Three-phase lag model for thermal conductivity of a thermo-viscoelastic porous medium

This paper investigates the propagation of waves and the thermal behavior in a thermoviscoelastic porous medium using the three-phase-lag (TPL) model which accounts for phase lags in the heat flux vector, temperature gradient and thermal displacement gradient. The study aims to capture the interactions between thermal, mechanical, and structural properties of the thermo-viscoelastic porous, isotropic, homogeneous medium. The governing equations, incorporating the TPL heat conduction law and constitutive relations for the viscoelastic porous material, are derived and analyzed. The impact of relaxation times, porosity, and viscoelastic parameters on heat propagation is investigated through analytical solutions by normal modal analysis. Analytical representations of various physical quantities (stresses components, displacements, temperature,...) in the material's domain are derived. These expressions are then assessed numerically for a specific material, with the outcomes depicted graphically. A comparison is made between the predictions of the three-phase-lag (TPL), the dual-phase-lag (DPL) and Lord-Shulman (L-S) theories in the absence and presence of voids.