A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model

Author(s)
Ahmed E. Abouelregal

Abstract

The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.

The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.

Keywords

Generalized Thermoelasticity, Dual-Phase-Lag Model, Semi-Infinite Medium, Laplace Transform

Generalized Thermoelasticity, Dual-Phase-Lag Model, Semi-Infinite Medium, Laplace Transform

Cite this paper

nullA. Abouelregal, "A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model,"*Applied Mathematics*, Vol. 2 No. 5, 2011, pp. 619-624. doi: 10.4236/am.2011.25082.

nullA. Abouelregal, "A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model,"

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