Hotspot Size Effect on Conductive Heat Spreading

Solid heat spreaders, particularly those made of copper or graphite, are often benchmark solutions for hotspot thermal management. In this paper, we present exact and approximate analytical solutions of steady-state hotspot cooling with a planar heat spreader, which is subjected to adiabatic conditions except for a hotspot centered at the top surface and a constant temperature at the bottom surface. The approximate solution bridges exact solutions at two limits of hotspot size: infinitesimal hotspot at the center and uniform heat flux across the spreader. The approximate solution accounts for variable hotspot size and anisotropic thermal conductivity in a compact form, which is useful for estimating thermal parameters such as conduction shape factor and effective thermal conductivity.