Temperature fields generated by a circular heat source (CHS) in an infinite isotropic medium: Treatment of contact resistances with application to thin films

Abstract

The temperature fields and heat fluxes created by a circular heat source (CHS) are derived for the case of a CHS embedded between two identical and isotropic semi-infinite media, when different thermal contact resistances (CRs) are present on each surface of the CHS. Three different temperature fields are derived: on the CHS surface and in each one of the media surrounding the CHS. The derivation of the three-dimensional heat flow solution uses first principles with no prior assumptions, and employs the Hankel and Laplace transforms. The analytical solution presented here is exact with no approximations, but is given in integral form, which requires a facile numerical evaluation. Finite element simulations performed with COMSOL Multiphysics are provided and validate the analytical solution. The application of the solution to thin film thermal conductivity virtual measurements is demonstrated. Regressions of the numerical results yield thin film resistances in excellent agreement with the actual values (all within 1.5% error), which can readily be translated into thin film thermal conductivities.