Generalized Thermo-Diffusion Interaction in an Elastic Medium under Temperature Dependent Diffusivity and Thermal Conductivity

Aatef Hobiny and Ibrahim Abbas
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Aatef Hobiny: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 22254, Saudi Arabia
Ibrahim Abbas: Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 22254, Saudi Arabia

Mathematics, 2022, vol. 10, issue 15, 1-16

Abstract: The purpose of this work is to investigate, within the context of extended thermo-diffusion theory, the transient thermo-diffusion responses for a half-space with variable thermal conductivity and diffusivity. The half-bounding space’s surface is traction-free and exposed to a time-dependent thermal shock, but the chemical potential is believed to be a known function of time. Because the nonlinear equations are complicated, the finite element technique is applied to solve these equations. Numerical outcomes are produced and graphically illustrated. The effects of varying thermal conductivity and diffusivity on the response are studied using parameter studies. Using the results of this study, researchers hope to understand better how thermo-mechanical fields interact in real materials. By ignoring the new parameter, a comparison of numerical results and analytical cases is produced, and the behavior of physical quantities for numerical solutions is studied to ensure that the proposed technique is accurate.

Keywords: thermoelastic diffusions; variable thermal conductivity; variable diffusivity; finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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