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Infinite speed behavior of two-temperature Green–Lindsay thermoelasticity theory under temperature-dependent thermal conductivity

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Abstract

The present work attempts to analyze the effects of temperature-dependent thermal conductivity on thermoelastic interactions in a medium with a spherical cavity under two-temperature Green–Lindsay thermoelasticity theory. An attempt is made to compare the results with the corresponding results under other three thermoelastic models. The thermal conductivity of the material is assumed to be depending affinely on the conductive temperature. It is assumed that the conductive temperature is prescribed at the stress-free boundary of the spherical cavity. Assuming spherical symmetry motion, the resulting thermoelastic system in one space dimension is solved by using the Kirchhoff transformation, Laplace transform technique and expansion in modified Bessel functions. The paper concludes with numerical results on the solution of the problem for specific parameter choices. Various graphs depict the behavior of the conductive and thermodynamic temperature, the displacement and two nonzero components of stress. A detailed analysis of the results is given by showing the effects of the assumed temperature dependence of the material property. The effect of employing the two-temperature model is discussed in detail. We observe an infinite domain of influence under the two-temperature model as compared to the classical Green–Lindsay model, which we hope will be a useful insight.

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Acknowledgements

The authors thankfully acknowledge the valuable comments and suggestions of reviewers, which have helped to improve the quality of the paper. One of the authors (Om Namha Shivay) thankfully acknowledges the full financial assistance as SRF fellowship (File. No. 21/06/2015-EU–V) under University Grant Commission (UGC) (Grant No. 433492), India, to carry out this work.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Anil Kumar, Om Namha Shivay & Santwana Mukhopadhyay

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  1. Anil Kumar
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  2. Om Namha Shivay
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  3. Santwana Mukhopadhyay
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Correspondence to Om Namha Shivay.

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Kumar, A., Shivay, O.N. & Mukhopadhyay, S. Infinite speed behavior of two-temperature Green–Lindsay thermoelasticity theory under temperature-dependent thermal conductivity. Z. Angew. Math. Phys. 70, 26 (2019). https://doi.org/10.1007/s00033-018-1064-0

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  • DOI: https://doi.org/10.1007/s00033-018-1064-0

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