Abstract
The present article deals with the thermal shock response in an isotropic thermoelastic medium with a moving heat source. In this context Green and Naghdi type III model of generalized thermoelasticity theory is considered. The basic equations are expressed as vector-matrix differential equation form. The considered formulation is applied to a semi-infinite solid space. The analytical formulations of the problem in the Laplace transform domain have been solved by eigenvalue approach technique. The inversion of Laplace transform is completed by Zakian method. The variation of the temperature, displacement and stress distributions for different values of time and heat source velocity are shown graphically for two different cases. In the first case, a thermal shock free surface is considered subjected to traction and in the second case the surface is under the influence of time dependent thermal shock. Finally, some comparisons of the results for different time and moving heat source velocity are presented. In presence of moving heat source all the thermophysical quantities have a great significant effect in all the distributions.
Highlights
The topic generalized thermoelasticity has increased more consideration of several researchers during last four decades due to its applications in so many fields of applied sciences and mathematics viz. earthquake engineering, nuclear reactor's design, soil dynamics, high energy particle accelerators, etc
The parabolic type heat equation is replaced by hyperbolic type heat equation supported by examinations which display the real existence of wave type heat transportation in solids, known as the second sound effect
Special cases: If we take K = 0 the problem will be reduced to Green-Naghdi II theory (GN-II)
Summary
The topic generalized thermoelasticity has increased more consideration of several researchers during last four decades due to its applications in so many fields of applied sciences and mathematics viz. earthquake engineering, nuclear reactor's design, soil dynamics, high energy particle accelerators, etc. The first generalization of the classical theory of thermoelasticity, determined by Lord and Shulman [4], included one relaxation time parameter in Fourier’s law of heat conduction equation It involved a heat transfer equation of hyperbolic nature declaring finite speed of thermal signals. Several authors including Gutfield and Netherchot [20], Taylor et al [21] conducted experiments with various solid bodies and showed that heat pulses do not propagate at infinite speed He and Cao [22] considered generalized magneto thermoelastic problem subjected to moving heat source. Lahiri et al [36] used matrix method of solution of coupled differential equation and showed its applications in generalized thermoelasticity In this present article, a problem of generalized thermoelasticity subjected to a moving heat source distributed over a plane area in an unbounded isotropic medium is considered. Source for copper material are derived numerically and presented graphically for two different cases
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