A detailed comparative study on responses of four heat conduction models for an axisymmetric problem of coupled thermoelastic interactions inside a thick plate

The objective of the present work is to analyze the thermoelastic interactions inside an infinitely extended thick plate due to an axisymmetric temperature distribution applied at the lower and upper surfaces of the plate under recent heat conduction models, namely Green-Naghdi-I model, Green-Naghdi-II model, dual phase-lag model and Green-Lindsay model. In order to investigate the problem under all these four heat conduction models simultaneously, we consider the basic governing equations under all these models and formulate our problem in a unified way. The potential function concept along with Laplace and Hankel transform techniques has been used to solve the problem. Inversion of Hankel transform has been carried out analytically to obtain the solution in Laplace transform domain. The short-time approximation technique is employed to invert the solutions obtained in Laplace transform domain and an appropriate analytical approach has been used to analyze the wave propagation and discontinuities of different wave fields. In addition, a numerical method has been used to invert the Laplace transform directly in order to find out the distributions of all the physical fields, like stress, temperature and displacement in the middle plane of the plate. Results are analyzed to make a comparative analysis of the predictions of Green-Naghdi-II model with the predictions by dual phase-lag thermoelastic model and other models. The special findings and differences among the predictions by four models have been highlighted.