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 travelingwave-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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

We compare traveling-wave-type solutions between two models describing heat transfer, one including nonlinearities due to microstructural contributions and heat-flux-driven phase transition, and the other being the Maxwell-Cattaneo's scheme. Our closed-form results based on asymptotic-type analysis reveal how microstructural effects perturb the evolution of temperature traveling waves. Furthermore, our findings indicate a hidden link between initial conditions of heat flux and temperature, even in the Maxwell-Cattaneo's scheme.