Analysis to Thermoelastic Interactions under a Heat Conduction Model with a Delay Term

The present work is concerned with a heat conduction model an exact heat conduction model with a delay term. A generalized thermoelasticity theory was proposed by Roychoudhuri (2007) based on the heat conduction law with three -phase-lag effects for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. However, the model define ill-posed problem. Hence, Recently, Quintanilla (2011) has proposed to reformulate this constitutive equation as a heat conduction theory with a single deley term and has investigated the spatial behavior of the solutions for this theory. A Phragmen- Lindelof type alternative is obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction to the delay term and Phragmen-Lindelof type alternative is obtained for the forward and backward in time equations. The formulation is then is applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to exponential decrease in temperature and zero stress. The homotopy analysis method is applied to obtain the solution of the problem. . The problem is discussed with different graphs of numerical values of the field variables.