Generalized Three-Dimensional Heat Source Problem for Small Time

This paper is concerned with the three-dimensional fundamental solutions in the generalized thermoelastic infinite body subjected to a continuous source of heat by using the inverse Laplace transform in an approximate manner for small values of time. It is found that there exist two coupled waves, of which is predominantly elastic wave and the other is predominantly thermal. Exact expressions for discontinuities in the field functions that occur at the wavefronts are computed and analyzed. Numerical results are presented graphically along with a comparison of the three theories due to Lord and Shulman, Green and Lindsay, and the classical coupled thermoelasticity. A discussion concerning which of the three theories is the most physically acceptable is given, and conclusions are stated.

Keywords:

• Generalized Thermoelasticity
• Fundamental Solution
• Laplace Transform
• Discontinuity