Three-dimensional natural convection flow and heat transfer were numerically studied for a three-by-three array of discrete protruding heat sources on a horizontal substrate in an air-filled, rectangular, narrow-aspect-ratio enclosure with length, width, and height ratio of 6:6:1. The governing equations for natural convection in air, coupled with conjugate conduction and radiation within the enclosure were solved using a finite volume method. The study examines the complex thermal interactions between the heat sources, substrate, and enclosure walls as affected by the thermal conductance of the walls and substrate with the intent of determining which physical effects and level of detail are necessary to accurately predict thermal behavior of discretely heated enclosures. The influence of radiation on the overall heat transfer is given particular attention. The three-dimensionality of the problem was evident in the overall flow characteristics and in the convective heat transfer edge effects on the heat source surfaces. Excellent agreement between temperature predictions on the heat sources and substrate and experimental measurements was obtained for modified Rayleigh numbers in the range of 9.7 × 105 to 1.6 × 107.

Issue Section:
Multimode Heat Transfer
Keywords:
Conjugate Heat Transfer, Enclosure Flows, Natural Convection
Topics:
Flow (Dynamics), Heat, Heat conduction, Heat transfer, Natural convection, Radiation (Physics)
1.
EI Sherbiny
 
S. M.
,
Hollands
 
K. G. T.
, and
Raithby
 
G. D.
,
1982
, “
The Effect of Thermal Boundary Conditions on Natural Convection in Vertical and Inclined Air Layers
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
104
, pp.
515
–
520
.
2.
Fusegi
 
T.
,
Hyun
 
J. M.
,
Kuwahara
 
K.
, and
Farouk
 
B.
,
1991
, “
A Numerical Study of Three-Dimensional Natural Convection in a Differentially Heated Cubical Enclosure
,”
Int. J. Heat Mass Transf.
, Vol.
34
, pp.
1543
–
1557
.
3.
Globe
 
S.
, and
Dropkin
 
D.
,
1959
, “
Natural-Convection Heat Transfer in Liquids Confined by Two Horizontal Plates and Heated From Below
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
81
, pp.
24
–
28
.
4.
Holland
 
K. G. T.
,
Raithby
 
G. D.
, and
Konicek
 
L.
,
1975
, “
Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water
,”
Int. J. Heat Mass Transf.
, Vol.
18
, pp.
879
–
884
.
5.
Holometrix Product Literature, 1996, Holometrix, Inc., Bedford, MA.
6.
Howell, J. R., 1982, A Catalog of Radiation Configuration Factors, McGraw-Hill, New York.
7.
Huang
 
Y. H.
, and
Aggarwal
 
S. K.
,
1995
, “
Effect of Wall Conduction on Natural Convection in an Enclosure With a Central Heat Source
,”
ASME Journal of Electronic Packaging
, Vol.
117
, pp.
301
–
306
.
8.
Incropera
 
F. P.
,
1988
, “
Convection Heat Transfer in Electronic Equipment Cooling
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
110
, pp.
1097
–
1111
.
9.
Kang
 
B. H.
, and
Jaluria
 
Y.
,
1990
, “
Natural Convection Heat Transfer Characteristics of a Protruding Thermal Source Located on Horizontal and Vertical Surfaces
,”
Int. J. Heat Mass Transf.
, Vol.
33
, pp.
1347
–
1357
.
10.
Kim
 
D. M.
, and
Viskanta
 
R.
,
1984
a, “
Study of the Effects of Wall Conductance on Natural Convection in a Differentially Oriented Square Cavity
,”
J. Fluid Mech.
, Vol.
144
, pp.
153
–
176
.
11.
Kim
 
D. M.
, and
Viskanta
 
R.
,
1984
b, “
Effect of Wall Conduction and Radiation on Natural Convection in a Rectangular Cavity
,”
Num. Heat Transf
, Vol.
7
, pp.
449
–
470
.
12.
Larson
 
D. W.
, and
Viskanta
 
R.
,
1976
, “
Transient Combined Laminar Free Convection and Radiation in a Rectangular Enclosure
,”
J. Fluid Mech.
, Vol.
78
, pp.
65
–
85
.
13.
Meyer
 
B. A.
,
Mitchell
 
J. W.
, and
El-Wakil
 
M. M.
,
1982
, “
The Effect of Thermal Wall Properties in Natural Convection in Inclined Rectangular Cells
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
104
, pp.
111
–
117
.
14.
Moffat, R. J., and Ortega, A., 1988, “Direct Air-Cooling of Electronic Components,” Advances in Thermal Modeling of Electronic Components and Systems, Vol. 1, A. Bar-Cohen and A. D. Kraus, eds., Hemisphere, New York, pp. 129–282.
15.
Ortega, A., and Lall, B. S., 1996, “Natural Convection Air Cooling of a Discrete Source on a Conducting Board in a Shallow Horizontal Enclosure,” Proc. Twelfth IEEE Semiconductor Thermal Measurement and Management Symposium, Austin, TX, pp. 201–213.
16.
Ostrach
 
S.
,
1988
, “
Natural Convection in Enclosures
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
110
, pp.
1175
–
1190
.
17.
Papanicolaou
 
E.
, and
Gopalakrishna
 
S.
,
1993
, “
Natural Convection in Shallow, Horizontal Air Layers Encountered in Electronic Cooling
,”
ASME Journal of Electronic Packaging
, Vol.
117
, pp.
307
–
316
.
18.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.
19.
Peterson
 
G. P.
, and
Ortega
 
A.
,
1990
, “
Thermal Control of Electronic Equipment and Devices
,”
Advances in Heat Transfer
, Vol.
20
., J. P. Hartnett and T. F. Irvine, Jr., eds., Academic Press, San Diego, pp.
181
–
314
.
20.
Torrence
 
K. E.
, and
Rockett
 
J. A.
,
1969
, “
Numerical Study of Natural Convection in an Enclosure With Localized Heating from Below—Creeping Flow to the Onset of Laminar Instability
,”
J. Fluid Mech.
, Vol.
36
, pp.
33
–
54
.
21.
Torrence
 
K. E.
,
Orloff
 
L.
, and
Rockett
 
J. A.
,
1969
, “
Experiments on Natural Convection in Enclosures With Localized Heating from Below
,”
J. Fluid Mech.
, Vol.
36
, pp.
21
–
32
.
22.
Yang, K. T., 1988, “Natural Convection in Enclosures,” Handbook of Single-Phase Convective Heat Transfer, S. Kakac, R. K. Shah, and W. Aung, eds., John Wiley and Sons, New York, Chapter 13.
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