Effects of Three-Phase-Lag on Two Temperature Generalized Thermoelasticity for an Infinite Medium With a Spherical Cavity

Sukla Banik; M.Kanoria

doi:10.3879/j.issn.1000-0887.2012.04.007

Volume 33 Issue 4

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Sukla Banik, M.Kanoria. Effects of Three-Phase-Lag on Two Temperature Generalized Thermoelasticity for an Infinite Medium With a Spherical Cavity[J]. Applied Mathematics and Mechanics, 2012, 33(4): 460-474. doi: 10.3879/j.issn.1000-0887.2012.04.007

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Effects of Three-Phase-Lag on Two Temperature Generalized Thermoelasticity for an Infinite Medium With a Spherical Cavity

doi: 10.3879/j.issn.1000-0887.2012.04.007

Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India

Received Date: 2010-12-20
Rev Recd Date: 2011-10-15
Publish Date: 2012-04-15

Abstract

Abstract

The thermoelastic interaction for the three-phase-lag heat equation in an isotropic infinite elastic body with a spherical cavity was studied in the context of two temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of three-phase-lag was a hyperbolic partial differential equation with a fourth order derivative with respect to time. The medium was assumed initially quiescent. By using the Laplace transformation, the fundamental equations had been expressed in the form of a vector-matrix differential equation, which was then solved by state space approach. The general solution obtained was applied to a specific problem, when the boundary of the cavity was subjected to thermal loading (thermal shock and ramp type heating) and the mechanical loading. The inversion of the Laplace transform was carried out by the Fourier series expansion techniques. The numerical values of the physical quantity were computed for copper like material. Significant dissimilarities between two models (two temperature Green-Naghdi theory with energy dissipation (2TGNIII) and two temperature three-phase-lag model (2T3phase)) were shown graphically. The effect of two temperature and the ramping parameters were also studied.
- two temperature generalized thermoelasticity,
- Green-Naghdi model,
- three-phase-lag model,
- spherical cavity,
- state-space approach

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References

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