Influence coefficient method for calculating discrete heat source temperature on finite convectively cooled substrates

A simple method is developed for predicting discrete heat source temperatures on a finite convectively cooled substrate. The method is based on the principle of superposition using a single source solution for the mean or maximum contact temperature of an eccentric uniform heat source on a rectangular substrate. By means of influence coefficients, the effect of neighboring source strength and location may be assessed. It is shown that the influence coefficients represent localized thermal resistances, which must be weighted according to source strength. For a system of N heat sources, there exists N effects of source strength and position on any one heat source. This includes a self effect (source of interest) and N-1 influence effects (neighboring sources). The method is developed for isotropic, orthotropic, and compound systems. Convection in the source plane is addressed for isotropic and orthotropic systems. Expressions are developed for both mean and centroidal temperature.