Calculation of Heat Flow in a Medium the Conductivity of which Varies with Temperature

Abstract

It is shown that the heat flow in a single homogeneous medium of thermal conductivity σ(T), between boundaries at temperatures T₂ and T₁ is the same as that for the same geometry in a medium of unit thermal conductivity and boundary ``thermal potentials'' Σ(T₂) and Σ(T₁), where ${\mathrm{\Sigma (T)=\int }}_0^T\mathrm{\sigma (T\prime )dT\prime }$ . Some applications are given, as well as a short table of Σ(T) for common cryogenic temperatures and materials.