Analytical solutions are presented for the temperature field that arises from the application of a source of heat on an adiabatic plate or board when the fluid is represented as a uniform flow with an effective turbulent diffusivity, i.e., the so-called UFED flow model. Solutions are summarized for a point source, a one-dimensional strip source, and a rectangular source of heat. The ability to superpose the individual kernel solutions to obtain the temperature field due to multiple sources is demonstrated. The point source solution reveals that the N−1 law commonly observed for the centerline thermal wake decay for three-dimensional arrays is predicted by the point source solution for the UFED model. Examination of the solution for rectangular sources shows that the thermal wake approaches the point source behavior downstream from the source, suggesting a new scaling for the far thermal wake based on the total component power and a length scale given by ε/U. The new scaling successfully collapses the thermal wake for several sizes of components and provides a fundamental basis for experimental observations previously made for arrays of three-dimensional components.

Issue Section:
Technical Papers
Keywords:
forced convection, cooling, wakes, temperature distribution, Green's function methods, thermal management (packaging), Cooling Electronics, Forced Convection, Thermal Wake, Green’s Function
Topics:
Cooling, Flow (Dynamics), Heat, Strips, Temperature, Wakes, Electronic components, Turbulence
1.
Moffat, R. J., and Ortega, A., 1988, “Direct Air Cooling of Electronic Components,” Advances in Thermal Modelling of Electronic Components and Systems, eds., A. Bar-Cohen and A. D. Kraus, Vol. 1, Chap. 3, Hemisphere Publishing Corp., New York, NY.
2.
Arvizu, D. E., and Moffat, R. J., 1981, “Experimental Heat Transfer from an Array of Heated Cubical Elements on an Adiabatic Channel Wall,” Report HMT 33, Department of Mechanical Engineering, Stanford University, Stanford, CA.
3.
Tribus, M., and Klein, J., 1952, “Forced Convection from Nonisothermal Surfaces,” Proc., Heat Transfer Symposium, University of Michigan, Ann Arbor, MI, pp. 211–235.
4.
Eckert, E. R. G., and Drake, R. M., 1972, Analysis of Heat and Mass Transfer, McGraw-Hill, New York, NY, pp. 445–466.
5.
Culham, J. R., Lee, S., and Yovanovich, M. M., 1991, “The Effect of Common Design Parameters on the Thermal Performance of Microelectronic Equipment; Part II—Forced Convection,” Heat Transfer in Electronic Equipment, ASME, New York, NY, pp. 55–62.
6.
Ellison, G. N., 1984, Thermal Computations for Electronic Equipment, Appendix II, Van Nostrand Reinhold Co., New York, NY.
7.
Culham, J. R., and Yovanovich, M. J., 1987, “Non-Iterative Technique for Computing Temperature Distributions in Flat Plates with Distributed Heat Sources and Convective Cooling,” Proc., Int. Electronics Packaging Conference, pp. 403–409.
8.
Kays, W. M., and Crawford, M. E., 1980, Convective Heat and Mass Transfer, 2nd Edition, McGraw-Hill, New York, NY, pp. 204–205.
9.
Moffat, R. J., Arvizu, D. E., and Ortega, A., 1985, “Cooling Electronic Components: Forced Convection Experiments with an Air-Cooled Array,” Heat Transfer in Electronic Equipment—1985, ASME HTD-Vol. 48, pp. 17–27.
10.
Sridhar, S., Faghri, M., Lessmann, R. C., and Schmidt, R., 1990, “Heat Transfer Behavior Including Thermal Wake Effects in Forced Air Cooling of Arrays of Rectangular Blocks,” Thermal Modeling and Design of Electronic Systems and Devices, ASME HTD-Vol. 153, p. 15–26.
11.
Ortega
,
A.
, and
Kabir
,
H.
,
1992
, “
Substrate Conduction Mechanisms in Convectively Cooled Simulated Electronic Packages
,”
IEEE Trans., Components, Hybrids, and Manufacturing Technology
,
15
, pp.
771
–
777
.
12.
Rosenthal
,
D.
, 1946, “The Theory of Moving Sources of Heat and Its Application to Metal Treatment,” ASME J. Heat Transfer, pp.849–866.
13.
Crisp, J. N., and Stokey, W. F., 19XX, “Moving Heat Sources for Bodies of Finite Dimensions,” Civil Eng. Prac. Des. Eng., Vol. 4, pp. 905–922.
14.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd Edition, Oxford University Press, New York, NY, pp. 255–270.
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