Exact solution of Maxwell–Cattaneo–Vernotte model: Diffusion versus second sound

Abstract

In this work we study the Maxwell–Cattaneo–Vernotte model for heat transport by conduction. We present a methodology to find the exact solution of the model without decoupling the system, so we do not need the restriction (∂T/∂t)(x,0)=0. Furthermore, we found a critical value for the thermal relaxation time depending on the physical constants of the system, which allows us to classify heat transport as diffusion or second sound. Finally, we conducted computer simulations and demonstrated that the relaxation time may not be as small as expected for certain initial conditions.