A Homotopy Analysis Approach to a Thermoelastic Interactions under the Boundary Condition: Heat Source Varying Exponentially with Time and Zero Stress

In this work, we consider a one-dimensional problem for a half-space in the context of the L-S theory of generalized thermo elasticity with one relaxation time parameter. The surface of the half-space is assumed to be traction free and subjected to the effects of a heat source varying exponentially with time at the boundary. The main objective of this present paper is to study the above problem based on the LS theory with the help of Homotopy analysis method proposed by S. J. Liao (1992). See the Appendix for details. The inversion of the Laplace transform solutions are carried out numerically using Bellman method (Bellman et al. , 1966) and the obtained results are presented graphically. The effects of the heat source varying with time and zero traction force are studied on temperature, stress and displacement. Also we see the numerical result with the help of graph.