Thermal Spreading Resistance of Arbitrary-Shape Heat Sources on a Half-Space: A Unified Approach

Thermal spreading/constriction resistance is an important phenomenon where a heat source/sink is in contact with a body. Thermal spreading resistance associated with heat transfer through the mechanical contact of two bodies occurs in a wide range of applications. The real contact area forms typically a few percent of the nominal contact area. In practice, due to random nature of contacting surfaces, the actual shape of microcontacts is unknown; therefore, it is advantageous to have a model applicable to any arbitrary-shape heat source. Starting from a half-space representation of the heat transfer problem, a compact model is proposed based on the generalization of the analytical solution of the spreading resistance of an elliptical source on a half-space. Using a “bottom-up” approach, unified relations are found that allow accurate calculation of spreading resistance over a wide variety of heat source shapes under both isoflux and isothermal conditions.