Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity |
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Authors: | S Banik M Kanoria |
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Institution: | (Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India) |
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Abstract: | The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical
cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory
of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed
to be initially quiescent. By the Laplace transformation, the fundamental equations are expressed in the form of a vector-matrix
differential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem,
when the boundary of the cavity is subjected to the thermal loading (the thermal shock and the ramp-type heating) and the
mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion techniques. The
numerical values of the physical quantity are computed for the copper like material. Significant dissimilarities between two
models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase))
are shown graphically. The effects of two-temperature and ramping parameters are also studied. |
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Keywords: | two-temperature generalized thermoelasticity Green-Naghdi model threephase-lag model spherical cavity state-space approach |
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