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The aim of this article is to build a mathematical model to study the problem of generalized thermoelastic porous medium according to the Lord–Shulman model and refined multi-phase lags model. The medium is considered to be homogeneous, isotropic and porous, such that changes in the size of the fracture field are in two dimensions. Four ordinary differential equations of the modified couple stress of thermoelastic porous media are obtained instead of partial differential equations and they solved precisely. The harmonic wave analysis procedure is proposed to find systematically the appropriate solutions to the variables of stresses, displacements, the change in the temperature, and in the volume fraction field. The outcomes of the physical variables have been computed numerically and clarified graphically. The comparison between both refined multi-phase lags and Lord–Shulman models are carried out for particular values of distance and various values of thermal relaxation times. This article’s findings may be useful to many researchers and scientists in the subject of materials science, especially porous media, as well as those working on creating modern technological materials.

Effects of thermal relaxation times and porosity in a Lord-Shulman and refined multi-phase lags model of generalized thermoelasticity