Thermal spreading analysis of a transversely isotropic heat spreader

An analytical solution for the steady-state temperature distribution in a transversely isotropic (TI) heat spreader is provided and validated using three-dimensional finite element (FE) analysis. The dimensionless maximum temperature and corresponding thermal spreading resistance were determined for various Biot numbers, dimensionless heat spreader thicknesses, source-to-spreader area ratios, and thermal conductivity ratios (ratio of out-of-plane to in-plane thermal conductivities). The heat spreader investigated consists of uniformly-distributed fibers/channels aligned in the heat spreader's thickness direction. Solutions are presented graphically for various geometric, material, and operating mode combinations. The analytical solutions differ by less than 1% from the FE solutions, indicating that the analytical solution, with cosine solution form, is both effective and accurate in predicting the thermal spreading resistance of a TI heat spreader for many parameter combinations. These results can aid the design or analysis of non-traditional media for thermal spreading, including polymer composites, metal matrix composites, nanocomposites, heat pipes and electronics packaging materials with uniformly-distributed thermal vias.