On the axi-symmetric equations of a rigid heat conductor: discontinuity waves in a non-constant state

Abstract

By requiring the invariance with respect to a stretching group of transformations the non-linear system of equations governing the heat propagation in a rigid conductor is mapped in a form which has a constant state solution in terms of suitable similarity variables. It has been shown that constant state solutions become special non-constant state solutions in the original variables. In particular, we prove that the temperature dependence of the propagation of discontinuity waves along a solid in an equilibrium state well reproduces the temperature behaviour of the second sound speed.