ohm)
V  Line voltage (volts)
a  Coefficient of thermal resistance of the wire (ohms/ohm/oF)
U  Overall heat transfer coefficient (BTU/(hrft2  OF))
Do  Fluid velocity at inlet (ft/s)
xi
vfr  Volumetric flow rate (ft3/min)
P Coefficient of thermal expansion (l/R)
g  gravitational acceleration (32.2 ft/s2
)
Lc  Characteristic length (ft)
u  kinematic viscosity (ft2/s)
k thermal conductivity of fluid (Btu/hrftOF)
u  uncertainty
p  density of fluid (lbm/ft3
)
Cp  Specific heat of air at constant pressure (0.24 Btu/IbmOF)
Ar  Archimedes Number
Or  OrashofNumber
Pr  Prandtl Number
J  Jet momentum number
xii
1 INTRODUCTION
1.1 Overview
Ofthe three fundamental heat transfer processes occurring in buildings,
conduction, radiation and convection, convection is the least understood. In the analysis
by simulation of a building's cooling and heating load, the conductive and radiative heat
transfer can be predicted relatively accurately, but the prediction of the convective heat
transfer is imprecise and relies on experiments performed 60 years ago using vertical, free
standing flat plate geometry that is not typical of buildings. The inability to accurately
predict the convective heat transfer component can lead to improper design of the heating
and air conditioning system.
This thesis describes the design and development of an experimental facility for
the study of convective heat transfer in buildings. The interior dimensions of the
experimental room are 12 feet by 16 feet by 10 feet; these dimensions may be made
smaller to study smaller enclosures such as attics and plenum spaces.
The goal of this project is to develop a versatile and operational facility for the
study of natural and forced convection in buildings. The facility should be unique in
design and not limited by the types of surfaces that can be studied, or only to convective
heat transfer on surfaces.
1.2 Literature Review
To date, convective heat transfer in buildings has been studied in scale models and
full size enclosures, with particular emphasis on natural convection heat transfer that
occurs at Rayleigh numbers on the order of 1010. Some of these test models and
enclosures are discussed here.
2
1.2.1 Scale Models
Lawrence Berkeley Laboratory (LBL)
Fred Bauman et ale
Bauman's study (Bauman et aI., 1980) used a table top size scale model utilizing
water as the working fluid. This model was designed to measure natural convection
within a single zone, or, with the insertion of a partition (to simulate a doorway), between
two geometrically identical zones. The model had dimensions of 30 inches by 10 inches
by 5 inches. The two opposing 30 inch by 5 inch walls were constructed from 0.2 inch
copper plate. The remaining four surfaces were constructed from 0.5 inch plexiglass.
The removable partition was constructed from 0.25 inch plexiglass.
One copper plate served as the hot wall while the other served as the cold wall.
The hot wall had a constant heat input provided by six thermofoil heaters attached to the
outside surface. The cold wall was chilled with 59°F tap water running through four
horizontal 0.4 inch outside diameter cold rolled copper tubes glued to the outside surface
of the wall with high conductivity epoxy. The entire model was covered with 0.5 inch
polyethylene sheeting and a 2 inch shell of styrofoam. No measurements of temperature
were made to calculate losses from the model to the surroundings.
Experiments performed covered the Rayleigh number range of 1.6x109 to
5.4x10 10. Data that was obtained agreed well with previous studies dealing with
convective heat transfer in a single zone. Due to Prandtl number differences between
water and air, strict similarity to full scale enclosures could not be obtained. This leads to
possible limitations in use of the data obtained from the model in the development of
correlations for full scale enclosures using air as the working fluid.
Lawrence Berkeley Laboratory (LBL)
Mark Nansteel et ale
Nansteel et al. (1981) expanded upon Bauman's work by using a model with
dimensions of33 inches by 12 inches by 6 inches. Again the two longest walls were a
3
hot wall  cold wall combination. The hot wall was manufactured from 0.2 inch copper
plate and heated by 18 thermofoil heaters in three vertical columns of six each. The cold
wall was 0.6 inch aluminum plate with two rectangular channels machined into the
aluminum. These channels traversed the full breadth of the enclosure seven times. Tap
water was used as the coolant for the wall.
The rest of the surfaces were made of 0.5 inch plexiglass. The joints between the
plexiglass and the metal walls were sealed with cork gasket to minimize conduction. The
ceiling, however, was removable and thermally isolated from the metal walls by air gaps.
A removable partition made of 3.75 inch plexiglass could be inserted through the ceiling
of the model so that partition lengths of 0, 1.5,3, and 4.5 inches could be studied in the
model. Two other partitions could also be used in the model. One of these was a highly
conductive partition fabricated from aluminum. The other partition was an adiabatic
partition fabricated from polystyrene foam encased in 0.004 inch stainless steel sheets.
The entire model was enclosed in a polyurethane foam shell and the outer surface
was covered with aluminum foil to reduce radiative heat transfer to the surroundings.
However, no estimate of the conduction losses or of the radiative heat transfer was
apparently made in the experiment. Water was used as the working fluid in the model.
The Rayleigh number range for Nansteel's experiments was 2.3xl010 to 1.1xl011 .
Again the high Prandtl number limited the correlations that could be developed; however,
two correlations were developed for conducting and non conducting partitions. These
two correlations are:
Nu = O.748Ap0.256RaO.226
Nu = O.762Ap0.473RaO.226
conducting partitions
nonconducting partitions
(1.1)
(1.2)
where: Nu = the Nusselt number
Ap = the aperture ratio, which is the product of the height and width of the
partition divided by the product of the height and width of the
enclosure
Ra = the Rayleigh number
4
The effect higher Prandtl number had on the heat transfer could not be determined.
Solar Energy Research Institute (SERI)
Mark Bohn et ale
The model used by Bohn et al. (1983) was a cubical enclosure with interior
dimensions of 12 inches. The model was constructed from eight aluminum plates that
were 0.5 inches thick. The four inner plates overlapped one another and were screwed
together with neoprene gaskets in the joints. The four outer plates provided heating and
cooling to the four inner plates of the enclosure. These four outer plates were sealed and
bolted to the enclosure walls. The aluminum walls were either heated or cooled by
pumping water through channels that were machined in the outer plates of the enclosure.
The top and bottom of the enclosure consisted of 0.5 inch Lucite plates. These plates
were screwed to the enclosure walls and had neoprene gasket joints.
The aluminum walls were insulated with 3.25 inch thick urethane foam board
insulation. Conductive heat losses were estimated based on wall temperature, outer
surface temperature of the insulation and thermal resistance of the insulation. The top
was uninsulated and the losses through it were estimated based on the highest
temperature on the outside surface, ambient temperature and an assumed convection
coefficient. The bottom plate was near ambient temperature, and both the top and bottom
plates were assumed to be adiabatic.
The working fluid in the enclosure was deionized water. Experiments covered
the Rayleigh number range from 0.3xl010 to 5xl010. High Prandtl numbers still
resulted; however, a correlation indicated a laminar boundary layer flow heat transfer
mechanism. The correlation that was presented is:
Nu = O.62RaO.25 (1.3)
where: Nu = the Nusselt number
Ra = the Rayleigh number
however, a transition to turbulence was present at high Rayleigh numbers.
5
The Rayleigh number for this correlation used the temperature difference between
the hot and cold walls, or the overall temperature difference for the model. However,
when the film coefficient was calculated, the temperature difference between the wall
temperature and the bulk temperature was used.
By rotating the model, studies on heat transfer on the floor and the ceiling as well
as two walls could be performed. From these experiments, turbulent flow was produced
when the floor was heated. The primary heat transfer from the floor was the release of
thermals. This influenced the heat transfer of the vertical surfaces when it interfered with
the wall boundary layers.
University ofTennessee
M Keyhani et ale
Keyhani's model was made from a rectangular box (Keyhani et aI., 1991) with
interior dimensions of 5.5 inches by 5.5 inches by 6.7 inches. The box was fabricated
from 0.5 inch plexiglass. The end walls were made out of 0.25 inch plate glass. A
copper heat exchanger plate covered the top surface cavity and a constant temperature
water bath was used to heat the copper plate.
The actual enclosure, however, was formed by placing a movable vertical plate
and the copper plate inside the plexiglass box and glass end walls. To minimize losses,
the movable plate, the copper plate, and the bottom plate were instrumented with
siliconerubber thermofoil guard heaters. Differential thermopiles were used to determine
conductive heat losses.
In the model, ethylene glycol was used as the working fluid. The Rayleigh
number range for the experiments was 2.5x106 to 4.6x1010. The resulting Prandtl
number was much higher than that for the experiments performed by other researchers
using water as the working fluid. This would exacerbate the problem of applying the
correlations to full size enclosures that use air as the working fluid. The correlation that
was developed from this scale model is:
where:
Nu = O.296RaO.223AO.53
Nu = the Nusselt number
Ra = the Rayleigh number
A = the aperture ratio
The Rayleigh number in this correlation also used the temperature difference
6
(1.4)
between the hot surface and the cold surface. The development of the film coefficient for
the experiments performed also used the same temperature difference. The bulk
temperature was not used in any of the calculations.
University ofCaliforniaBerkeley
L. Neiswanger et ale
The experimental apparatus used by Neiswanger et al. (1987) was a model with
dimensions of7.9 inches by 10.8 inches by 7.9 inches. An inlet and an outlet, each with
dimensions of2.7 inches by 7.9 inches, were located opposite each other in the center of
each of the two square walls.
The two end walls with the inlet and outlet along with the top and bottom of the
enclosure were fabricated from 0.5 inch transparent acrylic plastic. These surfaces
permitted flow visualization. Water was used as the working fluid in the model. The
water's temperature was kept near the temperature of the laboratory to help in minimizing
the conductive losses through all surfaces of the model. The two long vertical walls had a
sheet of 0.1 inch thick Inconel foil stretched over 1 inch thick polystyrene foam
insulation. An electric current was passed through the Inconel sheet to generate a
uniform heat flux. Conductive losses were minimized by using the thin Inconel and the
polystyrene foam insulation.
It was concluded that the results obtained from this experimental apparatus were
only applicable for the Prandtl number and geometry studied. The Rayleigh number
range that the experiments covered was 5xl09 to lxlO li . The primary use ofthis model
7
was for studying mixed convection heat transfer. The following correlation for mixed
convection coefficient was presented:
hmix == (hnaturala + hforceda)l/a
where a is a constant.
(1.5)
Natural convection could not be studied with this model since a cold wall was not
present. Even though the two walls were heated, only one was studied due to symmetry
of the model. This was the only model to use an inlet and outlet for the water, but the
configuration for the inlet and outlet are not typical of full size rooms.
Massachusetts Institute ofTechnology (MIT)
D. A. Olson et ale
The model used here was an actual scale model of a full size enclosure (Olson et
aI., 1990), which will be discussed in the next section. The model used R114 gas as the
working fluid. The model used the same Rayleigh number and had the same
dimensionless hot wall  cold wall temperatures as the full scale enclosure. Radiative
heat transfer was not scaled between the two, however, but this had no apparent effect on
the results obtained from the two facilities.
The model had dimensions of 53.5 inches by 26.8 inches by 18.5 inches. The
vertical walls were fabricated from three vertical sections of 0.25 inch thick aluminum
plates. Foil faced polyurethane strips insulated the wall sections and the assembled wall
from the floor and ceiling. Electric resistance strip heaters were used to make one wall
hot, while copper cooling tubes soldered to the back of the opposite wall created a cold
wall.
The ceiling was a double pane plexiglass window with a 1 inch gap between the
panes. The floor was also a plexiglass pane. The model was encased in 6 inches of
polyurethane board. An insertable partition was fabricated from 0.6 inch thick
polyurethane insulation.
8
Significant differences were found in temperature profiles and flow patterns as
compared to the studies conducted in scale model enclosures using water as the working
fluid. Experiments covered the Rayleigh number range of 1.3xl010 to 3.4x1010. No
correlation was developed from the data relating the Nusselt number to the Rayleigh
number, however, the data did agree favorably with the correlations from previous studies
conducted by Bohn and Nansteei.
1.2.2 Discussion of Scale Model Research
Scale models are advantageous in that they are relatively inexpensive to construct
and do not require a large area in which to operate. Also, water is opaque to radiation, so
the heat transfer that occurs in the model is convective. The higher Prandtl number that
occurs with water and the other working fluids that were used allows Rayleigh number
similarity with small scale models.
There are, however, many drawbacks to using them. The higher Prandtl number
forces transition from laminar flow to turbulent flow at a higher Rayleigh number. The
applicability of the laminar correlations obtained using water as the working fluid may be
in doubt for the high end of the Rayleigh number regime. Also, in the mixed convection
regime, flow is driven by both buoyancy and inlet/outlet flows. It is generally impossible
to scale both phenomenon simultaneously.
1.2.3 Full Scale Enclosures
Massachusetts Institute ofTechnology (MIT)
D. A. Olson et al.
This is the full size enclosure (Olson et aI., 1990) corresponding to the scale
model discussed above. The room had dimensions of 12.8 feet by 25.9 feet by 8.2 feet.
One end wall consisted of electric radiant heating panels with 0.06 inch thick aluminum
sheeting to provide an isothermal, reflective surface. This served to reduce radiative heat
transfer from the wall, which was estimated along with the conductive losses. It appears
9
no attempt was made to verify the estimates of the conduction losses or the radiative heat
transfer to the surroundings. The opposing wall served as the cold wall and was cooled
using copper solar collector panels mounted on the inside surface.
A partition constructed from 1 inch thick aluminum foil faced polyurethane
insulation panel was mounted midway between the hot wall and cold wall and extended
from the floor half way up the height of the room. Air was used as the working fluid in
the full size enclosure and the results obtained from the room agreed well with the results
from the model. However, the results from the room matched the results from the scale
model research using water as the working fluid in Bohn's and Nansteel's experiments
within thirty percent. The Rayleigh number range used in the experimental room was
from 2.0xl0 10 to 3.lxI010.
This facility can only be used to study natural convection. No air inlet or air
outlet is present so forced convection cannot be studied in this facility.
Energy Monitoring Company (EMC)
Chris Martin et ale
The facility built by EMC (Martin et aI., 1988) was a cube with internal
dimension of 7 feet. The walls, floor and ceiling were made from brick with 5 inches of
styrofoam insulation covering the outside surfaces of the cube.
A metered wall was installed inside the cube. The wall was divided into three
horizontal sections, each heated by a tubular heater. The back of the wall was covered
with 4.3 inches of styrofoam to reduce conductive losses. Highly polished stainless steel
covered the wall surface to minimize radiative heat transfer. A uniform wall temperature
was achieved by using fans along with a ventilation system to move air between the three
wall sections. Back losses for the wall were nearly twice the design figure of 10%. This
affects the uncertainties in the calculated back loss, but not to an unacceptable level.
This facility is useful for studying only one surface, a wall. Due to size
limitations, a room cannot be studied inside the brick enclosure. No mention is made of
10
the air inlet's location in respect to the surface of the wall, or of an air outlet from the
room. The location of these two could affect the heat transfer of the wall. No discussion
of a Rayleigh number range was made and no correlations were developed.
Florida Solar Energy Center (FSEC)
S. Chandra
This facility was a 17.7 foot by 11.7 foot by 8.1 foot naturally ventilated room
(Chandra et aI., 1989) which was part of the Passive Cooling Laboratory. The room was
located in the southeast comer of the lab. Two windows, which were actually unglazed
holes in the wall, were located in the same wall. Two exterior wing walls were used to
create a positive pressure on one window and a suction on the other, depending upon the
wind direction. This created a crossventilation in the room.
The floor of the room was a slabongrade floor with a rubber pad and carpeting.
The walls were lightly insulated, conventional stud frame walls. The ceiling was also
lightly insulated and had a 4 foot ceiling fan hanging from it. All internal surfaces were
unfinished bare 0.5 inch thick gypsum wall board.
Heat transfer was measured on the wall opposite the one with the windows. The
windows were first closed and the room heated with two convective heaters while the
ceiling fan was operating. The heaters and the ceiling fan were then turned off and the
temperature in the room allowed to stabilize. The heaters were then removed and the
windows opened to naturally ventilate the room.
Three panels of 4 foot by 7.87 foot gypsum wall board, with a thickness of 0.5
inches, were nailed on top of the existing wall board and covered with a thermocouple
grid on the front and the back. These thermocouples were used to calculate the radiative
component of the total heat transfer; no measurement of the conductive component was
made.
This facility was used to measure the convective heat transfer on only one surface,
the wall opposite of the window wall, which was a rough surface. Since no other
11
ventilation system was connected to the room, only natural ventilation could be studied in
this facility. No flow visualization work was performed to see how the air flowed across
the wall or if the boundary layer on the wall was laminar or turbulent. A Rayleigh
number range for the experiments was not given and the only correlation developed was
that the convective heat transfer coefficient is a function of local air velocity. It was
shown that this correlation that was developed for a rough vertical surface does not agree
with the equation or data presented in the ASHRAE Handbook of Fundamentals which
was obtained from experiments performed on a copper plate.
Colorado State University (CSU)
J. Neymark
The facility built at CSU (Neymark et al., 1988) was a cube with internal
dimension of 8 feet. This full size enclosure used air as the working fluid and was
geometrically similar to the apparatus at SERI (see previous section on scale models).
The hot wall was constructed from eight electrical resistance heaters utilizing a
graphite heating element with a uniform resistance over the entire surface. Aluminum
foil covered the heater surface to provide a low emissivity and reduce the radiative
component of the total heat transfer. A heated air gap on the back side of the wall was
used to minimize losses to the surroundings.
The cold wall was fabricated from copper solar collector absorber plates. Water
entered through a manifold in the bottom of the plate and exited from an upper manifold.
Water flow was at a rate such that the water temperature difference between the two
manifolds was less than O.3°F. The remaining four surfaces of the enclosure were
constructed from styrofoam sheets with aluminum foil facing. These remaining four
surface were insulated from the surroundings with 18 to 36 inch fiberglass insulation. A
partition used to divide the test cell into two zones was fabricated from two 1 inch thick
aluminum foil faced styrofoam sheets set inside the enclosure, parallel to the hot wall 
cold wall combination.
12
Conduction losses from the enclosure were measured by placing thermocouples
on the outside surface of the fiberglass insulation and only running the hot wall of the
enclosure. Radiation heat transfer from the interior surfaces were measured using surface
mounted thermocouples and the measured absorptivity of the six surfaces.
Since no ventilation system exists, this full size enclosure can only be used to
perform studies of natural convection. The Rayleigh number range for the experiments
was from 4x1011 to 1x1013 and this facility was used to make an important discovery in
that at Rayleigh numbers on the order of 1012, the lower half of the hot wall's boundary
layer was laminar in the water filled model, while in the full size air filled model, a
turbulent boundary layer was present. The correlation developed from the data obtained
in the full scale enclosure was:
Nu=aRab (1.6)
where: Nu =the Nusselt number
Ra = the Rayleigh number
a and b = constants dependent upon the aperture ratio.
SulzerInnotec, Research and Development
Andreas Schachenmann
This experimental room (Schachenmann et aI., 1990) with interior dimensions of
22 feet by 14.8 feet by 9.7 feet was constructed for verifying numerical methods of pure
ventilation and free convection. An air inlet was located near the ceiling in one of the
14.8 foot walls, while the air outlet was located near the floor in one of the 22 foot walls.
The heat transfer surfaces of the room, which were the floor and the 22 foot wall opposite
the air inlet, consisted of plate heaters with many passes through them. The surface was
made either hot (91°F) or cold (54°F) by running hot water or chilled water through the
circulation system. The ceiling and the rest of the walls were insulated. All surfaces of
the experimental room were covered with aluminum foil to reduce the radiative
component of heat transfer. Removable partitions could be set up anywhere on the floor
of the experimental room. The experimental room was located inside a building so that
13
experiments could be performed year round; however, the experimental room itself was
not enclosed inside a guard space. Conduction losses into the building were measured,
but apparently no attempt was made to reduce the losses from the two heat transfer
surfaces.
A Rayleigh number range for the experiments was not given. The correlation
developed was similar to that developed by Neiswanger for the convective heat transfer
coefficient, except that Schachenmann applied it to the Nusselt number instead.
Only one inlet/outlet configuration is possible for this room. It can be used to
perform experiments for natural convection, but only between the floor and one wall, not
between two facing walls. The concept of a movable partition is a good idea in that the
partition can be set at any position, at any height, and at any angle to the air inlet or air
outlet. This concept along with a movable inlet/outlet combination would permit an
unlimited number of flow fields to be studied.
University ofIllinois  Urbana Champaign (UIUC)
JeffSpitler et ale
The first facility built at VIVC (Spitler et aI., 1987) was constructed from 8 inch
concrete block. The room was enclosed by a guard space and both interiors were
temperature controlled. The guard space was divided into two thermally separate Lshapes,
one heated to simulate a typical summer design day, and the other space a freefloating
temperature space.
The concrete block room had internal dimensions of 14.6 feet by 11.9 feet by 8.5
feet. Heat flux transducers were installed on the north and east walls (adjacent to the
heated portion of the guard space), and the walls were then painted black. Depending on
the experiment being performed, the remaining two walls either had aluminum foil
covering them, or had a black painted surface.
The floor and ceiling were insulated with 3.9 inches of aluminum foil faced
styrofoam. This made these surfaces nearly adiabatic and reduced the number of heat
14
transfer processes occurring in the room. The insulation for the floor lay on the
laboratory floor. 5.9 inches of concrete covered the ceiling's insulation and separated it
from the guard space.
A diffuser located at the center of the ceiling provided conditioned air to the
room. A return duct attached to the south wall was used as an air outlet from the room.
The mass flow rate of air into the room could be varied using a damper.
Losses due to conduction were not calculated and cooling load calculations for the
room showed that the assumption of an adiabatic floor and ceiling were incorrect.
Radiative heat transfer was calculated and subtracted from the total heat flux to determine
the convective heat transfer component.
Only two surfaces could be studied with this room, only one air inlet/outlet
configuration could be used, and the ventilation system could only provide a low flow
rate. The two passive walls had no control whatsoever. A range of Rayleigh numbers
and a correlation were not presented; however, several regression analyses were
performed to determine on what variables the convective heat transfer coefficient was
dependent. The laboratory floor may have had an effect on the floor of the room,
especially if it were a cold concrete floor, which would invalidate the adiabatic
assumption.
The second facility constructed at DIDe (Spitler et aI., 1991) had internal
dimensions of 15 feet by 9 feet by 9 feet. The walls, floor and ceiling were well insulated
with a typical R value of 57 °Fft2/Btu. The 6 surfaces were made up of 53 individually
controlled wire resistance heater panels. Surface temperature measurements made with
thermocouples were used to control the panels.
A fan system was used to deliver conditioned air to one of two inlets to the room.
One inlet was located in the center of the ceiling, while the other was located in a side
wall, in the center of the left side of the wall. The outlet from the room was located on
the opposite wall from the air inlet to the room, in the bottom left comer.
15
Radiation heat transfer was minimized by maintaining the room surfaces at nearisothermal
conditions. Conduction heat transfer was minimized by the high resistance
value found behind all six surfaces and by enclosing the room in a temperature controlled
guard space.
This facility had a number of beneficial features, one of which is that six surfaces
can be studied at once. One limitation of this feature, though, is that the wire resistance
panels were fixed, and could not be removed. Since the panels could not be removed, the
dimensions for the experimental room were fixed. Another plus for this facility is the use
of two different inlets; however, their positions in the ceiling and the side wall are fixed,
as well as the position of the outlet, due to the fixed panel concept. This facility is useful
for studying either forced or natural convection. One of the walls with heater panels has
cold plates behind the panels, so that a hot wall  cold wall configuration can be used to
generate a natural convection loop. The floor of the room sits on the laboratory floor and
losses due to conduction through the floor cannot be controlled since the temperature
outside the floor cannot be controlled.
1.3 Objectives
The objective of this project is to develop a versatile experimental facility for the
study of convective heat transfer and air flow in buildings. The experimental room
should be able to be set up for a multitude of air inlet/outlet configurations. Multiple
room configurations should also be possible. This means that the room should be able to
be configured as an attic or a plenum space, about which very little is known in the area
of heat transfer. This demand also includes vertical partitions for the study of heat
transfer between two zones.
The room should also be useful for studying different types of surfaces, such as
building exteriors, different roughness of walls that are found inside buildings today, and
fenestration. Losses due to conduction and the radiative heat transfer for all six surfaces
of the room must be minimized as much as possible.
16
The experimental room should not be limited to the study of convective heat
transfer on surfaces only. It should also be capable of being used to perform experiments
for the measurement of radiative and convective fraction of heat gain from equipment
such as computers, photo copying machines, printers and other modem office equipment.
Computer programs using computational fluid dynamics algorithms have been
written to predict air flow and temperature inside a room. The experimental room can be
used to validate these computer programs.
A heating system that has become popular recently is hydronic radiant floor
heating. There is debate over the modeling and controlling of this type of system. The
experimental room with it's removable panel scheme is an excellent facility for
conducting studies on hydronic radiant floor heating systems.
Accuracy is of utmost importance. In order to obtain excellent results, the
temperature measurement is very important since all data reduction and any derivation of
correlations will depend upon the temperature measurement. In the same regards, the
control of the heated panels is very important. The use of a proportional controller should
give better results than any other facility has obtained with previously used control
algorithms.
17
2 EXPERIMENTAL FACILITY
2.1 The Experimental Room
The experimental room is a 12 foot by 16 foot by 10 foot (inside dimensions)
enclosure with one hundred and eighteen "honeycomb" cells. A total of one hundred and
eighteen panels may be used for natural convection experiments, while one hundred and
sixteen panels may be used for a forced convection experiment (two "honeycomb" cells
are for the air inlet to the room and the air outlet from the room). Provisions have been
made to enclose the experimental room with a temperature controlled guard space with
dimensions of 21 feet by 27 feet by 22 feet. An unlimited number of air inlet/outlet
configurations can be set up due to a removable panel scheme in which one removable
panel covers one "honeycomb" cell. This removable panel scheme also allows different
heated panels or cooled panels to be studied. It will also permit the study of heat transfer
in different types of room configurations.
18
13'
//
//
/
Figure 2.1: The experimental facility
2.1.1 The Floor of the Experimental Room
The floor of the experimental room is elevated above the floor of the laboratory
with twenty six 2 inch by 10 inch by 5 foot planks placed around the perimeter of the
floor. Four 2 inch by 10 inch by 5 foot planks are placed in the center of the floor to
prevent any possible sagging of the floor. All of the legs for the room are attached to
each other with 2 inch by 4 inch boards in order to stiffen the supports. All legs are
attached to the floor of the experimental room with two 0.375 inch bolts per leg.
19
3/8" Bolt 3.5"
2x4 Spacer Placed
Between the 2x4 Cross
Members
•
3/8" Bolt 5" Long
asten
•• ~
e>
•
Figure 2.2: Leg supports for the floor (typical)
By lifting the floor of the experimental room off the laboratory floor, the
temperature underneath the room can be controlled to a desired set point. This will assist
in reducing the conduction losses through the floor, something no other facility has done.
The floor is constructed from 2 inch by 8 inch boards. The floor is essentially two
layers of 2 inch by 8 inch boards assembled to create a 2 foot o.c. by 4 foot o.c.
"honeycomb" of twenty four cells. Figure 2.3 shows the honeycomb layout of the floor
as well as the leg placement.
20
0'
L12x8for
outside legs to
bolt to
Jiro..
2X10~ 0.5 inch Plywood./'
'' LJ
Insulation Border
~ r'1 sI. [ ] ~
1 [
Qi "E [ 2~V"
0 Qi
CD "E c: 0
0 CD
~ c: 12.0
"S ~ ~ 0
(/) ~
E [ "S
~ (/) E ~
[ ~ l~ •
E4.OO'~~ ~ ~
Insulation Border 2x8 Floor Joist (2)
~ rt
I 16.00' 
x8 Bolted to outside legs~
Figure 2.3: Plan view of the floor
The insulation border around the perimeter of the floor is filled with R19
insulation. This insulation border is 18 inches wide and supports the walls.
2x8 For Legs
0.5" Plywood Note: All Joints Are Epoxy Joints
2x8 Cross Piece
46.5" Long
2x8 Floor Joist
Insulation Border (R19)~
Figure 2.4: Profile view of floor
21
xperlmenta oom
2x8 12' Long Floor Joist
Epoxy Joints
2x8 46.5" Long _J
3.5" Screws
""' 2x8 12' Long Floor Joist
, ,
/.·/~X
I
I
I
I
,I
,,I
: 2x8
\\
~,............................._...._..
Figure 2.5: Floor joint detail
2.1.2 The Walls of the Experimental Room
The walls of the experimental room are constructed from 2 inch by 4 inch studs
and are formed to create a 2 foot o.c. horizontal by 4 foot o.c. vertical "honeycomb" of
sixty eight total wall cells. Two walls are 16 feet in length and the other two are 12 feet
in length. All walls are 10 feet high. Figures 2.6 and 2.7 show the "honeycomb" and
dimensions of the north, south and west walls respectively.
22
2x4 Wall Frame Member
/\
V ~~
10.00'
r~
"
I: 4.00'.j
12.00' 
Figure 2.6: View of north and south walls
/1; 2x4 Wall frame Member
v
23
10.00'
I=:4.00'_1_.16.00'.~1
Figure 2.7: View of west wall
"
24 A 2x4 Wall Frame Member
v
10.00'
Doorway
1......:_4.00'_1_.16.00' .~I
Figure 2.8: View of east wall
Figure 2.8 shows a 3 foot wide by 5.7 foot high doorway for access to the interior
portion of the room. This doorway is filled with an insulation pillow and has three panels
that cover it on the inside of the room. Access is gained by removing the plywood
backing, then the styrofoam back and then the insulation pillow.
The thickness of each wall is 18 inches. This is created by setting two of the wall
frames over the insulation border of the floor. This way the weight of the walls is
concentrated on the leg supports of the room. The bottom of the walls are set 2 inches
above the floor and back 2 inches from the floor edge to allow for the panels, which are 2
inches thick. The two wall frames are connected with 0.25 inch masonite that is glued
and nailed to the 2x4's. The gap between the two frames is filled with two pieces of 0.75
inch thick styrofoam. The ends of the frames and the tops of the frames are fastened
together with 0.5 inch plywood. The bottoms of the frames set on 0.25 inch masonite,
25
which in tum is attached to the leg supports. Figure 2.9 shows a typical cross section of a
wall.
2x4
3/4" Styrofoam 1/4" Masonite
1/4" Masonite
2x4
Figure 2.9: Typical wall cross section looking from side or from top of wall
.:.:.:::.:.:.: :.:.: :::113.5"
~.5"
2x4 10 feet long ~ Epoxy Joint
Looking From Inside Room
,_ 2x4 Horizontal Piece
(12 feet NS Walls, 16 feet EW Walls)
Bottom of Wall
Figure 2.10: Wall joints detail
26
The corners of the walls match up as shown in Figure 2.11 so that the panels can
be installed on the face of the walls. The comer space between the walls runs the full
exterior height of the experimental room, and this space is filled with R19 insulation
from the bottom of the floor to the top of the ceiling. The outside frames of the walls are
attached to each corner of the insulation border of the floor with 0.5 inch plywood.
Figure 2.11 shows the comer details viewed from the top of the experimental room.
Furring strip
2x4's of wall ..
1/2" Plywood
Backing
Panels _I
Figure 2.11: Comer details of the experimental room
2.1.3 The Ceiling of the Experimental Room
The ceiling of the experimental room is, in essence, the floor sitting on top of the
walls. The 2 inch gap that is necessary for the panels is created by attaching 2 inch by 4
inch studs to the 0.5 inch plywood that is on top of the walls. Joists constructed from two
27
2 inch by 8 inch planks glued together on their edges span across the 12 foot distance.
These joists are spaced at 4 foot o.c. Two 2 inch by 8 inch planks that are glued together
on edge are cut to 46.5 inch lengths to fit between the joists and are placed on 2 foot
centers. This frame work creates twenty four "honeycomb" cells in the ceiling.
An insulation border surrounds the ceiling and is filled with R19 fiberglass
insulation. This border is sealed on the top of the room with 0.5 inch plywood.
0.5 Inch plywoo _.~
Insulation Border
~~
Q>
"E
CD 0m
"E c: 0
0 m
~ c: 12.00'
:i .2
.U=) co :i
U) .=
~
]:,
! ,r
Insulation Border ~ 2x8 Ceiling Joists
~4.00'~ ~0.5 inch plywood
~ 16.00' 
Figure 2.12: Ceiling plan view
27
2 inch by 8 inch planks glued together on their edges span across the 12 foot distance.
These joists are spaced at 4 foot O.c. Two 2 inch by 8 inch planks that are glued together
on edge are cut to 46.5 inch lengths to fit between the joists and are placed on 2 foot
centers. This frame work creates twenty four "honeycomb" cells in the ceiling.
An insulation border surrounds the ceiling and is filled with R19 fiberglass
insulation. This border is sealed on the top of the room with 0.5 inch plywood.
0.5 Inch plywood _.~
Insulation Border
•
Cii
"'C
m0 CD "E c: 0
0 en
~ c: 12.00'
:i 0
.U=) ~:i
U) .=
~
):,
~ •
Insulation Border ~ 2x8 Ceiling Joists
4.00'~ ~0.5 inch plywood

. 16.00' 
Figure 2.12: Ceiling plan view
28
0.5" Plywoo
2x8 Cross Piece
46.5" Long
Note: All Joints Are Epoxy Joints
Figure 2.13: Ceiling profile view
2x8 Ceiling Joist
2.2 The Guard Space
This section describes the concept of the guard space which is yet to be
completed. Currently the north and east walls have been constructed, but have not been
insulated. The south and west walls are completed. Since the walls are not finished, the
heating system is non existent. When future researchers wish to finish out the guard
space, then this section will provide them with the information and ideas that were used
to construct the guard space to its present condition.
The guard space is a 21 foot by 27 foot by 22 foot enclosure in which the
experimental room sits. The south and west walls of the guard space utilize the existing
concrete walls of the laboratory. These two walls are covered with 0.75 inch aluminum
foil faced styrofoam with a 1.5 inch air gap between the concrete walls and the styrofoam.
The north and east walls of the guard space are constructed from 2 inch by 4 inch
studs. The north wall has a 4 foot by 7 foot doorway to provide access to the guard space
from the laboratory. The east wall has a 4 foot by 12 foot door across from the
experimental room's door. This door provides access to the guard space and to the room
for the movement of equipment into and out of the room. The two stud walls have
provisions for R11 fiberglass insulation between the studs, and both sides ofthe walls
are to be covered with plastic. The ceiling of the guard space is the ceiling of the
laboratory. Aluminum foil faced styrofoam should be glued to the ceiling for insulation
purposes.
The guard space will be a temperature controlled environment. A possibility for
the heating system is as follows. A fan is used to pull the air down from the top of the
29
guard space through a header duct to the floor of the guard space. The air is passed
through the fan and exhausted through a duct on the floor and underneath the room. Two
electric heaters placed on the floor of the guard space heats the air as it is exhausted from
the fan. This is done to create a uniform 100°F temperature distribution throughout the
guard space and minimize conduction losses from the wire resistance panel surfaces
inside the experimental room.
2.3 Surface Heat Balance
The fundamental purpose of the experimental room is to study convective heat
transfer from or to a surface. The convective heat transfer coefficient, or film coefficient,
h, needs to be determined over a range of forced and free convection conditions. Figure
2.14 shows the heat balance for a typical surface of the experimental room.
convection
Q ..
radiation
Inside Experimental
Room
Q.
In
Figure 2.14: Surface heat balance for a typical surface
The surface heat balance equation is:
Qin = Qconvection + Qradiation + Qconduction
Plywood Back
Guard Space
3/4" Styrofoam
(2.1)
30
Qconduction is minimized in two ways. The first way is by utilizing a high  thermal resistance
insulation. The second way is to keep the guard space temperature within a
few degrees Fahrenheit of the panel surface temperature, thus minimizing back losses
through the insulation.
If Qconduction is negligible, the surface heat balance equation reduces to:
Qin = Qconvection + Qradiation
Qconvection and Qradiation are functions of the panel surface temperature and of the
(2.2)
room conditions. The measurement and control of the panel surface temperature are of
utmost importance since the two fundamental heat transfer components that have to be
determined rely on this temperature.
The surface heat balance equation can be simplified further by minimizing
Qradiation. By covering the surface of the panel with a material (such as aluminum foil)
with a low emissivity, the radiative heat transfer component is minimized. By operating
at isothermal conditions, Qradiation can also be reduced. However, Qradiation will still
have to be estimated since an isothermal condition cannot be met for all experiments.
Also aluminum foil is not a good backdrop for flow visualization experiments; however,
by implementing a removable panel scheme, the panel can be removed and the aluminum
foil eliminated for a flow visualization experiment. By accurately measuring the power
input to the wire resistance panel, Qin may be accurately determined.
2.4 Panel Surface Temperature
The panel surface temperature is important in determining the heat transfer due to
convection and radiation inside the experimental room. This temperature has to remain
constant over the panel area. The convective heat transfer equation is:
where:
Qconvective = hA(Tpanel surface  Tair)
Qconvective == the convective heat transfer (Btu/hr)
h == the convective heat transfer coefficient (Btu/hrft2_0F)
A == the area of the panel (ft2)
(2.3)
where:
31
Tpanel surface == the temperature on the surface of the panel (OF)
Tair == the temperature of the air at the outlet (OP)
The radiative heat transfer equation from surface 1 to all other surfaces j is:
Qradiation == I AF1 jcr(T4
1, panel surface  T4 j, panel surface) (2.4)
j
Qradiation == the radiative heat transfer (Btu/hr)
A == the area of the panel (ft2)
FIj == the grey interchange factor
(J == the Stefan  Boltzmann constant
T1, panel surface == temperature of panel surface 1 (OF)
Tj, panel surface == temperature of panel surface j (OF)
Each panel is individually controlled to a specified surface temperature by a personal
computer that receives data from a datalogger that reads the panel surface temperature
with a thermocouple.
2.5 Unit Resistance for the Elements of the Experimental Room
The electrical resistance equivalent of the unit resistance of the floor is shown in
Figure 2.15.
1/2" Plywood 3/4" Styrofoam Fiberglass
Insulation (3 Layers R19)
Figure 2.15: Electrical resistance equivalent of the floor's unit resistance
The resistance ofthe floor is calculated to be 46.7 hroFft2/Btu. Since the ceiling
is the same construction as the floor, it has the same resistance. If the temperature
difference between the panel surface and the guard space is 2°F, then the conductive loss
32
from the panel through the floor and the ceiling is 0.34 Btu/hr for each panel, or 8.2
Btu/hr for each surface. A total heat input of 700 Btu/hr for the floor and 210 Btu/hr for
the ceiling is expected, so the conductive losses will not be significant in the overall heat
balance on these two surfaces.
The equivalent resistance diagram for the walls is shown in Figure 2.16.
2x4 Boards
1/4" Masonite
1/2" Plywood 3/4" Styrofoam Fiberglass
Insulation (4 Layers R19)
Figure 2.16: Electrical resistance equivalent of the wall's unit resistance
The unit resistance value for the walls is calculated to be 66.7 hrft2_oF/Btu. With
a 2°F temperature difference between the panel surface and the guard space, the
conductive losses through the walls are 0.24 Btu/hr per panel, or 3.6 Btu/hr for the north
and south walls and 4.8 Btu/hr for the east and west walls. A total heat input of 175
Btu/hr is expected for the walls, so the conductive losses will not be significant in the
overall heat balance.
2.6 Panel Heating
This section discusses the design of the heated panel and the estimate of the
conditions that will be encountered during an experiment.
33
Heat from the panel is generated by embedding nickelchromium (NiCr)
resistance wire in a plastering material. Figure 2.17 shows a typical cross section for a
panel.
Ni r Wire 1/2" Plaster
5/8" Gypsum Drywall Board
Figure 2.17: Typical cross section for a panel
A FORTRAN program (see Appendix A) was written to predict the panel surface
temperature for a 0.5 inch thick gypsum plaster embedding material with a thermal
conductivity of 5.6 Btuinlft2hroF. A wire temperature and a surface type (ceiling, wall
or floor) is inputted and the program calculates the surface temperature using a finite
difference method for predicting temperatures. Figure 2.18 shows the boundary
conditions used in the program for the finite difference method. The bottom and two
sides are considered symmetry planes and are adiabatic surfaces. The top surface is
exposed to the air and has to utilize an equation that has the film coefficient as a term to
predict the surface temperature. The air temperature at a distance also has to be estimated
to predict the surface temperature of the panel and for these cases, the air temperature at
an infinite difference from the panel is assumed to be 75° F.
34
onvectlve
Plane
Adiabati
Surface
Symmetry f Plane ,cWire Mounting Surface
Adiabatic
Surface
Figure 2.18: Boundary conditions for calculating the panel surface temperature
The temperature profile across the panel is sinusoidal, and it is desired to minimize the
~T as much as possible so that a uniform temperature profile is seen across the panel.
max Tmin
DeitaTI
Figure 2.19: Temperature profile for a panel
Ultimately, a high thermally conductive epoxy would result in the best
minimization of ~T; however, due to a limited budget for this project, an epoxy panel
cannot be developed at this time. Table 2.1 shows the maximum temperature, minimum
35
temperature and delta temperature for the panel surface at different wire temperatures
when 0.5 inch thick plaster is used as the embedding material.
Table 2.1: Panel Surface Temperatures(OF) at Different Wire Temperatures(OF)
Ceiling Wall Floor
Wire Max. Min. Delta Max. Min. Delta Max. Min. Delta
Temp Temp. Temp. Temp. Temp. Temp. Temp. Temp. Temp. Temp.
140°F 85.3°F 81°F 4.3°F 87.6°F 82.8°F 4.8°F 87.4°F 82.6°F 4.8°F
145°F 87.8°P 83.3°F 4.5°F 91.8°F 86.7°F 4.9°F 91.3°F 86.2°F 5.1°F
150°F 90.3°F 85.6°F 4.7°F 96.3°F 91.1°F 5.2°F 95.5°F 90.3°F 5.2°F
155°F 92.9°F 87.9°F 5.0°F 100°F 95.2°F 4.8°F 99.5°F 94.3°F 5.2°F
160°F 95.4°F 90.3°F 5.1°F
165°F 97.9°F 92.6°F 5.3°F
170°F 100.5°F 95.0°F 5.5°F
It is desired to have a maximum temperature of 100°F on the panel surface. This
is so that the heat pump that is used as the chiller for the ventilation system operates more
efficiently. Once the surface temperature of 100°F was reached, calculations were
terminated for that surface.
The ~t between the minimum and maximum temperature could be further reduced
by covering the panel with aluminum foil. This would also help reduce the radiative
component of the total heat transfer that is occurring on the panel. At this time, however,
there is no plan to cover the panels with aluminum foil due to budget constraints and the
amount of aluminum foil required.
Table 2.1 shows that on the ceiling a wire temperature of 170°F is required. The
wall and floor require a wire temperature of 155°F. Using values for the convective heat
transfer coefficient obtained by experimental work performed by Spitler at UIve (Spitler,
1990), the convective heat transfer for a panel can be determined using the equation
where:
Qconvective = hA(Tpanel surface  Tair)
Qconvective = the convective heat transfer (Btu/hr)
h = the convective h~at transfer coefficient (BtuJhrft2_OF)
A = the area of the panel (ft2)
Tpanel surface = the temperature on the surface of the panel (OF)
Tair = the temperature of the air at the outlet(OF)
(2.5)
36
The temperature of the air is measured at the outlet and this measurement is used
for the calculation of the convective heat transfer. The temperature at this point is chosen
as a reference temperature due to previous research results, especially at low volumetric
flow rates (Spitler, 1990).
Once the convective heat transfer has been estimated for each surface, the
resistance required can be determined by using the equation
V 2
Ro =  {1+a (Twire  To)}
Q
(2.6)
where: Ro = the wire resistance (ohm)
V = the line voltage (volts)
Q= the convective heat transfer for the panel (BtuJhr)
a = the coefficient of thermal resistance of the wire (ohms/ohm/OF)
Twire = the wire temperature (OF)
To = a reference temperature (77°F)
The convective portion of the total heat transfer is used in this equation since the
facility had minimized the conduction losses and the radiation losses. Therefore, the total
heat transfer in the room could be considered all convective heat transfer.
The following resistances are obtained and the current is found by dividing the
line voltage by the resistance of the panel.
Table 2.2: Wire Resistance and Current for the Different Surfaces
Surface Resistance (Ohms) Current (Amps)
Ceiling 20.5 5.4
Wall 82.1 1.3
Floor 68.4 1.6
The wire spacing on the panel is at 1 inch. It takes 100 feet of wire to cover a 2
foot by 4 foot panel. The above resistance values are divided by 100 to obtain the
resistance per foot value and these values are compared to numbers provided by the
manufacturer. This determines the diameter of wire to use on each panel.
Table 2.3: Wire Diameter for the Different Surfaces
Surface Diameter (inch) A.W.G.
Ceiling 0.05707 15
Wall 0.02846 21
Floor 0.03196 20
37
~I
b
o
N
NiCr wire at 1 inch
spacing, 0.5 inch away
from all edges of panel
TypeT
Thermocouple
(24.0",12.25")
"Crimp connector to 14 gage braided
copper wire
Figure 2.20: Panel plan view
2.7 Control of the Heated Panels
A control program (Appendix C) which uses a "pattern" control method (Fisher,
1989) is used to maintain the panel surface temperatures at 105°F. The "pattern" control
method operates as follows:
1. The room is brought up to steadystate using a simple on/off control algorithm.
2. All panels are turned off for 10 cycles
3. All panels are turned on for 1 cycle, then off for 10 cycles. The temperature
responses are recorded.
4. Step 3 is repeated with 2 cycles on and then with 3 cycles on.
5. The results from steps 3 and 4 are converted into three parameters:
DELTI is the maximum change in panel surface temperature due to 1 on
cycle
DELT2 is the maximum change in panel surface temperature due to 2 on
cycles
DELT3 is the maximum change in panel surface temperature due to 3 on
cycles.
38
6. The control program switches into "pattern control" mode.
7. Surface temperatures are measured. Then, DELT1, DELT2 and DELT3 are
used to select an on/off pattern to control each panel. The on/off pattern that will
result in the surface temperature staying closet to the setpoint is selected.
8. Step 7 is repeated until the experiment is finished.
Switching of the panels is done with solid state relays that receive either a high
signal (5 VDC) or a low signal (0 VDC) from a Metrabyte digital i/o board located in the
computer.
2.8 Experimental Configuration
For the initial shakedown tests of the facility, three experiments were performed,
all at different flow rates and without the guard space being operational. The inlet was
created in the south wall, midway up the wall, by attaching a flexible supply air duct to
the back of a "honeycomb" cell. The other half of the cell was insulated. An inlet of 4
square feet was then formed (Figure 2.21). The outlet was formed by attaching a flexible
return air duct to the back of the north wall's bottom cell adjacent to the east wall
"honeycomb" cell. The other half of this cell was also insulated to form an outlet of 4
square feet (Figure 2.22). Twelve heated panels were placed on the west wall, covering
the first three levels from the ·floor. Ideally, more panels would have been used, but time
constraints precluded the installation of additional panels. The rest of the surfaces were
covered with "passive" panels. The floor's passive panel was made out of 0.5 inch
plywood mounted on 2x4's so that a person could walk around inside the room. Figure
2.23 shows the construction of the floor for the experiments. The walls and ceiling were
covered with two layers of 0.75 inch aluminum faced styrofoam panels with a 0.5 inch air
39
gap between the two panels. Figure 2.24 shows the wall passive panel construction. The
ceiling is of similar construction.
Inlet
10.00'
1
.......: 4.00' ~
.'1 12.00' .......
Figure 2.21: Air inlet location in south wall of experimental room
40
10.00'
Outlet
1:4.0011
~'f12.00'~
Figure 2.22: Air outlet location in north wall of experimental room
Floor Joist
4.0' o.c.
41
0.5 inch Plywood
18 inch
hick wall
Figure 2.23: Floor passive panel cross section
0.75 inch styrofoam
0.5 inch plywood strip, 2 inches
wide along length of wall to serve
as convective loop breaker.
0.5 inch thick plywood block
located at bottom, top and 8 feet
from bottom.
Figure 2.24: Wall passive panel cross section
Figure 2.25 shows the west wall configuration with a passive panel above the twelve
heated panels.
42
PASSIVE PANEL
10.00'
HEATED PANELS
•
I=: 4.00'_1_
b 16.00'.~1
Figure 2.25: West wall configuration for the experiments
The guard space is not operational for these "shakedown" experiments. This will
result in a "worse case" conduction loss from the panels on the west wall. If the
temperature difference between the panel surface and the guard space is 25°P, then the
expected loss is 3 Btu/hr, which is acceptable since the expected total heat input for the
wall is 175 Btu/hr.
43
3 Analysis of Experimental Data
3.1 Data Analysis
This section describes the data analysis procedures. The data analysis procedures
were implemented in a FORTRAN program, included in Appendix E. Each experiment
generated two data files, one of which contains data recorded by the Fluke datalogger and
one of which contains data recorded by hand..
A Fluke datalogger read the heated panel temperatures, the temperatures of the
passive panel surfaces and the air temperatures at the measurement box, the room inlet
and the room outlet. The control program, written in Basic (Appendix C), read the data
from the Fluke and recorded it along with the time and the control bit for each heated
panel. A scan was made and written to the hard drive approximately every 5 seconds.
This data file of measured temperatures and control bits would contain approximately 900
scans, or 1.25 hours of experimental data.
The other datafile was an auxiliary data file that contained data recorded by hand
during the experiment. This data included the line voltage, the static pressure in the
measurement box, the pressure drop across the nozzle bank in the measurement box and
which nozzles in the bank are open or closed.
3.2 Determining the Heated Panel Fluxes
3.2.1 Power Input to a Panel
The primary concern of the experiments is the determination of the convective
heat transfer coefficient. In order to determine this coefficient, the power input to each
panel has to be determined. The power input is simply:
Qpower = V2
/ R *3.41
Where: Qpower is the power input to a panel (Btu/hr)
V is the line voltage
R is the panel resistance (n)
3.41 is a conversion factor from watts to BtuJhr
44
(3.1)
There are times during the experiment, however, that a panel is off, so there is no
current flowing to the panel. In order to determine the power input to a panel during an
experiment, an average is determined by summing the power consumed by a panel during
an experiment and dividing by the number of readings during the experiment.
Qpower, j =
N
~::CQpower.j,i * control biti)
i=l
N
(3.2)
Where Qpowerj,i is the power input to the /h panel at reading i (BtuJhr)
control biti is 1 if the panel is on, 0 if the panel is off during the ith reading
N is the number of readings
3.2.2 Backlosses From a Panel
The backlosses, or conduction fluxes, from the panel are determined by taking the
difference between the panel surface temperature and the temperature outside the room,
and dividing this temperature difference by the thermal resistance of the wall. The
surface temperature of the panel is used for this calculation instead of the temperature on
the backside of the panel since no temperature measurements were made on the backside
of the panel. This will be a safe assumption since the conduction fluxes are relatively
small compared to the overall heat fluxes.
Qcond, j, i
Tpanel j, i  Toutside
R
(3.3)
45
Where: QcondJ,i is the backloss from panel j at reading i (Btu/hr)
Tpanel j,i is the temperature of panel j at reading i (OF)
Toutside is the temperature of the outside surface of the room (OF)
R is the thermal resistance of the wall (hroF/Btu)
An average backloss for each panel for each experiment is determined by
summing the backlosses from a panel during the experiment and dividing by the number
of readings.

Qcond, j
N LQcond,j,i
i=l
N
(3.4)
Where: QcondJ,i is the backloss from panel j at reading i (Btu/hr)
N is the number of readings
3.2.3 Radiative Flux From a Panel
The radiative flux from the heated panels is calculated using Hottel's grey
interchange method. The room is modeled simply as an 18 surface enclosure. Twelve of
the surfaces are the heated panels with a surface emissivity of 0.9. The plywood floor is
one surface and has a surface emissivity of 0.9. The north, south and east walls, ceiling
and the passive panel on the west wall make up the other five surfaces, all with a surface
emissivity of 0.25. The room air is considered a nonparticipating media (Spitler, 1990).
Direct view factors for all eighteen surface interactions and total grey interchange
factors are determined using a FORTRAN program provided by Spitler (Spitler, 1990).
Spitler's program incorporated Walton's (Walton, 1986) program for determining view
factors and Pedersen's (Pedersen, 1989) program for computing grey interchange factors.
46
In order to use Hottel's method, black body emissive power must be determined
using the StefanBoltzman law:
E = crTs4
Where:E is the black body emissive power (Btu/hrft2
)
cr is the StefanBoltzman constant (1.714*109 Btu/hrft2R4
)
Ts is the surface temperature of each area (OF)
After the black body emissive powers are calculated for each panel at each
temperature reading, the radiative flux for a panel can be determined by summing the
individual net fluxes to each of the other surfaces.
(3.5)
Qi j
n n LLSiSj(Ei  Ej)
i=l j=i
(3.6)
Where: Qij is the radiative flux from panel i to panel j (Btu/hr)
SjSj is the total grey interchange area from panel i to panel j (ft2)
Ej , Ej are the black body emissivities of panel i and panel j (Btu/hrft2)
An average radiative flux for each panel is determined by summing the calculated
radiative flux from each reading for each individual panel and dividing by the number of
readings.
Qrad, j
N LQrad,j,i / Aj
i=l
N
(3.7)
Where: Qradj j is the radiation flux from panelj at reading i (BtuJhrft2)
Aj is'the area ofpanelj (ft2)
N is the number of readings
47
3.2.4 Convective Flux for a Panel
The experimental average convective heat transfer can now be determined for
each panel by using the following equation:

Qconv, j = Qpower, j  Qrad, j  Qcond, j
3.3 Determination of the Convection Coefficient
(3.8)
Once the average convective heat transfer has been determined for each heated
panel, the average convection coefficient, or film coefficient, can be determined by
dividing the convective heat transfer value by a temperature difference. The temperature
difference is the difference between the panel surface temperature, which is averaged over
the experiment, and a reference temperature.
Qconv, j
For these experiments the reference temperature is selected to be the time average air
temperature at the room outlet (Spitler, 1990).
3.4 Characteristic Parameters
(3.9)
There are certain characteristic parameters that are of interest for each experiment
performed. Discussion of the calculation of each of these parameters is now presented.
3.4.1 Volumetric Flow Rate
Determination of the volumetric flow rate of air entering the room is of particular
importance since it will lead to the calculation of several more characteristic parameters.
The volumetric flow rate is determined by measuring the pressure drop across a nozzle
bank and the static pressure entering the nozzle bank with two piezometer rings of
48
pressure taps in the measurement box that are connected to an inclined manometer.
Using the equations specified by ASHRAE Standard 511985, "Laboratory Methods of
Testing Fans for Rating", the volumetric flow rate (VFR) is determined in units of cubic
feet per minute (cfm). Further discussion of this measurement is reported by Ferguson
(1995).
3.4.2 Inlet Velocity
Determination of several other parameters is dependent upon the velocity of the
air entering the room. The inlet velocity, in feet per minute or fpm, is determined by
dividing the volumetric flow rate by the area of the inlet.
VFR
Uo =
Ainlet
3.4.3 Air Changes per Hour
(3.10)
Air changes per hour (ACH) for an experiment is calculated using the following
equation.
ACH= VFR *60
VOLroom
3.4.4 Archimedes Number
(3.11 )
The Archimedes number is used to predict the trajectory of the inlet jet. The
general form of the Archimedes number is:
PgLc~To
Ar=
Uo2 (3.12)
Where: P is the coefficient of thermal expansion (I/R)
g is gravitational acceleration (32.2 ft/s2
)
Lc is a characteristic length, in this case the length of the wall that the jet
washes (ft)
~To is the temperature difference between the room outlet and inlet (OF)
49
Vo is the fluid velocity (fils)
The most likely use of the Archimedes number is to characterize the flow regime
rather than correlate to the heat transfer coefficient. In the same regard, the relationship
would also be dependent upon whether the inlet location is in a wall, in the ceiling or
even in the floor. The Archimedes number can be considered as a ratio of buoyant forces
to momentum flux, so the Archimedes number's significance upon inlet location is
important since buoyant forces will act differently on each different type of inlet location.
For the sidewall case which was used for the experiments, a low Archimedes number,
since the buoyant forces are small, should indicate that the jet from the inlet is capable of
transversing the room and impinging on the wall opposite from the inlet. A high
Archimedes number, since the buoyant forces are large, should indicate that the jet drops
upon entering the room and settles to the floor. Intermediate values would suggest that
the jet travels a certain distance into the room, then falls to the floor of the room. In
relation to the film coefficient, a low Archimedes number would suggest that the natural
convection component of the overall convection flux is larger than the forced convection
component. The opposite would hold true for a high Archimedes number in that the
forced convection component is larger than the natural convection component. It is
difficult to determine what the upper and lower bounds of the Archimedes number are
without using a flow visualization technique inside the room.
3.4.5 GrashofNumber
The Grashof number characterizes the ratio of the buoyancy force to the viscous
force. Written in equation form:
A g (TSllff  Tfs) L3
Gr = P
u 2
where: Pis the coefficient of thermal expansion (l/R)
g is gravitational acceleration (32.2 fi/s2
)
Tsurf is the temperature of the surface (OF)
Tfs is the fluid free stream temperature (OF)
L is the height of the wall(ft)
u is the kinematic viscosity (fi2/s)
It is difficult to estimate the fluid free stream temperature for the three
50
(3.13)
experiments performed since air temperature was measured at the room inlet and the
room outlet. The assumption will be used then that the free stream air temperature is the
same as the average temperature of the ceiling, floor and nonactive walls.
3.4.6 Prandtl Number
The Prandtl number is the ratio of the kinematic viscosity to the thermal
diffusivity. This can be defined as the diffusion of momentum divided by the diffusion of
heat. The Prandtl number can be used to estimate the ratio of the velocity boundary layer
thickness to the thermal boundary layer thickness. For a Prandtl number greater than 1.0,
the thermal boundary layer is thinner than the velocity boundary layer. For a Prandtl
number equal to 1.0, the respective boundary layer thicknesses are the same. When the
Prandtl number is less than 1.0, the velocity boundary layer is thinner than the thermal
boundary layer.
3.4.7 Rayleigh Number
The Rayleigh number is the product of the Grashofnumber and the Prandtl
number. The Rayleigh number is typically correlated to the Nusselt number with the
form:
51
(3.14)
where: Nu is the Nusselt number
C is an empirically determined constant
n is an empirically determined exponent (typically 1/3 for laminar flows;
1/4 for turbulent flows
3.4.8 Nusselt Number
The Nusselt number is defined as the ratio of the temperature gradient at the wall
to the overall temperature difference. Written in equation form, the Nusselt number is:
hL
Nu =
k
where: h is the film coefficient (Btulhrft2OF)
L is the height of the wall (ft)
k is the thermal conductivity of the fluid (BtuJhrftOF)
(3.15)
The Nusselt number is often correlated to the Rayleigh number. Some ofthe
correlations developed relating Nusselt number to Rayleigh number will be investigated
in Chapter Four.
3.4.9 Jet Momentum
The jet momentum flux of the air at the room inlet is determined by multiplying
the mass flow rate of the air (Ibm/min) by the velocity of the air entering the room (fpm).
The jet momentum number is nondimensionalized (Spitler, 1990) by using the following
equation:
J
VFR *Uo
g *Vroom
(3.16)
Where:VFR is the volumetric flow rate (cfm)
Uo is the velocity of the air entering the room (fpm)
g is gravitational acceleration
Vroom is the volume of the room (ft3)
52
3.5 Experimental Uncertainties
The difference between a measured result and the true value of that quantity is
error. By assigning a value to that error., an uncertainty is defined. The uncertainties in
each individual measurement lead to uncertainties in the experiment.
3.5.1 Uncertainties in Fluke Datalogger Temperature Measurements
Sources of error that cause uncertainty in the temperature measurements are the
type T thermocouple wire properties., the cold junction compensation in the Fluke
datalogger and the emf voltage measurement of the thermocouple. The thermocouple
wire has an uncertainty of ±O.9°F. The estimated error for the cold junction
compensation is ±O.l OF. The voltage measurement of the thermocouple by the Fluke
translates into a ±O.9°F error at the heated panel setpoint of 105°F. The error, then, in
temperature measurements made with the Fluke is:
(3.17)
3.5.2 Uncertainties in Panel Power Measurement
The errors associated with the panel power measurement are the voltage
fluctuations and the resistance of the panel changing as the NiCr wire heats up. Other
errors are attributed to the digital multimeter used to measure the panel resistance and the
line voltage.
Line voltage is measured once at the end of the experiment when the hand
collected auxiliary data is being recorded. It is estimated that the voltage changes by a
maximum of ±2 volts during an experiment. Uncertainty in the voltmeter is ±O.1 volts.
53
The change in resistance of the panel due to temperature changes is negligible. The
uncertainty in the measurement of the panel resistance is ±O.lQ. This is approximately
0.1% when using 75Q as the typical panel resistance. The total uncertainty in the panel
power can be approximated by:
up (
2(2)) 2 + (~) 2 ~ 3%
120 75
(3.18)
3.5.3 Uncertainties in Volumetric Flow Rate Measurement
ASHRAE Standard 511985 is used to measure the flow rate of air supplied by
the fan to the room. The appendix of the standard presents a detailed error analysis for
the error in volumetric flow rate. The variables used in the equation are as follows, with
values assigned to them in parentheses.
Uc =Fractional error in nozzle discharge coefficient (0.012)
UA = Fractional error in nozzle area (0.005)
UN = Fractional variation in fan speed (0.01)
uf = Fractional error in pressure drop across the nozzle bank (0.1)
up = Fractional error in static pressure at fan outlet (0.1)
Values for the fractional errors in nozzle properties are from the ASHRAE
Standard and apply to nozzles built to the specifications. Pressure measurement errors
are estimated based on the manometer having gradations of 0.2 inches. The fluid level
fluctuates during an experiment and the pressure reading is estimated. It is assumed that
the pressure reading is accurate within 0.1 inches. When substituting the values into the
uncertainty equation:
2
Uf + UA 2 + UN
2 +
2
2 + up
2
(3.19)
54
an uncertainty in the volumetric flow rate of approximately ±10% is obtained.
3.6 Uncertainties in Derived Quantities
This section covers uncertainties in quantities calculated from the quantities
measured during an experiment.
3.6.1 Uncertainties in the Calculation of the Air Heat Gain
An energy balance is performed on the room by comparing the power input to the
panels to the air heat gain.
The air heat gain is given by:
Qair = p(VFR)CpLlT (3.20)
where: p(VFR) is the density of the air times the volumetric flow rate, which is equal to
the mass flow rate of air entering the room (lbm/hr)
Cp is the specific heat of air at constant pressure (0.24 Btu/IbmOF)
~T is the temperature difference between the room outlet and room inlet.
Assuming that density and Cp are determined with negligible error, then the error
in the air heat gain can be stated in the form:
(3.21)
UVFR has already been determined to be approximately 10%. The error in ~T is dependent
upon the inlet and outlet temperature measurements. Using the ±1.3°F error in
temperature measurements leads to the following equation:
Qair p(VFR)Cp dT ± (0.1)2 + (~~r (3.22)
~T is the temperature difference between the room outlet temperature and the
room inlet temperature. These two temperatures are averaged over the duration ofthe
55
experiment, therefore ~T is the experimental average temperature difference between the
room outlet and the room inlet. For example, let the average ~T for an experiment
performed be equal to 10°F. When substituting this assumption into the equation above,
the uncertainty is determined to be approximately 21 %. Therefore the equation for the
energy balance on the air is simply:
Qair = p(VPR)Cp ~T ±21% (3.23)
As shown in section 3.5.2, uncertainty in the total power input to the panels is
assumed to be 3% since this uncertainty is dependent upon the measurement of the
voltage and the panel resistance.
3.6.2 Uncertainties in the Calculation of Film Coefficients
The uncertainties in the film coefficient are dependent upon the uncertainties in
the convective heat flux and the uncertainties in the temperature difference.
Uh
where: U~T J(UT, panel)
2 + (UT,outlet)2
Tpanel  Toutlet
(3.24)
The uncertainties in the temperature difference are calculated in the same way the
uncertainties in the temperature difference for the volumetric flow rate were calculated.
We will assume that the temperature difference on average between the wall average
temperature and the room outlet average temperature is 35°P. The uncertainties in the
Fluke datalogger temperature measurements, ±1.3°P, will be used for the uncertainties in
the temperatures measured. This results in U~T of approximately 30% for typical cases.
56
The uncertainties in the convective flux are dependent upon the uncertainties in
the power input, the backlosses and the radiation flux. The uncertainties in the backlosses
are dependent upon the temperature difference between the panel temperature and the
temperature outside the room. The temperature outside the room is not measured, and the
uncertainties in the temperature outside the room are assumed to be ±5°F. This results in
an uncertainty of 14% in the backlosses.
The uncertainty in the radiation is based on the uncertainty in the panel surface
temperatures and the uncertainty in the value of surface emissivity. The assumption that
uncertainty due to small errors in panel areas and view factors are negligible is made in
order to simplify the analysis. The radiation from one panel to all other surfaces is given
by:
Qrad,i  j
18
cr ISiSj (T4
j  T4 j)
j = 1
(3.25)
This equation can be rewritten as:
Qrad, i  j
18 18
cr I SiSj (T4i)  cr I SiSj (T4
j )
j = 1 j = 1
(3.26)
If a constant, random uncertainty for each surface temperature is assumed, then
the uncertainty in the second term on the right hand side is negligible compared to the
first term on the right hand side. An uncertainty will be introduced into the first term.
An uncertainty of ±O.9°F exists in the panel temperature measurements according
to section 3.5.1. An uncertainty in the temperature across the panel exists due to
temperature variations, however, this uncertainty is impossible to calculate since only one
57
thermocouple is used on each panel. This uncertainty will be ignored even though it
probably plays a role in the uncertainty of the radiation flux. A typical value of 565R is
used for Ti. Therefore, the uncertainty in the radiation flux due to panel surface
temperature is ±0.9%.
The assumed surface emissivity of the panels is 0.9±0.05. Knowing that the SjSj
terms sum to the surface emissivity leads to an uncertainty in the radiation correction of:
±o.os 601:
Ufo = (f9 = ± /0
The total error in the radiation correction is approximately ±6%.
(3.27)
The panel to room air radiation is neglected in this case. This assumption could
be endangered if the room air is high in humidity since water vapor in the air can absorb
and emit radiation. Spitler (1990) performed a "worse case" scenario for the panel to
room air radiation. This scenario, when applied to the experiments, results in an
uncertainity in the flux of 5%.
The uncertainty in the convective heat transfer can now be calculated knowing the
uncertainties in the panel power, radiation and backlosses. These uncertainties are
changed from percentages to numerical values based on fluxes. The uncertainties in the
three fluxes are as follows for a given case:
Panel power input: 57.3 Btu/hrft2 ± 1.7 Btu/hrft2
2 2 Backlosses: 0.04 Btu/hrft ± 0.006 Btu/hrft
Radiation: 3.43 Btu/hrft2 ± 0.2 Btu/hrft2
The above uncertainties are now added in quadrature to determine the uncertainty
in the convective heat flux. This uncertainty is determined to be 1.7 Btu/hrft2 (~3%).
58
This value is substituted into equation 3.24 knowing that the uncertainty in the
temperature difference has already been shown to be approximately 30%. Therefore, the
uncertainty in the film coefficient is approximately ±30%
h = hexp ± 30% (3.28)
where: hexp is the experimentally determined film coefficient for the wall.
59
4 Experimental Results and Discussion
4.1 Overview
Three experiments were performed at 15, 20 and 25 Air Changes per Hour
(ACH). The air heat gain for an experiment is compared to the total heat input for an
experiment to see if an energy balance is obtained within the uncertainties determined in
sections 3.5.2 and 3.6.1. The energy balance is of utmost importance. Without it, there is
little confidence in the experimental results. If an energy balance cannot be achieved,
then modifications will have to be made to the facility in order to reduce losses and bring
the facility to a balance.
Another area of interest is the control of the panels. The panels have to be able to
meet a desired set point and maintain that temperature within a reasonable range.
Another question relates to the amount of time necessary to reach steady state conditions,
or are steady state conditions ever achieved in the facility?
Finally as another check for the facility, the experimentally determined film
coefficient will be compared to published correlations for the film coefficient. The
correlations that are used for comparison do not apply to the conditions for which the
tests were run, but might be thought of as limiting cases. Three of these correlations are
for natural convection cases and can be considered as a lower bound to the experiments
performed. The other two correlations that are used for comparison to the experimentally
determined film coefficient are for forced convection cases and can be considered as a
upper bound to the experiments performed.
4.2 Experimental Results
Table 41 shows the experimental results and the derived quantities for the three
experiments of 15, 20 and 25 ach. Additional results from each experiment are included
in Appendices F, G and H.
Table 4.1: Experimental Results and Derived Quantities
Air Changes per Hour
15 20 25
Actual air changes per hour 15.26 20.31 24.30
Panel average temp (F) 103.97 103.24 103.80
Average temp west wall 73.07 70.15 71.04
above panels (F)
Average temp east wall (F) 73.03 70.50 71.49
Average temp south wall (F) 72.91 70.91 71.92
Average temp north wall (F) 71.54 68.95 70.36
Average temp floor (F) 74.38 72.70 74.57
Average temp ceiling (F) 75.29 71.60 71.53
Average air inlet temp (F) 56.29 55.80 60.30
Average air outlet temp (F) 65.55 64.30 66.90
Average free stream air temp 75.29 71.60 71.53
(F)
Average air inlet velocity 122.07 162.48 190.50
(fpm)
Average air volumetric flow 488.29 649.92 762.20
rate (cfm)
Average air mass flow rate 2250.81 2993.88 3497.00
(lbm/hr)
Average air density at inlet 0.077 0.077 0.076
(lbm/ft3
)
Average air kinematic 1.73e4 1.73e4 1.74e4
viscosity (ft2Is)
Average air thermal 0.868 0.868 0.871
diffusivity (ft2/hr)
Average air coefficient of 1.90e3 1.91e3 1.90e3
thermal expansion (I IR)
Average jet momentum 0.270e3 0.470e3 0.650e3
number
Average Prandtl number 0.718 0.718 0.718
Average Archimedes number 2.2 1.1 0.64
Average Grashof number 58.6e9 64.8e9 65.2e9
Average Rayleigh number 42.1e9 46.5e9 46.89
Average panel power input to 5448.15 5634.86 5518.46
room (Btu/hr)
Average air heat gain 5003.62 6111.42 5527.50
(Btu/hr)
Average convective flux for 52.90 54.72 53.58
panels (Btu/hrft2)
Average film coefficient 1.39 1.41 1.46
(Btu/hrft2F)
The Rayleigh number is calculated as the product of the Prandtl number and the
Grashof number. For all three experiments performed, the Rayleigh number is on the
60
61
order of 109
. Generally, if the Rayleigh number is less than 109 the flow is laminar,
whereas if the Rayleigh number is greater than 109 the flow is turbulent. These three
experiments would be at the transition point of laminar to turbulent flow, if they were
driven only by natural convection.
4.3 Panel Control Results
An important aspect of this experimental facility is control of the heated panels.
As stated before, the heated panels must maintain a desired setpoint in order to achieve
good experimental results. If the heated panels are constantly "hunting" the setpoint, then
it will be nearly impossible to achieve steady state conditions in the experimental room.
The "pattern" control method used does not completely eliminate "hunting", but does
reduce it greatly.
Figure 4.1 shows the temperature of panel number 1 during the 15 ach
experiment. Time 0.0 is the start of the data recording for the experiment. The panel was
allowed to reach the desired setpoint of 105°F before the fan was turned on. Immediately
the temperature of the panel started to decrease. The panel temperature was allowed to
drop until it seemed that the temperature of the panel had steadied. Panel number 1 was
located next to the inlet of the room, and was not capable of maintaining the desired set
point. Since panel number 1 was not capable of maintaining the set point at the lowest
flow rate that was studied, then it will not be able to maintain its setpoint it the two higher
flow rates that were studied.
When looking at the data, the flux input for panel number 1 is lower than
expected. Since the panel temperature is considerably lower than the desired setpoint, the
flux input should be closer to 80% of the full duty cycle. This could be due to the
incorrect "pattern" control being selected in the program and the panel is not "on" as
much as it should be. This could be corrected by using a better control scheme like a
proportional controller for the panels.
62
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.0
105,....r.....rr,,
i' ! I I
103 lIt_ll4_.:II
I : II
I i
101 ++~+___+_+_____+_4
i: 'I II· I I I
99 ++1Ifii!+It+:+j11
i I Ii III I I i~ II I I
97 t",I,f+I''.'..;.....,,Jf+_!+!+j+.
95 Ll~~JIli =~~tl~~....~! .......~~JI
i :! I i : II
I
I; I Ii ill'
93 1....1I_10 4 I + .!..__+I4
0.00
Time (minute.)
Figure 4.1: Panel number 1 temperature during 15 ach experiment
Figure 4.2 shows the temperature of panel number 8 during the 25 ach
experiment. Panel number 8 is representitive of panels 2 through 9 and panel 11. Panel
number 8 is located half way up the heated surface and to the right of center for the wall.
The center of this panel is located 2 feet below the centerline of the inlet and 10 feet away
from the inlet. Figure 4.2 shows that panel number 8 is capable of maintaining the
desired set point of 105°F to within O.5°F during the experiment. Since the panel is
capable of maintaining the setpoint to within an acceptable allowance during the 25 ach
experiment, then the panel should be able to maintain the desired setpoint at the lower
flow rates.
63
60 1
•
30 40 50
Time (min)
20
I ' i
i ! !
i : I j
10
. I. II I
• """ I i I
•
105.1
~
~
105 •
104.9
•
......... i. I: • .:. i ., .'.' i.. .1I. , •• ! • • ........ •1. ,_ •••i • ~. • • • ~ •• ~ • • I~~ ••.• ..... ~ •• ~., ~#
~..~I.~. = ·.+~.~· ..'I ..... •.•,.. <. ,.,.... S._.•..~.~et.....,~;.~_  • ... I . .. , ••, •• • ~~  ~I"" ~~.....;~_.... I
• .. • ~ .. ~ .. ··MI..V •~ .. ; : ,.•••
• • _......' ••• i •• • •••,.. • I • • ,I,:
• =r • • I • • ••• i>4.. =,.=i , • I :.. I •. · ...! j···I· I • .1 •• I i • I I 104.4 +~ ___+~+__...._+_l
o
104.8
~
a.
E
lit
I
104.7
104.6
104.5
Figure 4.2: Panel number 8 temperature during 25 ach experiment
The temperature of panel number 12 during the 15 ach experiment is shown in
Figure 4.3. Panel number 12 is located in the bottom right hand comer of the heated
wall. It appears that the panel is under powered and requires a larger total heat flux.
Since the panel is not capable of maintaining the desired setpoint at the low flow rate,
then it will not maintain the setpoint at the higher flow rates that were performed. It is
interesting to note though that the panel immediately above is capable of maintaining its
desired setpoint. It could be possible that the north wall and the floor is interacting with
panel number 12 somehow and that is the cause for the low temperature. Panel number
10 is behaving the same way as panel number 12, also. Possible explainations are that
the wrong "pattern" control is being selected, or that the north wall in its passive
condition is interacting somehow with the air flow over panels 10 and 12.
64
104.5 t+r<+++J+l
104 t++++++l
0.00 10.00 20.00 30.00 40.00 50.00 60.00 80.00 90.
I II
,JIi_+_+.Ii
70.00
102.5 LLLLll~___1:tY~~~W_Wli~
Time (min)
Figure 4.3: Panel number 12 temperature during 15 ach experiment
4.4 Transient Response of the Room
The transient response of the room was determined by allowing all the panels to
come up to the setpoint temperature of 105°F, then turning on the fan to deliver air to the
room. The temperature of the air inlet and outlet was monitored until the two
temperatures became reasonably steady. It was then determined that steady state
conditions had been obtained. Since these two temperatures were reasonable steady and
the temperature difference between the inlet and the outlet is steady, then it can be
concluded that the air heat gain has reached steady state. Figure 4.4a shows the
temperatures of the air inlet and outlet during the 25 ach experiment. It took
approximately one hour and forty five minutes for the panels to reach the setpoint
temperature. After the fan was turned on, it took approximately 30 minutes for the room
to reach steady state conditions. This was generally the case for the two experiments
performed at 15 ach and 20 ach, also.
65
Figure 4.4b shows the air inlet and outlet temperatures from the 30 minute mark
to the 55 minute mark.
+~~t~I++~
74~~++++i
72 t~=r~+++~
i 70 f~IB_._;;;~t_i_+_____i
... !
666~8r.:===J====:::~~~E~~~~~~~~;;;~==J
~~~tr+i
I
20 30 40 50 60
Tlmelml"1
Figure 4.4a: Air inlet and outlet temperatures during the 25 ach experiment.
From the 30 minute mark to the end of the experiment, the inlet air temperature
shows a slight rise and then a decrease. This is due to the cooling system in which a heat
pump is cycled on and off to maintain a chilled water temperature in a storage tank. This
water temperature cannot be kept constant during an experiment and it effects the
temperature of the air at the room inlet. A means of controlling the inlet air temperature
is needed.
66
68 r···_····················__··········...······................~_._ ......_.......~ ... I ..  !
1;"!fIIIe rt#J I. ~ I .. I I i
67.~..:i':",~'\.r\..,y::"'!i"*flll..~' ~...~ i
I ! !,. ~....",.""."w......, ~
66 I I 1 I .
! I .
I I
! i
I i
62 t+
I
++1+1<I
TIrM(mlnl
50 55
Figure 4.4b: Air inlet and outlet temperature during the last 25 minutes of the 25 ach experiment
4.5 Energy Balance on the Room
Ideally, if the room is perfectly balanced, the air heat gain will equal the panel
power. Figure 4.5 shows the energy balances for the three experiments and all are within
the predicted uncertainty. The diagonal line represents the ideal situation of when the
panel power input equals the air heat gain. The horizontal bars represent the uncertainty
in the panel power while the vertical bars represent the uncertainty in the air heat gain.
The uncertainty in the air heat gain is due primarily to the uncertainty of the volumetric
flow rate measurement. This uncertainty can be greatly decreased by improving the
measurement of the pressure drop across the nozzle bank of the flow measurement box.
The uncertainty in the panel power is due to the frequency of measurements of the
voltage during the experiments and could be improved by continuous measurement of the
AC line voltage.
67
7500 ._ __._..._.__._
7000
6500 
'C'
=3 6000
!.
c~
5500 ca
CD
:: 5000
~
4500 .
4000
5500 6000 6500 7000 7500
Power Input (Btu/hr)
4000 4500 5000
3500 ~_;.___l
3500
Figure 4.5: Energy Balance for the Three Experiments Performed Showing the Uncertainty in Panel Power
and Air Heat Gain
4.6 Previously Published Correlations
The film coefficient determined from previously published correlations are used
for comparison to the experimentally determined film coefficient to see if the results that
are obtained from the experimental room are reasonable and "in the ballpark". These
correlations that are used for comparison do not apply for the conditions in which the
three tests were run and are to be thought of as limiting cases only.
4.6.1 Natural Convection Correlations
By determining the Rayleigh, Grashof and Prandtl numbers for each experiment,
the experimentally determined film coefficient can be compared to the film coefficient
determined from correlations relating the Nusselt number to the Grashof and Prandtl
numbers, and from correlations relating the Nusselt number to the Rayleigh and Prandtl
numbers. The natural convection correlations that will be used to determine the film
coefficient for comparison to the experimentally determined film coefficient are as
follows:
68
The first correlation was presented by Eckert and Drake (1951). It is based on an
approximate solution of the laminar boundary layer equations for the vertical isothermal
flat plate.
(4.1)
The second correlation was presented by Churchill and Chu (1975) for laminar
free convection on a vertical isothermal surface over a wide range of Prandtl numbers.
Note that this is the mean value of the Nusselt number, which is equivalent to 4/3 NUx=L
for any case where Nu = f(Gr)l/4.
(4.2)
0.67 Ra1
/
4
Nu = 0.68 + [ ]4/9
1 + (0.492 / Pr)9116
The third correlation for the mean Nusselt number developed by Churchill and
Chu (1975) is:
Nu = [0.825 + 0.387 Ra1/6 8/27 ]2
[1 + (0.492 / Pr)9/16]
(4.3)
This correlation is valid in both the laminar and turbulent flow regimes, however,
it is not as accurate in the laminar region as the correlation presented for laminar free
convection.
4.6.2 Forced Convection Correlations
The ASHRAE Handbook of Fundamentals (HOF) (1989)lists the following
correlation for vertical plane surfaces for velocities less than sixteen feet per second:
h' = 0.99 + O.21V (4.4)
In this case though, the film coefficient is based on an "initial temperature difference".
The HOF does not define the "initial temperature difference", but it appears to be the
difference between the adjacent air temperature and the wall temperature.
All of the correlations listed above deal with free standing vertical surfaces. The
last correlation that will be used for comparison was developed by Spitler (1990) for
69
enclosures. The correlations developed by Spitler related the film coefficient to the inlet
jet momentum number. The correlation that is of interest for these particular experiments
is Spitler's correlation for the north wall when an east wall inlet was used.
h = 1.6 + 127Jo.5 (4.5)
This correlation was developed for Archimedes numbers less than 0.3 and a range ofjet
momentum numbers of 0.002 to 0.011. The three experiments that were performed all
have Archimedes numbers greater than 0.3 and jet momentum numbers less than the
lower bound set on the correlation. The correlation gives the film coefficient in SI units.
This is easily converted to IP units for comparison to experimentally derived film
coefficients.
4.6.3 Comparison
The values in Table 4.2 for the ASHRAE HOF (eq. 4.4) correlation are obtained
using the inlet velocity, as if'it was maintained over the entire wall, and not the local
velocity. This value of the film coefficient can be viewed as a maximum film coefficient
for the experiment performed. Measurements of local air velocity were not made and it
can be concluded that the film coefficient from equation 4.4 would be significantly less if
the local velocity is used for the calculation. Notice that the film coefficients determined
from the natural convection correlations are substantially lower than the experimentally
determined film coefficient. Data from Table 4.2 is shown in Figure 4.6 with the
uncertainty in the experimentally determined film coefficient shown also.
70
Table 4.2: Comparison of Experimental Film Coefficient to the Correlation Determined Film Coefficient
Method ofDetermining Film Air Changes per Hour
Coefficient
(Btu/hrft'F) 15 20 25
Experimental 1.39 1.41 1.46
Eckert and Drake correlation 0.31 0.32 0.32
(eq.4.1)
Churchill and Chu laminar 0.29 0.30 0.30
correlation (eq. 4.2)
Churchill and Chu laminar and 0.50 0.52 0.52
turbulet correlation (eq. 4.3)
ASHRAE HOF correlation 1.42 1.56 1.66
(eq.4.4)
Spitler's jet momentum 0.65 0.77 0.85
correlation (eq 4.5)
The only correlation presented above that was developed in an enclosure similar
to the one used for these experiments is Spitler's correlation (eq. 4.5). However, for the
three experiments performed, the Archimedes number was greater than the 0.3 limitation
on Spitler's correlation and the jet momentum number was less than Spitler's lower
bound on the jet momentum number for the correlation. Spitler (1990) shows that at the
higher Archimedes number, the film coefficient will increase, possibly even double that
of the film coefficient calculated from the correlation. Figure 4.7 is reprinted from Spitler
(1990) and shows this increase in the film coefficient.
71
1.8
2r~
I
o
1.6
1.4
u: 1.2
co:.
<~
~
"3
~~
0.8
0.6
0.4 
x
,.
x
,.
x
,.
• experimental
• Eckert &Drake
Churchill &Chu Laminar
eASHRAE HOF
X Churchill &Chu Turbulent
X Spitler
0.2
15 20 25 30
O+l
10
Air Changes per Hour
Figure 4.6: Film Coefficients Determined Experimentally and by Correlations at Each Flow Rate
IS I , I I
G 10  
0
~ (goo **
~ •
S  .c
.0
o
0.0
,
0.2
,
0.4
I
0.6
,
0.8 1.0
Bulk Air Velocity (mls)
Figure 4.7: h versus Bulk Air Velocity for Floor with East Wall Inlet, 22 Tests
(Size is proportional to Archimedes number)
72
To summarize, the experimentally determined coefficients were considerably
higher than those estimated from the natural convection correlations. This is to be
expected, because of the significant effect of the inlet jet. The experimentally determined
film coefficients were significantly higher than Spitler's correlation, which might also be
expected since the experiments were performed outside the range of Archimedes number
and jet momentum numbers for the correlation. In this case, the Archimedes number was
much higher than Spitler's, implying more significant buoyancy effects. The
experimentally determined film coefficients were slightly lower than the ASHRAE HOF
correlation., which is expected since the assumption that the inlet velocity remains
constant over the entire wall was made. This assumption set an upper bound, or
maximum value, for the film coefficient, which it did not exceed.
73
5 Conclusions and Recommendations
The following conclusions can be made about the Building Heat Transfer Facility
constructed at Oklahoma State University:
1. A unique and versatile facility for the study of convective heat transfer and air flow in
buildings has been developed. The experimental room utilizes a "honeycomb" frame
with removable panels. This feature allows a multitude of configurations and
phenomena to be investigated. Examples include:
• Vertical or horizontal partitions can be added to the experimental room to allow for
the study of heat transfer between zones, such as plenums or attic spaces.
• The removable panel system allows for the study of the effect on the heat transfer due
to different types of surface roughnesses that are found in buildings today.
• The experimental room is not limited only to the study of convective heat transfer and
air flow. It can also be used to study radiative and convective fraction of heat gain
from equipment.
• It can also be configured to study different types of heating systems, such as hydronic
floor heating systems.
2. Losses due to conduction have been minimized by heavily insulating the floor, ceiling
and walls. The losses due to conduction through the floor have further been
minimized by supporting the experimental room off of the concrete floor of the
laboratory. It has been shown that the energy balance criterion for the facility has
been satisfied.
74
3. The experimentally determined film coefficients compare favorably to the film
coefficients that are derived from the published correlations. These published
correlations should be thought of as setting an upper bound (forced convection) and a
lower bound (natural convection) for the experimental situation.
4. The majority of the twelve panels were controlled successfully to within ±1 OF ofthe
desired setpoint. Three panels were not capable of reaching the desired setpoint and
will require either a greater total heat flux or better control in future experiments. The
present panels are capable of yielding a heat flux of 84.5 Btu/hrft2 at full duty cycle
and this may not be sufficient. The "pattern" control method is a simplistic control
method and could also be the cause for the low flux on three of the twelve panels.
5. The final uncertainty in the air heat gain may be higher than what is desired. This can
be reduced in future experiments with improved measurement of the volumetric flow
rate of air entering the room.
Since these experiments were the first performed as "shakedown" tests, there is still a lot
of work to be done to the facility. Some recommendations are:
1. A proportional controller for the panels so better control of the panel temperature
can be achieved. This was an objective that could not be met at this time.
2. Investigation of using an epoxy  filled panel with a high thermal conductivity and
a low thermal mass. The time to reach steady state conditions would be reduced
and the temperature variation over the panel would be minimized. A low
emissivity surface would reduce the radiative component of the heat transfer.
75
3. A larger air handling system, minimum of3200 cfm, with a fan speed controller
so larger ventilation rates can be achieved. The fan speed controller would allow
for small ventilation rates to be used. The larger air handling system will allow
for a higher pressure differential across the nozzle bank, thus reducing the
uncertainty in the volumetric flow rate. The present system is capable of
providing 800 cfm of air to the room.
4. The installation of a high accuracy manometer and/or electronic pressure
transducers connected to the datalogger to measure the air flow through the
measurement box. This would greatly reduce the uncertainties in the air flow
measurement.
5. The completion of the heated guard space to further reduce the conduction losses
from the room. Once the guard space is completed, the conduction losses will be
negligible in the calculations.
6. The placement of thermocouples inside the room to measure the air temperature at
different locations inside the room. An even better solution would be an
automated device inside the room to measure the air temperatures. This will
allow for the determination of a bulk air temperature inside the room for
calculating different dimensionless parameters.
7. The installation of a reheat coil connected to a controller in order to better control
the room air inlet temperature and the LlT between the wall surface temperature
and the room air inlet. Currently, the air inlet temperature cannot be controlled.
8. Perform experiments at Archimedes numbers less than 0.3 and compare the
results to Spitler's jet momentum correlation, and development of a correlation
for the film coefficient at Archimedes numbers greater than 0.3.
76
77
6 References
Bauman., F., A. Gadgil, R. Kammerud and R. Greif 1980. Buoyancydriven Convection
in Rectan~ular Enclosures: Experimental Results and Numerical Calculations. ASME.
Paper No. 80Ht66.
Nansteel, M. W. and R. Greif. 1981. Natural Convection in Undivided and Partially
Divided Rectangular Enclosures. Journal of Heat Transfer, Vol. 103, pp. 623629.
Bohn, M. S., D. A. Olson and A. T. Kirkpatrick. 1983. Experimental Study of Three
Dimensional Natural Convection at High Rayleigh Number. ASME/JSME Thermal
Engineering Joint Conference, Honolulu, HI. pp. 289297.
Keyhani, M., L. Chen and D. R. Pitts. 1991. The Aspect Ratio Effect on Natural
Convection in an Enclosure With Protruding Heat Sources. Journal of Heat Transfer, Vol.
113, No.4, pp. 883891.
Neiswanger, L., G. A. Johnson and V. P. Carey. 1987. An Experimental Study of High
Rayleigh Number Mixed Convection in a Rectangular Enclosure With Restricted Inlet
and Outlet Openings. Journal of Heat Transfer, Vol. 109, pp. 446453.
Olson, D. A., L. R. Glicksman and H. M. Ferm. 1990. SteadyState Natural Convection
in Empty and Partitioned Enclosures at High Rayleigh Numbers. Journal of Heat
Transfer, Vol. 112, pp. 640647.
Martin, Chris and Martin Watson. 1988. Measurement of Convective Heat Transfer
Coefficients in a Realistic Room Geometry. Technical Report. Energy Monitoring
Company, Ltd.
Chandra, S. and A. A. Kerestecioglu. 1984. Heat Transfer in Naturally Ventilated Rooms:
Data from Fullscale Measurements. ASHRAE Transactions, Vol. 90, Pt.lb, pp. 211224.
Neymark, J., A. Kirkpatrick, C. Boardman and R. Anderson. 1988. High Rayleigh
Number Natural Convection in Partial Water Filled Enclosures. ASME Procedin~s of the
1988 National Heat Transfer Conference, HTD96, Vol. 93, pp. 383390
Schachenmann, Andreas, Donald Wiss and Gerhard Metzen. 1990. Numerical
Calculation of Room Air Currents and Comparison With LDA Measurements Under Free
and Forced Convection. Sulzer Technical Review, Vol 72, pp. 3035
Spitler, J. D. and C. o. Pedersen. 1987. Experimental Study of Interior Convective and
Radiative Heat Transfer in Buildings. Heat Transfer in Buildings and Structures,
Pittsburgh, Pennsylvania. pp. 6776.
78
Spitler, J. D., C. O. Pedersen, D. E. Fisher, P. F. Menne and J. Cantillo. 1991. An
Experimental Facility for Investigation of Interior Convective Heat Transfer. ASHRAE
Transactions, Vol. 97, Pt.1, pp. 497504.
Spitler, J. D. 1990. An Experimental Investi~ation of Air Flow and Convective Heat
Transfer in Enclosures Having Lar~e Ventilative Flow Rates. Thesis. University of
Illinois at UrbanaChampaign.
Eckert, E. R. G. and R. M. Drake, Jr. 1951. Introduction to the Transfer of Heat and
Mass. McGrawHill. New York.
Churchill, S. W. and H. H. S. Chu. 1975. Correlating Equations for Laminar and
Turbulent Free Convection from a Vertical Plate. International Journal Heat Mass
Transfer. Vol 18, pp. 10491053.
ASHRAE. 1989. ASHRAE Handbook. Fundamentals Volume. American Society of
Heating, Refrigeration and AirConditioning Engineers. Atlanta
Pedersen, C.O., INTFAC subroutine, personal communication with Jeff Spitler, 1989.
Walton, G.N. October, 1986. Algorithms for Calculating Radiation View Factors
Between Plane Convex Polygons With Obstructions, NBSIR 863463.
Ferguson, Jeff. date pending. Experimental Convective Heat Transfer Facility: Testin~
and Validation. Thesis. Oklahoma State University.
Fisher, D.E. 1989. Design of an Experimental Facility for the Investi~ation of Convective
Heat Transfer in Enclosures. Thesis. University of Illinois at UrbanaChampaign.
Appendices
79
80
Appendix A: Conduction Program for Predicting the Panel Surface Temperature
C CONDUCTION PROGRAM FOR PANEL DESIGN
C SCOTT SANDERS FALL 1993
C THIS PROGRAM SIMULATES THE HEAT CONDUCTION THRU A MATERIAL
C WITH A WIRE EMBEDDED IN IT. THE GRID SIZE IS 0.01 INCHES
C
INTEGER JMAX
REAL H
DIMENSION T(60,60), TOLD(60,60)
OPEN(UNIT=1,FILE='PC90.0UT')
C 2 WRITE(*,*) 'ENTER MATERIAL THICKNESS INCHES(O.125,O.25,0.375,0.5)'
C READ(*,*) THICK
C WRITE(*,*) 'ENTER MATERIAL CONDUCTIVITY IN ENG. UNITS'
C READ(*,*) AK
CC
SET UP THE MAXIMUM NUMBER OF POINTS IN THE Y DIRECTION DEPENDING
C ON THE THICKNESS THAT IS SELECTED BY THE USER.
C
2 THICK = 0.5
AK = 5.6
IF (THICK .EQ. 0.125) JMAX = 12
IF (THICK .EQ. 0.25) JMAX = 25
IF (THICK .EQ. 0.375) JMAX = 37
IF (THICK .EQ. 0.5) JMAX = 50
CC
THE MAXIMUM NUMBER OF POINTS IN THE X DIRECTION IS 50
C
IMAX = 50
WRITE(*,*) 'ENTER WIRE TEMP IN DEGREES F'
READ(*,*) TWIRE
CC
ONE BOUNDARY CONDITION OF THIS PROBLEM IS A CONVECTIVE HEAT
C TRANSFER SURFACE. THE USER WILL SELECT IF THE CALCULATION
C IS TO BE PERFORMED ON THE CEILING, FLOOR, OR WALL. FROM THIS
C A CONVECTIVE HEAT TRANSFER COEFFICIENT WILL BE SELECTED BASED
C ON PREVIOUS EXPERIMENTS. THEY ARE:
C H(CEILING) = 7.04 BTU/(ftA 2F)
C H(WALL) = 1.76 BTU/(ftA 2F)
C H(FLOOR) = 2.11 BTU/(ftA 2F)
C
WRITE(*,*) 'ENTER 0 FOR THE CEILNG,l FOR THE WALL,2 FOR THE FLOOR'
READ(*,*) L
IF(L .EQ. 0) H 7.04
IF(L .EQ. 1) H 1.76
IF(L .EQ. 2) H 2.11
C TINF IS THE AIR TEMPERATURE AT INFINITE DISTANCE FROM THE
C SURFACE, IT IS ASSUMED TO BE 75 DEGREES F.
C
TINF = 75
DELTX 0.01
DELTY 0.01
C INITIALIZE THE GRID TO 75 F.
DO 3 I = l,IMAX+l
DO 3 J = 1,JMAX
T(I,J) = 75.0
3 CONTINUE
DO 5 N = 1,5000
C
C BOUNDARY CONDITIONS
C THE BOTTOM AND TWO SIDES ARE CONSIDERED ADIABATIC SURFACES
DO 10 I=l,IMAX+l
T(I,l) = T(I,3)
10 CONTI:NUE
DO 20 J=l,JMAX
T(l,J) = T(3,J)
T(IMAX+l,J) = T(IMAXl,J)
20 CONTINUE
C SET WIRE BOUNDARY CONDITIONS
DO 30 I =2,6
DO 30 J =2,6
T(I,J) = TWIRE
30 CONTINUE
C CALCULATE INTERIOR NODE POINTS TEMPERATURE
C (REF. INCOPERIA AND DEWITT
C "FUNDAMENTALS OF HEAT TRANSFER")
DO 40 I = 7,IMAX
DO 40 J = 2,JMAXl
T(I,J)=(T(I,J+l)+T(I,Jl)+T(I+l,J)+T(Il,J))/4
40 CONTINUE
DO 45 I = 2,6
DO 45 J = 7,JMAXl
T(I,J)=(T(I,J+l)+T(I,Jl)+T(I+l,J)+T(Il,J))/4
45 CONTI:NUE
C CALCULATE TEMPERATURE ON SURFACE
C (REF. INCOPERIA AND DEWITT
C "FUNDAMENTALS OF HEAT TRANSFER")
DO 50 I = 2,50
T(I,JMAX) =(T(Il,JMAX)+T(I+l,JMAX) +2*T(I,JMAXl)+2*H*DELTX
$ *TINF/AK)/(2*(H*DELTX/AK + 2))
50 CONTINUE
CHECK = 0.0
C CHECK FOR CONVERGENCE OF SOLUTION
DO 60 I = 2,IMAX
DO 60 J = 2,JMAX
IF (ABS(T(I,J)TOLD(I,J)) .GT. CHECK) THEN
CHECK = ABS(T(I,J)  TOLD(I,J))
ENDIF
60 CONTINUE
DO 65 I=2,IMAX
DO 65 J=2,JMAX
81
TOLD(I,J) = T(I,J)
65 CONTINUE
IF (CHECK .LE. 0.01) THEN
GOTO 500
ENDIF
5 CONTINUE
C WRITE THE SURFACE PANEL SURFACE TEMPERATURES
c 500 DO 400 J=l,JMAX
500 DO 450 I=2,IMAX
WRITE (1,900) T(I,JMAX)
450 CONTINUE
400 CONTINUE
WRITE(l,*) 'NUMBER OF ITERATIONS',N
WRITE(*,*) 'TYPE 1 TO RUN ANOTHER CASE'
READ(*,*) M
IF(M .EQ. 1) GOTO 2
900 FORMAT (50(F6.2,2x))
STOP
END
82
83
Appendix B: Calculation of Unit Resistance for the Floor, Ceiling and Walls of
the Experimental Room
The thermal resistance is calculated by finding the conductance, UA, of the room
element.
For the floor and ceiling, since they are identical constructions:
UA = IUA = UstudAstud + UstyinsAstyins
Where: U = the overall heat transfer coefficient (Btu/(hrft2_0F))
A = the area (ft2)
The subscripts refer to the element of the floor or ceiling. Stud is the joist and styins
refers to the styrofoam and fiberglass insulation.
RValues and Areas of Elements (Ref 1989 ASHRAE Handbook of Fundamentals)
Element Material R Element R UFactor Area (ft2)
Value (hrft2 Value (hrft2 (Btu/hrft2_0F)
°F/Btu) °F/Btu)
15" Thick Joist 1.0 15.0 0.067 0.734
0.75" 3.56 2.7 7.266
Styrofoam
Fiberglass 19 57 0.017* 7.266
Insulation
* Combined Styrofoam and Insulation
Multiplying the UFactors by the areas to obtain the conductance, and summing the
conductance results in a value of 0.171 Btu/(hrOF)
The thermal resistance is found by inverting the conductance value.
1/0.171 =5.84hroF/Btu
The unit resistance for the floor and ceiling is found by multiplying the thermal resistance
by the unit area of a "honeycomb" cell, in this case, 8 ft2.
5.84 *8 = 46.7 hr F _ft2 I BTU
84
The unit resistance for the walls is found the same way.
UA = LUA = Ustud  styAstud  sty + UmasonAmason + Uins  styAins  sty
The subscripts stud  sty refers to the two 2x4 wall studs and the 11 inches of styrofoam
between them, mason refers to the masonite and ins  sty refers to the fiberglass insulation
and the styrofoam.
RValues and Areas of Elements (Ref. 1989 ASHRAE Handbook of Fundamentals)
Element Material R Element R UFactor Area (ft2)
Value (hrft2 Value (hrft2 (Btu/hrft2_0F)
of/Btu) of/Btu)
Wall Stud 1.0 7.0 0.022* 0.734
Styrofoam in 3.57 39.25 0.734
Walls
Fiberglass 19 76 0.013** 7.03
Insulation
0.75" 3.56 2.7 7.03
Styrofoam
18" Thick 1.0 18 0.056 0.24
Masonite
* Combined Wall Stud and Styrofoam
** Combined Insulation and Styrofoam
The conductance is calculated to be 0.12 Btu/(hrF). Inverting this value gives a thermal
resistance of 8.33 hrF/Btu. Multiplying this value by the unit area of 8 ft2 will give a
unit resistance of 66.7 hrFft2/Btu for the walls.
Appendix C: Control of Heated Panels and Temperature Recording Program
DECLARE SUB ALL.PANELS.OFF ()
DECLARE SUB ALL.PANELS.ON ()
DECLARE SUB CALC.PANEL.RESPONSE ()
DECLARE SUB COMPUTE.CONTROL.BYTES ()
DECLARE SUB COMPUTE.NEXT.SERIES ()
DECLARE SUB COPY.DATAFILE ()
DECLARE SUB DELETE.DATAFILE ()
DECLARE SUB DELETE.DELT.FILE ()
DECLARE SUB DISPLAY ()
DECLARE SUB ERROR.HANDLE (ERRCODE$, OTHERCODE$)
DECLARE SUB FIND.SURF.TCS ()
DECLARE SUB INIT.PORTS ()
DECLARE SUB INITIAL.COND ()
DECLARE SUB INPUT.CONFIG.FILE ()
DECLARE SUB MAKE.AUXDATA.FILE ()
DECLARE SUB OPEN.FLUKE.COM ()
DECLARE SUB PULSE.PANELS.OFF ()
DECLARE SUB PULSE.PANELS.ON ()
DECLARE SUB READ.AND.STORE.DATA ()
DECLARE SUB READ.WARMUP.DATA ()
DECLARE SUB SHUTDOWN ()
DECLARE SUB SIMPLE.SETPT.CTRL ()
DECLARE SUB TRIGGER.FLUKE.ONE ()
DECLARE SUB TRIGGER.FLUKE.TWO ()
DECLARE SUB UPDATE.ONOFF.ARRAYS ()
DECLARE SUB USER.INPUT ()
DECLARE SUB WARM.UP.LOOP ()
DECLARE SUB WARMUP.CONTROL.BYTES ()
'BUILDING HEAT TRANSFER LABORATORY, OKLAHOMA STATE UNIVERSITY
'INITIAL CONTROL PROGRAM. WRITTEN BY SCOTT SANDERS, BASED ON THE
'UIUC FACILITY CONTROL PROGRAM WRITTEN BY DAN FISHER. THIS PROGRAM
'WAS WRITTEN FOR SHAKEDOWN TESTS INVOLVING 12 PANELS ON THE WEST WALL.
'THE THERMOCOUPLES FOR THESE 12 PANELS ARE LOCATED ON CHANNELS 0 THRU 11
'AND AFTER MORE PANELS ARE ADDED, THEY SHOULD BE MOVED TO THEIR PROPER
'LOCATION. THE PANELS ARE PLUGGED INTO THE FIRST 12 SOCKETS FOR THE
'PANELS AND LATTER THEY SHOULD BE MOVED INTO THEIR PROPER LOCATION ON
'THE POWER BOX.
'DIMENSION THE PROGRAM ARRAYS
DIM SHARED TCDAT#(100), AVTEMP(100), TCADD%(IOO), TCDAT(100), TCINDAT(102)
DIM SHARED ONOFF%(64), CNTRL%(10), TEMP(21, 10), NEWDATA$(23)
DIM SHARED SURFTC(100), TCDAT%(100), TC$(100), RESIS(12)
DIM SHARED ONOFFl%(21), ONOFF2%(21), ONOFF3%(21), ONOFF4%(21), ONOFF5%(21)
DIM SHARED DELTl(21), DELT2(21), DELT3(21), DELT(21)
'DIM SHARED INCBALl(500), INCBAL2(500)
'DEFINE VARIABLES AS GLOBAL
85
"
86
COMMON SHARED porta%, PORTB%, PORTC%, PANUM%, TCNUM%, SETPT, NEWSCRN
COMMON SHARED TITLE$, N%, OK, CALCLAG, SCANS.PER.SAVE, TIME, ERA$
COMMON SHARED WARM.START, INTEMP, CEILING, SIDE, INLET.FLAG$, IFLAG, OUTTEMP
COMMON SHARED PM#, 01#, 02#, D3#, CAPI$, CAP2$, CAP3$, Q#, ACH#, HT#
COMMON SHARED DP#, SP#, A$, HOURS, MIN, SEC, HOUR$, MIN$, SEC$, INV
COMMON SHARED ICOUNT%, CP, DENS#, TOUTLET, TINLET, MDOT#, QAIR, QPANEL
COMMON SHARED HBALANCE, AVGBAL, RHOI#, RHOR#, DELTIME, RSTFLG%, HTN#
COMMON SHARED HTS#, HTN, HTS, INVN, INVS, AIRSIDE, PANSIDE, NOZTEMP
CLS
INVN = 1
INVS = 1
ERA$ ="
CALL ALL.PANELS.OFF
NEWSCRN= 1
RSTFLAG%=O
CALL INITIAL.COND
CALL USER.INPUT
CALL INPUT.CONFIG.FILE
CALL INIT.PORTS
CALL OPEN.FLUKE.COM
CALL TRIGGER.FLUKE.ONE
OPEN "C:\DATAFILE\OUTPUT\DATAFILE.DAT" FOR OUTPUT AS #2
PRINT #2, TIME$, DATE$," ", TITLE$
IF WARM.START = 0 THEN
CALL WARM.UP.LOOP 'controls warm up period for the room
CALL CALC.PANEL.RESPONSE 'calc. the panel on and off temp setpts
ELSE
FOR 1= 1 TO PANUM%
ONOFFI%(1) = 2
NEXT I
END IF
N%=O
NEWSCRN= 1
OK = 1: TIMEO = TIMER
SCANS.PER.SAVE = 25
DELTIME=O
WHILE OK
CALL READ.AND.STORE.DATA 'retrieves and stores fluke data
CALL FIND.SURF.TCS 'extracts surface temps from fluke data
CALL UPDATE.ONOFF.ARRAYS 'panel on and off setpts based on temp slopes
CALL COMPUTE.CONTROL.BYTES 'cales control bytes and switches panels
KEY$ = INKEY$
IF KEY$ = " " THEN CALL ERROR.HANDLE("INTERRUPT", " ")
CALL DISPLAY
IF RSTFLG% = 1 THEN TIMEO = TIMER
DELTIME = TIMER  TIMEO
HOURS = INT(DELTIME / 3600): MIN = INT(DELTIME / 60)  HOURS * 60
SEC = INT((DELTIME * 10) / 10  HOURS * 3600  MIN * 60)
Q = Q#: ACH = ACH#: HTN = HTN#: HTS = HTS#
HOUR$ = STR$(HOURS)
IF HOURS < 10 THEN HOUR$ = "0" + RIGHT$(HOUR$, 1) ELSE HOUR$ = RIGHT$(HOUR$,
LEN(HOUR$)  1)
MIN$ = STR$(MIN)
IF MIN < 10 THEN MIN$ = "0" + RIGHT$(MIN$, 1) ELSE MIN$ = RIGHT$(MIN$, LEN(MIN$)  1)
SEC$ = STR$(SEC)
IF SEC < 10 THEN SEC$ = "0" + RIGHT$(SEC$, 1) ELSE SEC$ = RIGHT$(SEC$, LEN(SEC$)  1)
LOCATE 22, 1: PRINT "ELAPSED TIME It; HOUR$; ":"; MIN$; ":"; SEC$
LOCATE 22, 29: PRINT "AVG INLET TEMP = "; USING "##.#"; INTEMP
'LOCATE 22,48: PRINT"FLOW RATE = ";USING "####.##";Q;" CFM"
LOCATE 23, 1: PRINT "STATIC PRESSURE = "; USING "#.####"; SP#
LOCATE 23, 29: PRINT "NOZZLE TEMP ="; USING "##.#"; NOZTEMP
'LOCATE 23,29: PRINT "DELTA PRESSURE = "; USING "#.####"; DP#
'LOCATE 23,51: PRINT"AIR CHANGES/HOUR = ";USING"##.##";ACH
LOCATE 23, 51: PRINT "AVG OUTLET TEMP = "; USING "##.#"; OUTTEMP
IF RSTFLG% = 1 THEN
CALL DELETE.DATAFILE
CALL TRIGGER.FLUKE.TWO
END IF
'IF N% = SCANS.PER.SAVE THEN
, CALL COPY.DATAFILE
, CALL TRIGGER.FLUKE.TWO
'END IF
N%=N%+ 1
WEND
IF KEY$ <> "q" THEN PRINT "PROGRAM TIMED OUT. SHUTDOWN ROUTINE INITIATED"
CALL SHUTDOWN
END
'**********************************************************************
SUB ALL.PANELS.OFF
'TURNS ALL PANELS OFF REGARDLESS OF PREVIOUS CONDITION
OUT porta%, 0
OUT PORTB%, 0
OUT PORTC%, 0
END SUB
'**********************************************************************
SUB ALL.PANELS.ON
'TURNS ALL PANELS ON REGARDLESS OF PREVIOUS CONDITION
OUT porta%, 255
OUT PORTB%, 255
OUT PORTC%, 255
87
END SUB
'**********************************************************************
SUB CALC.PANEL.RESPONSE
'CALCULATES RESPONSE OF EACH PANEL TO A SERIES OF "ON OFF" PULSES
CLS
PRINT "CALCULATING CONTROL PARAMETERS"
CALL ALL.PANELS.OFF
SLEEP 15
CALL PULSE.PANELS.ON
SLEEP 17.5
CALL PULSE.PANELS.OFF
FOR 1= 1TO 9
FOR J = 1 TO PANUM%
TEMPDEL = TEMP(J, I + 1)  TEMP(J, 1)
IF TEMPDEL > DELTl(J) AND TEMPDEL < 5 THEN DELT1(J) = TEMPDEL
NEXTJ
NEXT I
CLS
PRINT "DELTI ARRAY COMPLETE"
PRINT "REENTERING WARMUP LOOP"
PRINT "PRESS ANY KEY TO BEGIN DELT2 ARRAY"
SLEEP 15
CLS
CALL WARM.UP.LOOP
CLS
PRINT "CALCULATING CONTROL PARAMETER DELT2"
CALL ALL.PANELS.ON
SLEEP 35
CALL PULSE.PANELS.OFF
FOR 1= 1 TO 9
FOR J = 1 TO PANUM%
TEMPDEL = TEMP(J, 1+ 1)  TEMP(J, 1)
IF TEMPDEL > DELT2(J) AND TEMPDEL < 5 THEN DELT2(J) = TEMPDEL
NEXTJ
NEXT I
CLS
PRINT "DELT2 ARRAY COMPLETE"
PRINT "REENTERING WARMUP LOOP"
PRINT "PRESS ANY KEY WHEN READY TO CALCULATE DELT3 ARRAY"
CLS
PRINT "CALCULATING CONTROL PARAMETER DELT3"
CALL ALL.PANELS.OFF
SLEEP 15
CALL PULSE.PANELS.ON
SLEEP 52.5
CALL PULSE.PANELS.OFF
88
PRINT "CONTROL PARAMETER CALCULATIONS COMPLETE"
FOR I = 1 TO 9
FOR J = 1 TO PANUM%
TEMPDEL = TEMP(J, 1+ 1)  TEMP(J, 1)
IF TEMPDEL > DELT3(J) AND TE