Mathematical significance of strain rate and temperature rate on heat conduction in thermoelastic material due to line heat source

Abstract

Abstract The primary purpose of the present article is to investigate the effect of strain rate and temperature rate factors on a homogeneous, unbounded isotropic elastic medium originating due to continuous line heat source. This study is based on the modified Green-Lindsay Model (MGL) theory proposed by Yu et al. (2018). This model eliminates the discontinuous nature of the displacement field reported under the temperature-rate-dependent thermoelasticity theory (GL) established by Green and Lindsay. The present work obtains the analytical solution for the distributions of stress components, temperature and displacement through the potential function approach accompanied by the Laplace transform method. The inverse Laplace transformation is performed by using short-time approximation method to find the approximated analytical solution of the problem in space-time domain. A detailed analysis of solution is discussed for MGL model and compared to the results predicted by other existing generalized thermoelastic models. The effect of strain-rate and temperature-rate-terms is acknowledged explicitly in mathematical formulation and other significant effects are notified. However, this new model predicts the infinite speed of disturbance analogous to classical theory.