Heat Conduction in 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.