Convection and Conduction Cooling of Substrates Containing Multiple Heat Sources

An analysis is made of the steady-state temperature distribution in a substrate with heat inputs from multiple sources. The problem is of interest in connection with integrated and thin film circuits mounted on ceramic or glass substrates. In these applications, convective heat transfer is present with either conduction along the leads joining the substrate to the heat sink or conduction to one end of the substrate which is heat sinked. A formal three-dimensional solution is obtained which is evaluated for various geometries, thermal conductivities, coefficients of convection and heat-sinking conditions.