Comparison of two nonlinear formulations of the Maxwell-Cattaneo equation in heat pulse transmission

The nonlinear terms resulting from temperature dependence of thermal conductivity and relaxation time must be considered when studying systems undergoing very short thermal pulses with non-negligible amplitude of the temperature perturbation. Two nonlinear formulations of the Maxwell-Cattaneo-Vernotte equation for thermal transport with relaxation effects are introduced. A comparison of the consequences of these two different nonlinear Cattaneo type equations on thermal pulse propagation is obtained and discussed. The differences in the corresponding velocities and in the corresponding heights of the perturbation peaks turn out to be significant and could be experimentally detected.