Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

doi:10.1007/s10483-020-2612-8

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (6): 927-938.doi: https://doi.org/10.1007/s10483-020-2612-8

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

T. SAEED¹, I. A. ABBAS^1,2

1. Nonlinear Analysis and Applied Mathematics(NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21441, Saudi Arabia;
2. Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

收稿日期:2019-12-30 修回日期:2020-02-27 发布日期:2020-06-08
通讯作者: I. A. ABBAS E-mail:aabbas5@kau.edu.sa
基金资助:
Project supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah (No. DF-782-130-1441)

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

T. SAEED¹, I. A. ABBAS^1,2

1. Nonlinear Analysis and Applied Mathematics(NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21441, Saudi Arabia;
2. Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

Received:2019-12-30 Revised:2020-02-27 Published:2020-06-08
Contact: I. A. ABBAS E-mail:aabbas5@kau.edu.sa
Supported by:
Project supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah (No. DF-782-130-1441)

摘要/Abstract

摘要： In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical (CD) coupled, the Lord-Shulman (LS), and the Green-Lindsay (GL) models.

关键词: Fourier-Laplace transform, thermal relaxation time, porous medium, eigenvalue approach

Abstract: In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical (CD) coupled, the Lord-Shulman (LS), and the Green-Lindsay (GL) models.

Key words: Fourier-Laplace transform, thermal relaxation time, porous medium, eigenvalue approach

中图分类号:

74F05
76S05

T. SAEED, I. A. ABBAS. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 927-938.

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Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

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