Thermoelastic Memory-dependent Responses to an Infinite Medium ‎with a Cylindrical Hole and Temperature-dependent Properties

Document Type : Research Paper


1 Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia

2 Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt


The present research discusses a generalized thermoelastic model with variable thermal material properties and derivatives based on memory. Based on this new model, an infinitely long homogeneous, isotropic elastic body with a cylindrical hole is analyzed for thermal behavior analysis. The governing equations are deduced by the application of the principle of memory-dependent derivatives and the generalized law on heat conduction. In a numerical form, the governing differential equations are solved utilizing the Laplace transform technique. Numerical calculations are shown in graphs to explain the effects of the thermal variable material properties and memory dependent derivatives. In addition, the response of the cylindrical hole is studied through the effects of many parameters such as time delay, the kernel function and boundary conditions. The results obtained with those from previous literature are finally verified.


Main Subjects

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