Modeling of thermoelastic diffusion plate under two temperature, fractional-order, and temperature-dependent material properties,ZAMM - Journal of Applied Mathematics and Mechanics

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Modeling of thermoelastic diffusion plate under two temperature, fractional-order, and temperature-dependent material properties
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-05-12 , DOI: 10.1002/zamm.202000321
Ankit Bajpai ₁ , P. K. Sharma ₁ , Rajneesh Kumar ₂

Affiliation

A mathematical model is formulated to study the thermoelastic diffusion in the plate using two temperature fractional order theory in materials having temperature-dependent elastic properties. Governing equations for the considered two-dimensional problem are deduced. The plate is considered as unstrained and unstressed at uniform temperature initially. Governing equations are non-dimensionalized and simplified by making use of potential functions. A combination of Laplace and Fourier transform is used to reduce the problem to ordinary differential equations. The arbitrary constants in solution are obtained by considering the loading environment on surfaces. The physical quantities like stresses, temperature field, mass concentration and chemical potential are determined analytically in the closed-form. A numerical transform inversion technique is used to obtain the resulting quantities for the original region and displayed in the form of graphs to present the different physical effects.

中文翻译：

两种温度、分数阶和温度相关材料特性下的热弹性扩散板建模

在具有温度相关弹性特性的材料中，使用两个温度分数阶理论制定了数学模型来研究板中的热弹性扩散。推导出所考虑的二维问题的控制方程。该板最初被认为是在均匀温度下无应变和无应力的。通过使用势函数，控制方程是无量纲化和简化的。拉普拉斯和傅立叶变换的组合用于将问题简化为常微分方程。溶液中的任意常数是通过考虑表面上的加载环境而获得的。应力、温度场、质量浓度和化学势等物理量以封闭形式分析确定。

更新日期：2021-05-12

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