Determination of Temperatures and Heat Fluxes on Surfaces of Multi-Domain Three-Dimensional Electronic Components

A new algorithm that uses the boundary element method (BEM) has been developed for determining steady thermal boundary conditions on surfaces of three-dimensional solids where such quantities are unknown. Given temperature and heat flux on surfaces where such data is readily available, the algorithm computes, non-iteratively, the temperature field within the entire object and any unknown thermal boundary conditions on the surfaces where thermal boundary values are unavailable. An inverse BEM computer program has been developed and was successfully tested on several simple geometries where the analytic solutions of the well-posed problem were known. Our non-iterative algorithm for inverse determination of unknown thermal boundary conditions is very fast and highly flexible in treating complex three-dimensional geometries including interior cavities, mixed thermal boundary conditions and multiple domains with different thermal properties. Besides surface input data, this algorithm accepts also temperatures and heat fluxes at isolated interior points as input data.