The thermal and mechanical properties of materials show differences depending on the temperature change, which necessitates consideration of the dependence of the properties of these materials on this change in the analysis of thermal stress and deformation of the material. As a result, in the present work, a mathematical framework for thermal conductivity was formulated to describe the behavior of non-simple elastic materials whose properties depend on temperature changes. This derived model includes generalized fractional differential operators with non-singular kernels and two-stage delay operators. The fractional derivative operators under consideration include both the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative, in addition to the traditional fractional operator. Not only that, but the system of governing equations includes the concept of two temperatures. Based on the proposed model, the thermodynamic response of an unlimited, constrained thermoelastic medium subjected to laser pulses was considered. It was taken into account that the thermal elastic properties of the medium, such as the conductivity coefficient and specific heat, depend on the temperature. The governing equations of the problem were formulated and then solved using the Laplace transform method, followed by the numerical inverse. By presenting the numerical results in graphical form, a detailed analysis and discussion of the effects of fractional factors and the dependence of properties on temperature are presented. The results indicate that the fractional order coefficient, discrepancy index, and temperature-dependent properties significantly affect the behavior fluctuations of all physical domains under consideration.
Citation: Ibrahim-Elkhalil Ahmed, Ahmed E. Abouelregal, Doaa Atta, Meshari Alesemi. A fractional dual-phase-lag thermoelastic model for a solid half-space with changing thermophysical properties involving two-temperature and non-singular kernels[J]. AIMS Mathematics, 2024, 9(3): 6964-6992. doi: 10.3934/math.2024340
The thermal and mechanical properties of materials show differences depending on the temperature change, which necessitates consideration of the dependence of the properties of these materials on this change in the analysis of thermal stress and deformation of the material. As a result, in the present work, a mathematical framework for thermal conductivity was formulated to describe the behavior of non-simple elastic materials whose properties depend on temperature changes. This derived model includes generalized fractional differential operators with non-singular kernels and two-stage delay operators. The fractional derivative operators under consideration include both the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative, in addition to the traditional fractional operator. Not only that, but the system of governing equations includes the concept of two temperatures. Based on the proposed model, the thermodynamic response of an unlimited, constrained thermoelastic medium subjected to laser pulses was considered. It was taken into account that the thermal elastic properties of the medium, such as the conductivity coefficient and specific heat, depend on the temperature. The governing equations of the problem were formulated and then solved using the Laplace transform method, followed by the numerical inverse. By presenting the numerical results in graphical form, a detailed analysis and discussion of the effects of fractional factors and the dependence of properties on temperature are presented. The results indicate that the fractional order coefficient, discrepancy index, and temperature-dependent properties significantly affect the behavior fluctuations of all physical domains under consideration.
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Ibrahim-Elkhalil Ahmed, Ahmed E. Abouelregal, Doaa Atta, Meshari Alesemi. A fractional dual-phase-lag thermoelastic model for a solid half-space with changing thermophysical properties involving two-temperature and non-singular kernels[J]. AIMS Mathematics, 2024, 9(3): 6964-6992. doi: 10.3934/math.2024340
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