One dimensional nonlinear nonsteady state heat conduction I: general solution by perturbation theory

Abstract

Taking into account the dependence of the heat capacity and heat conductivity on temperature, one obtains a nonlinear field equation of temperature. This nonlinear partial differential equation is resolved by perturbation theory for the particular case of a homogeneous system. The solution is checked by some criteria of control derived from thermostatics, from steady state transport, and from spatial symmetry. It forms the theoretical framework of nonlinear heat waves to be discussed in a future paper.