Study of a Half-Space Via a Generalized Dual Phase-lag Model with Variable Thermal Material Properties and Memory-Dependent Derivative

The aim of this work is to investigate a generalized dual phase-lag model with variable thermal material parameters and memory dependent derivatives (VMDPL). In view of this model, the thermoelastic behavior on a half-space under an external body force and subjected to exponentially varying heat is analytically investigated. The governing differential equations are numerically solved using the Laplace transform approach. The effects of the variable thermal material properties and memory dependent derivative on all the physical quantities of a half-space are discussed. The obtained results demonstrate that the physical fields of a half-space depend not only on the distance, but also on the memory time delay and the variable thermal parameter. Furthermore, the variable thermal parameter and the variable thermal parameter has a clear effect on the temperature and the stress but has a negligible effect on the displacement. Finally, the validity of results is acceptable by comparing the displacement, stress and temperature according to the present generalized model (VMDPL) with those due to other thermoelasticity theories