Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source

Abstract

Thermoelastic interactions in a linear, isotropic and homogeneous unbounded solid resulting from a continuous line heat source are investigated utilizing modified temperature-rate-dependent two-temperature thermoelasticity theory (MTRDTT, recently proposed by Shivay and Mukhopadhyay in J Heat Transf 142:4045241, 2019). By incorporating the temperature-rate terms of thermodynamic temperature and conductive temperature, the two-temperature relation is modified in this theory. The problem is studied with the unified version of two-temperature relation to compare the results for displacement, temperatures and stresses in the MTRDTT model with the corresponding results of the two-temperature Green-Lindsay (TTGL) model. To solve the problem, Laplace and Hankel transforms are employed. Explicit expressions for these field variables are obtained for the short-time approximation case. Further, the computational tool is used to graphically depict the analytical findings and compare the results obtained from both models. Some important observations about these models are highlighted. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.