Analysis of Heat Transfer in the Case of Non-linear Hyperbolic Conduction Equation Coupled with Radiation or with Thermoelectricity

Abstract

Nonlinear hyperbolic heat conduction problems are analyzed thanks to the Cattaneo-Vernotte model, which takes what happens at very short times into account. First, the case of the coupled conductive-radiative heat transfer in planar and spherical media is considered. The accuracy of the Lattice Boltzmann heat conduction model coupled with an analytical layered spherical harmonics solution of the radiative transport equation is investigated. The effects of different parameters such as scattering albedo on both temperature and conductive heat flux distributions within the medium are studied for steady and transient states. The present predictions agree well with literature benchmarks. It is also shown that the parameters have a significant effect on both temperature profile and hyperbolic sharp wave front. Second, the non-Fourier heat conduction in a thermoelectric thin layer is investigated under several boundary conditions by performing a specific quadrupole method. The expressions of the temperature and the heat flux of the small-scale thermoelectric materials are obtained and the whole matrix formulation is given explicitly. Good agreement is observed between quadrupole temperature predictions and analytical results for the Fourier heat conduction problems.