Transient memory response of a thermoelectric half-space with temperature-dependent thermal conductivity and exponentially graded modulii

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In this work, we consider a problem in the context of thermoelectric materials with memory-dependent derivative for a half space which is assumed to have variable thermal conductivity depending on the temperature. The Lame's modulii of the half space material is taken as a function of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lame's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions. Affectability investigation is performed to explore the thermal impacts of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of tissue temperature. The correlations are made with the results obtained in the case of the absence of memory-dependent derivative parameters.