An investigation on coupled thermoelastic interactions in a thick plate due to axi-symmetric temperature distribution under an exact heat conduction with a delay

Abstract

Present work is concerned with a recently proposed heat conduction model: an exact heat conduction model with a single delay term. The main purpose of this paper is to examine the effects of the single phase-lag parameter/delay term on wave propagation in an infinitely extended thick plate due to axisymmetric temperature distribution applied in the lower and upper surfaces of the plate. The problem is formulated by using the new heat conduction model in such a way that other existing models can be extracted as special cases. Potential function concept including the Laplace and Hankel Transform method is used to find the solution in the transformed domain. Inversion of Hankel Transform is done analytically to obtain the solution in Laplace transform domain. By using a suitable analytical approach, the complete analysis on the wave propagation and discontinuities of different wave fields are found out. Furthermore, a numerical method for the Laplace inversion is applied to obtain the distributions of different physical fields like, temperature, displacement and stresses in the middle plane of the plate. Analysis of the results obtained under new model along with a comparison of the respective results obtained in other models is presented in detailed way. The findings in the present work are believed to bring out some lights concerning the new heat conduction model that involves a single delay parameter.