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# On the Application of the Adomian’s Decomposition Method to a Generalized Thermoelastic Infinite Medium with a Spherical Cavity in the Framework Three Different Models

Najat A. Alghamdi1, Hamdy M. Youssef2,3,*

1 Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia.
2 Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt.
3 Mathematics Department, Faculty of Engineering, Umm Al-Qura University, Makkah, Saudi Arabia.

* Corresponding Author: Hamdy M. Youssef. Email: .

Fluid Dynamics & Materials Processing 2019, 15(5), 597-611. https://doi.org/10.32604/fdmp.2019.05131

## Abstract

A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity. A generalized set of governing equations is formulated in the context of three different models of thermoelasticity: the Biot model, also known as “coupled thermoelasticity” model; the Lord-Shulman model, also referred to as “generalized thermoelasticity with one-relaxation time” approach; and the Green-Lindsay model, also called “generalized thermoelasticity with two-relaxation times” approach. The Adomian’s decomposition method is used to solve the related mathematical problem. The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain. Numerical results for the temperature, radial stress, strain, and displacement are represented graphically. It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields

## Keywords

Alghamdi, N. A., Youssef, H. M. (2019). On the Application of the Adomian’s Decomposition Method to a Generalized Thermoelastic Infinite Medium with a Spherical Cavity in the Framework Three Different Models. FDMP-Fluid Dynamics & Materials Processing, 15(5), 597–611.

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