On The Symmetry of the Heat-Conduction Tensor

Abstract

For a material satisfying the Fourier-Duhamel relation (7.1) for heat conduction, the heating fluxh depends linearly on the temperature gradient:

$$h = K{\text{ grad }}\theta {\text{,}}$$

((7A.1))

where the tensorK is thethermal conductivity. In general, K is for each material element a function of the deformation gradient F and the temperature θ:

$$K = K\left( {F,\theta } \right).$$

((7A.2))

In the linear “thermodynamics of irreversible processes” it is often claimed that K must be a symmetric tensor, this condition being one of the so-called Onsager relations. As explained in the lecture preceding, no firm theoretical basis has been found for this claim.