Solutions of linear and nonlinear schemes for non-Fourier heat conduction

We compare traveling-wave-type solutions to Maxwell-Cattaneo’s description of heat transfer with those of Capriz-Wilmanski-Mariano’s version, which includes nonlinearities due to microstructural contributions in the presence of heat-flux-driven phase transition in a conductor otherwise rigid. Our closed-form results for the nonlinear scheme, based on asymptotic-type analysis, show how temperature traveling-wave-type evolution is perturbed by the influence of microstructural effects. Also, our results underline how even in Maxwell-Cattaneo’s scheme initial conditions in terms of heat flux and temperature have some hidden link, although in the scheme these variables are a priori independent with each other.