The theory of two-temperature generalized thermoelasticity, based on Youssef's theory, was used to solve boundary value problems of one-dimensional generalized thermoelasticity half-space by heating its boundary with different types of heating. The governing equations are solved using new mathematical methods within the purview of the Lord-Şhulman (L-S) theory and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating-thermal shock type. The separation of variables method is used to get the exact expressions for distributions of displacement, the stresses, and temperature distribution. Variations of the considered functions through the horizontal distance are illustrated graphically. Comparisons are made with results between the two theories. Numerical work is also performed for a suitable material and results are discussed, specifically the conductive temperature, the dynamical temperature, and the stress and strain distributions are shown graphically when discussed.
In this work, the thermal effect of a laser pulse is taken into account when mechanical-thermodiffusion (METD) waves are studied. The nonlocal semiconductor material is used when interference between holes and electrons occurs. The fractional technique is applied on the heat equation according to the photo-thermoelasticity theory. The governing equations describe the photo-excitation processes according to the overlapping between the thermoelasticity and photothermal theories. The thermoelastic deformation (TD) and the electronic deformation (ED) for the dimensionless fields are taken in one dimension (1D). The Laplace transforms are applied to obtain the analytical solutions when some initial and boundary conditions are applied at the nonlocal surface. The complete nondimensional solutions of the main quantities are obtained according to some numerical simulation approximate during the inversion processes of Laplace transforms and Fourier expansion. The time-fractional order, nonlocal, and thermal memories are used to compare the wave propagations of the main fields and are discussed graphically for nonlocal silicon material.
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