Heat Conduction in Simple Metals

TLDR

Heat conduction is described by a nonlinear partial differential equation when thermal conductivity and heat capacity depend on temperature. The study investigates how thermal conductivity and heat capacity relate in simple metals using solid‑state theory and experimental data. The authors apply the linearized heat conduction equation to solve practical heat transfer problems. They find that the product KS is nearly constant with temperature, satisfying the transformation condition that requires the constancy of \([1/(KS)^{1/2}](d/dT)\log(S/K)^{1/2}\), and that this condition holds for simple metals.

Abstract

The partial differential equation of heat conduction is a nonlinear equation when the temperature dependence of the thermal parameters (i.e., the thermal conductivity, K, and S, the product of the density and the specific heat at constant pressure) is taken into account. It is shown that a mathematical condition for the transformation to linear form of the one-dimensional, nonlinear, partial differential equation of heat conduction is the constancy of [1/(KS)½](d/dT)log(S/K)½. This discovery is the motivation for an investigation of the relations between the thermal parameters of simple metals on the bases of the theory of solids and available experimental data. It is found that KS is essentially constant, its variation with temperature being much less than that of either K or S considered separately. It is also shown, as a result, that the condition for the above-mentioned transformation is valid for simple metals. Applications of the transformed equation to the solution of problems in heat conduction are considered.