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TECHNICAL PAPERS

On the Use of Point Source Solutions for Forced Air Cooling of Electronic Components—Part I: Thermal Wake Models for Rectangular Heat Sources

[+] Author and Article Information
Alfonso Ortega

Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721

Shankar Ramanathan

Center for Electronic Packaging Research, The University of Arizona, Tucson, AZ 85721

J. Electron. Packag 125(2), 226-234 (Jun 10, 2003) (9 pages) doi:10.1115/1.1569506 History: Received March 26, 2002; Online June 10, 2003
Copyright © 2003 by ASME
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References

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.
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.
Tribus, M., and Klein, J., 1952, “Forced Convection from Nonisothermal Surfaces,” Proc., Heat Transfer Symposium, University of Michigan, Ann Arbor, MI, pp. 211–235.
Eckert, E. R. G., and Drake, R. M., 1972, Analysis of Heat and Mass Transfer, McGraw-Hill, New York, NY, pp. 445–466.
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.
Ellison, G. N., 1984, Thermal Computations for Electronic Equipment, Appendix II, Van Nostrand Reinhold Co., New York, NY.
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.
Kays, W. M., and Crawford, M. E., 1980, Convective Heat and Mass Transfer, 2nd Edition, McGraw-Hill, New York, NY, pp. 204–205.
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.
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.
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.
Rosenthal,  D., 1946, “The Theory of Moving Sources of Heat and Its Application to Metal Treatment,” ASME J. Heat Transfer, pp.849–866.
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.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd Edition, Oxford University Press, New York, NY, pp. 255–270.

Figures

Grahic Jump Location
Direct air cooling of a PWB with two heat-dissipating components and parallel flow
Grahic Jump Location
Dimensionless temperature rise due to a point source of heat on an adiabatic surface; θ* defined in Eq. (11): U=8.5 m/s, ε=0.0025 m2 /s, Q=1 W
Grahic Jump Location
Dimensionless isotherms due to a point source of heat on an adiabatic surface; θ* defined in Eq. (11): U=8.5 m/s, ε=0.0025 m2 /s, Q=1 W
Grahic Jump Location
Configuration of two infinite strip sources of width 2b on an adiabatic plate
Grahic Jump Location
Surface temperature rise due to two strip heat sources on an adiabatic surface: U=1.0 m/s, ε=0.0025 m2 /s, b=0.5 cm,q=0.5 W/cm2,B=1
Grahic Jump Location
Dimensionless temperature rise due to a 2 cm×2 cm square source of heat; θ* as in Eq. (15): U=1.0 m/s, ε=0.0025 m2 /s, b=1.0 cm,l=1.0 cm,B=2,L=2
Grahic Jump Location
Dimensionless isotherms on an adiabatic surface due to a 2 cm×2 cm square source of heat; θ* as in Eq. (15): U=1.0 m/s, ε=0.0025 m2 /s, b=1.0 cm,l=1.0 cm,B=2,L=2
Grahic Jump Location
Dimensionless isotherms on an adiabatic surface due to a 2 cm×1 cm rectangular source of heat; θ* as in Eq. (15): U=1.0 m/s, ε=0.0025 m2 /s, b=1.0 cm,l=0.5 cm,B=2,L=1
Grahic Jump Location
Dimensionless isotherms on an adiabatic surface due to a 1 cm×2 cm rectangular source of heat; θ* as in Eq. (15): U=1.0 m/s, ε=0.0025 m2 /s, b=0.5 cm,l=1.0 cm,B=1,L=2
Grahic Jump Location
Isotherms on an adiabatic surface due to three rectangular sources: U=1.0 m/s, ε=0.0025 m2 /s
Grahic Jump Location
Comparison of the spanwise centerline temperature for an infinite strip source and rectangular source at low Peclet number, Peb=5.0:b=1.0 cm,U=1.0 m/s, ε=0.002 m2 /s
Grahic Jump Location
Comparison of the spanwise centerline temperature for an infinite strip source and rectangular source at high Peclet number, Peb=50.0:b=1.0 cm,U=1.0 m/s, ε=0.0002 m2 /s
Grahic Jump Location
The spanwise temperature distribution across the thermal wake at various streamwise positions, normalized by the spanwise centerline temperature at that position. For the square source, b=l=1.0 cm,U=1.0 m/s, ε=0.002 m2 /s, Peb=5.0
Grahic Jump Location
The spanwise temperature distribution across the thermal wake at various streamwise positions, normalized by the spanwise centerline temperature at that position. For the square source, b=l=1.0 cm,U=1.0 m/s, ε=0.0002 m2 /s, Peb=50.0
Grahic Jump Location
Illustration showing the relationship between streamwise row number, N, streamwise position, x, and component spacing, s:N=x/s
Grahic Jump Location
Centerline temperature rise normalized by centerline temperature rise at a downstream position x=s: 2 cm×2 cm source, U=1.0 m/s, ε=0.0025 m2 /s, Peb=4.0
Grahic Jump Location
Centerline temperature rise normalized by centerline temperature rise at a downstream position x=s: s=2.4, U=1.0 m/s, ε=0.0025 m2 /s, Peb=2.4, 4.0, and 8.0
Grahic Jump Location
Centerline temperature rise normalized by centerline temperature rise at a downstream position x=s:s=6.0 cm,U=1.0 m/s, ε=0.0025 m2 /s, Peb=2.4, 4.0, and 8.0
Grahic Jump Location
Centerline temperature made dimensionless by total component power, Q=q(2b×2b), and far-field length scale, ε/U: comparison with point source solution, 1(2πX*)

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