Abstract
In the present article, the generalized thermoelastic wave model with and without energy dissipation under fractional time derivative is used to study the physical field in porous two-dimensional media. By applying the Fourier-Laplace transforms and eigenvalues scheme, the physical quantities are presented analytically. The surface is shocked by heating (pulsed heat flow problem) and application of free traction on its outer surface (mechanical conditions) by the process of temperature transport (diffusion) to observe the full analytical solutions of the main physical fields. The magnesium (Mg) material is used to make the simulations and obtain numerical outcomes. The basic physical field quantities are graphed and discussed. Comparisons are made in the results obtained under the strong (SC), the weak (WC) and the normal (NC) conductivities.
Highlights
Porous media appear in many forms of environmental, natural, and synthetic implementations and in several technologies
We studied the impacts of strong, weak, and normal thermal conductivities in porous materials under the generalized fractional-order thermoelastic model
Generalized thermoelastic fractional-order models are considered as an advancement in the study of porous elastic materials
Summary
Porous media appear in many forms of environmental, natural, and synthetic implementations and in several technologies. To overcome the first insufficiency in the decoupled thermoelasticity theorem, in 1956, Biot [1] presented the coupled thermoelasticity theorem to control the first insufficiency in the decoupled thermoelastic model, which prognosticates two phenomena not suitable for physical observation. The thermal conductivity equation is parabolic, presenting an infinite propagation speed for thermal waves. Biot developed poroelasticity models [1,3,4] for a high–low-frequency range and built upon the coupled thermoelasticity hypothesis to overcome the inconsistency in the uncoupled hypothesis [1]. The heat conduction and elasticity equations in this theory are coupled. It includes a drawback of the uncoupled hypothesis in which the heat wave propagates with an infinite velocity that is impractical in nature. To solve the problem of the coupled hypothesis, generalized thermoelasticity models were expanded
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