Abstract In this work a spherical thermoelastic region problem with a permeating substance in contact of the bounding plane is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the use of potential functions. The resulting formulation is used to solve problem of a solid sphere. The surface is taken to be traction free, subjected to a given axisymmetric temperature distribution and the chemical potential also assumed to be a known function of time. The inversion of the Laplace transform is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, concentration, stress distributions as well as the chemical potential in the physical domain. Numerical results are represented graphically and discussed.

中文翻译：

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广义热弹性扩散理论背景下的二维球面问题

摘要 在这项工作中，在具有一个弛豫时间的广义热弹性扩散理论的背景下，考虑了渗透物质与边界平面接触的球形热弹性区域问题。通解是在拉普拉斯变换域中通过使用直接方法而不使用势函数来获得的。所得公式用于解决实心球体问题。表面被认为是无牵引的，受到给定的轴对称温度分布，化学势也被假定为时间的已知函数。拉普拉斯变换的反演是使用变换的反演公式和傅立叶展开技术来进行的。数值方法用于加速所得序列的收敛以获得温度，位移、浓度、应力分布以及物理域中的化学势。数值结果以图形方式表示和讨论。