Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source. (English) Zbl 1495.80006
Summary: 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 O. N. Shivay and S. Mukhopadhyay [“On the temperature-rate dependent two-temperature thermoelasticity theory”, J. Heat Transfer 142, No. 2, Article ID 4045241, 10 p. (2019; doi:10.1115/1.4045241)]. 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.
MSC:
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 74A15 | Thermodynamics in solid mechanics |
| 74B10 | Linear elasticity with initial stresses |
| 44A10 | Laplace transform |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
temperature-rate-dependent theory; two-temperature thermoelasticity; thermoelastic interactions; line heat sourceReferences:
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