On the Use of Point Source Solutions for Forced Air Cooling of Electronic Components—Part II: Conjugate Forced Convection From a Discrete Rectangular Source on a Thin Conducting Plate

Author:

Ortega Alfonso1,Ramanathan Shankar2

Affiliation:

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

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

Abstract

A model for uniform parallel flow over the surface of a rectangular source of heat on a conducting plate is used to demonstrate the use of analytic Green’s functions to formulate the conjugate problem. The Green’s functions are solutions to the temperature field that arises from a point source of heat on the surface. They provide a relationship between the local heat flux and surface temperature on the plate, effectively serving the same role as the heat transfer coefficient. By coupling the pointwise Green’s function to a finite element discretization of the thin plate, the surface temperature and convective heat flux distributions on the heat source and its substrate are found by a non-iterative procedure. A parametric study shows that at high Peclet numbers, the heat transfer from the source approaches the behavior of an infinite two-dimensional source of heat. The average Nusselt numbers for rectangular sources of different aspect ratios are found to be insensitive to source aspect ratio at high Peclet numbers. Board conduction reduces the average Nusselt numbers over the source when it is defined in terms of the freestream temperature. New correlations for the source Nusselt number as a function of flow Peclet number and board conductivity are presented.

Publisher

ASME International

Subject

Electrical and Electronic Engineering,Computer Science Applications,Mechanics of Materials,Electronic, Optical and Magnetic Materials

Reference30 articles.

1. Lasance, C. M., Vinke, H., Rosten, H., and Weiner, K. L., 1995, “A Novel Approach for the Thermal Characterization of Electronic Parts,” Proc., Eleventh Annual IEEE Semiconductor Thermal Measurement and Management Symposium (SEMITHERM), IEEE, Piscataway, NJ, IEEE No. 95CH35733, pp. 1–9.

2. Lehmann, G. L., and Wirtz, R. A., 1984, “Convection from Surface Mounted Repeating Ribs in a Channel Flow,” ASME Paper No. 84-WA/HT-88.

3. Sparrow, E. M., Niethammer, J. E., and Chaboki, A., 1982, “Heat Transfer and Pressure Drop Characteristics of Arrays of Rectangular Modules Encountered in Electronic Equipment,” Int. J. Heat Mass Transf., 25, pp. 961–973.

4. Wirtz, R. A., and Dykshoorn, P., 1984, “Heat Transfer from Arrays of Flat Packs in Channel Flow,” Proc., Fourth International Electronic Packaging Society Conference, New York, NY, pp. 318–326.

5. Sridhar, S., Faghri, M., Lessman, 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—1990, ASME HTD-Vol. 153, pp. 849–866.

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