An investigation on thermoelastic interactions under an exact heat conduction model with a delay term

Abstract

ABSTRACTThe present work is concerned with a very recently proposed heat conduction model: an exact heat conduction model with a single delay term. A generalized thermoelasticity theory was proposed by Roy Choudhuri based on the heat conduction law with three-phase-lag effects for the purpose of considering the delayed response in time due to the microstructural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in Hadamard sense. Quintanilla has recently proposed to reformulate this heat conduction model as an alternative heat conduction theory with a single delay term and subsequently, Leseduarte and Quintanilla investigated the spatial behavior of the solutions for this theory and they extended the results to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction with one delay term. In the present work, we consider the thermoelasticity theory based on this newly proposed heat conduction model and investigate a problem of thermoelastic interactions. State-space approach is used to formulate the problem and the formulation is then applied to a problem of an isotropic elastic half-space with its plane boundary subjected to sudden increase in temperature and zero stress. The integral transform method is applied to obtain the solution of the problem. A detailed analysis of analytical results is provided by finding the short-time approximated solutions of different field variables analytically and comparing the results of the present model with the corresponding results reported for other existing theories. An attempt has also been made to illustrate the problem and numerical values of field variables are obtained for a particular material. Results are analyzed with different graphs. To the best of the author\ extquoteright s knowledge, this thermoelastic model is not yet investigated by any researcher in this direction.