Essam Awwad - Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia
Ahmed Abouelregal - Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia
Amr Hassan - Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia

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.

Thermoelasticity, Phase-lags, variable thermal material properties, cylindrical hole, Memory dependent ‎derivative‎