Relaxation effects on thermoelastic interactions for time-dependent moving heat source under a recent model of thermoelasticity


In the present article, we investigate the thermal and elastic behaviour of an infinite thermoelastic material with a cylindrical cavity caused by a time-dependent moving heat source. The cavity surface is assumed to be subjected to a thermal shock. The formulation of the problem is applied for the recently proposed generalized thermoelastic model [Modified Green–Lindsay (MGL)] that takes into account the strain and temperature rates in the constitutive relations. We derive the governing equations in the present context along with the other two models, namely Lord–Shulman model and Green–Lindsay, by unifying governing equations under all these three models. The solutions are obtained for all three models in the Laplace transform domain, which are represented by unified expressions. The numerical computations for temperature, displacement and thermal stresses are carried out and depicted graphically. A detailed comparison is made amongst the results predicted by three models to highlight the effects of velocity of heat source and strain, temperature rate terms involved in the MGL model.

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Correspondence to Robin Vikram Singh.

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Singh, R.V., Mukhopadhyay, S. Relaxation effects on thermoelastic interactions for time-dependent moving heat source under a recent model of thermoelasticity. Z. Angew. Math. Phys. 72, 31 (2021).

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  • Generalized thermoelasticity theory
  • TRDTE theory
  • Modified Green–Lindsay theory
  • Thermal shock
  • Moving heat source problem

Mathematics Subject Classification

  • 74F05