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This work gives some results and develops the derivation of memory dependence heat conduction model with dual phase-lags using the modified definition of the fractional derivative of Caputo and higher-order memory-dependent derivative (MDD). The introduced model was derived by improving the heat conduction equation replacing the conventional Fourier's law and generalizing some of the previous models. As an application of the proposed model, we will consider an infinite thermoelastic long annular cylinder whose inner surface is thermally insulated and restricted, while the exterior surface is due to thermal shock and traction free. The numerical results of the physical fields are shown graphically against the position, and the effects of some basic parameters on them are estimated. Theoretical analysis and mathematical results confirm that the selection of an appropriate kernel, time delays and memory response can affect the turbulence in the thermal fields. [ABSTRACT FROM AUTHOR]

The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. The equations of the heat conduction and the mass diffusion have been modified by using Taylor's series of time-fractional order. In this new model, the Fourier and the Fick laws have been modified to include a higher time-fractional order of the heat conduction vector, the gradient of temperature, the diffusing mass flux and the gradient of chemical potential. We adopted the definitions of Caputo and Jumarie; for time-fractional derivatives. The work of Nowacki; Sherief, Hamza, and Saleh; and Aouadi; are deduced as limit cases from the current investigation. Applying this formulation, we have discussed a thermoelastic-diffusion problem for a half-space exposed to thermal and chemical shock with a permeable material in contact with the half-surface. We discussed the sensitivity of the different physical parameters in all studied fields in detail and the results are presented graphically as well as in tabular forms. [ABSTRACT FROM AUTHOR]

Moore-Gibson-Thompson (MGT) is an equation which appropriately describes the spread of sound waves in gasses and fluids as well as thermal/mechanical waves in elastic bodies. The objective of this article is to theoretically analyze the generalized thermoelasticity models that have been presented as the development of the Fourier's law dealing with the paradox of unlimited propagation velocities of thermal waves. For this purpose, a new model is presented which combines the third type of Green and Naghdi model (GN-III) with the generalized theory including the relaxation time based on the MGT equation. The proposed model may be considered as a generalization of previous thermoelastic theories. To examine the introduced approach, the behavior of thermoelastic waves within a homogeneous isotropic sphere in which its surface is exposed to thermal shock with varying heat source is investigated. The variations in different physical fields of a given substance have been computed by means of Laplace transform technique and an efficient numerical technique is implemented in Laplace inversion procedure. The effect of different forms of heat source are also examined and several comparisons for various thermoelasticity approaches are comprehensively conducted. [ABSTRACT FROM AUTHOR]