An Analysis of Forced Convection Heat Transfer in High-Density Circuit Packages

Abstract

The results of an investigation of the cooling characteristics of high-density packaging of solid state logic circuits are presented. The analysis is based on the theory of single-pass air-cooled heat exchangers with uniform heat flux for laminar and turbulent flow. General expressions are derived which predict the amount of cooling air required on a normalized basis as a function of parameters such as average package “filling factor” for both the laminar and turbulent flow cases. The general expression has been successfully solved using IBM 704 and IBM 7090 Data Processing Systems. Several trial runs have been made with what is believed to be a representative range of values of wattage density, thermal resistance of circuit blocks, and other relevant parameters. The results show (as expected) that there exists an optimum package height (air duct length) for any given packaging density and wattage density which results in a minimum blower power. The expression for computing blower power as a function of required air flow and package parameters is developed. The analysis is sufficiently general to be adaptable to air flow predictions for a broad range of package configuration through which cooling air can be forced. An appendix is included which discusses the results of certain tests on a heat transfer model. The results of the tests appear to support the theory quite well, especially considering the relatively crude approximation to a uniform heat flux heat exchanger that the model represents. Curves presenting the experimental data are included, along with some air flow predictions for a hypothetical model for 90°, 100°, and 110°F air inlet temperature, and 60 mw logic block dissipation. The predicted air flow appears quite reasonable.