Effect of Temperature-Dependent Thermal Conductivity on Spreading Resistance in Flux Channels

When the thermal conductivity of a material varies with temperature, the governing heat conduction equation becomes nonlinear and the use of constant thermal conductivity may produce unreliable results in thermal analysis. In this paper, analytical solutions for the temperature distribution and thermal resistance of a three-dimensional flux channel with temperature-dependent thermal conductivity are discussed and used to study the effect of the temperature-dependent thermal conductivity on the temperature rise and thermal spreading resistance for different conductivity functions. A single eccentric heat source is considered in the source plane of the flux channel that spreads the heat into a convective heat sink. The analytical solutions of the problem are illustrated by means of the Kirchhoff transform, which is considered a powerful technique for solving nonlinear conduction problems with temperature-dependent thermal conductivity. For validation purposes of the analytical results, the results are compared with numerical solution results obtained by solving the problem based on the finite element method using the ANSYS commercial software package.