The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux

Mathematics

Ibrahim A. Abbas¹  Tareq Saeed¹ 

[1]Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

关键词: Fourier-Laplace transforms;    porous material;    eigenvalues method;    fractional time derivative;   

DOI  :  10.3390/math9030207

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown