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A. M. Abd El-Latief 1 and S. E. Khader 2
Academic Editor:J. K. Chen and Academic Editor:X. H. Liu
1, Department of Mathematics, Faculty of Science, University of Alexandria, Egypt
2, Department of Mathematical and Theoretical Physics, Atomic Energy Authority, Egypt
Received 3 November 2013; Accepted 26 November 2013; 4 February 2014
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
In 1967, Lord and Shulman [1] introduced the theory of generalized thermoelasticity with one relaxation time for an isotropic body. This theory corrects the unrealistic conclusions of the older theories (the uncoupled and the coupled theories of thermoelasticity) that heat waves travel with infinite speeds. The Heat conduction law of this theory is the Cattaneo law which is different from Fourier's law utilized in both the coupled and the uncoupled theories. Among the contribution to the subject are the works in [2-6]. In 1972 Green and Lindsay [7] developed the theory of generalized thermoelasticity with two relaxation times, based on a generalized inequality of thermodynamics. In this theory both the equations of motion and of heat conduction are hyperbolic. The heat conduction law is the same as Fourier's law when the system has a centre of symmetry. Among the contributions to this theory are the works in [8, 9].
Green and Naghdi [10-12] have formulated three new models of thermoelasticity. In one of these models Green and Naghdi [12] predict that the internal rate of production of entropy is identically zero; that is, there is no dissipation of thermal energy. This theory (GN theory) is known as thermoelasticity without energy dissipation theory. In the development of this theory the thermal displacement gradient is considered as a constitutive variable, whereas in the conventional development of a thermoelasticity theory, the temperature gradient is taken as a constitutive variable [12]. A couple of uniqueness theorems have been proved in [13, 14], and one-dimensional waves in a half-space and in an unbounded body have been studied in [15, 16]. In view of some experimental evidence available in favour of finiteness of heat propagation speed, generalized thermoelasticity theories are...