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Fractional order thermoelastic interactions in an infinite porous material due to distributed time-dependent heat sources

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Abstract

In the present work, a fractional order Lord & Shulman model of generalized thermoelasticity with voids subjected to a continuous heat sources in a plane area has been established using the Caputo fractional derivative and applied to solve a problem of determining the distributions of the temperature field, the change in volume fraction field, the deformation and the stress field in an infinite elastic medium. The Laplace transform together with an eigenvalue approach technique is applied to find a closed form solution in the Laplace transform domain. The numerical inversions of the physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of Laplace transform. Numerical results are shown graphically and the results obtained are analyzed .

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Acknowledgments

We are grateful to Prof. (Dr.) S. C. Bhattacharya of the Department of Chemistry, Jadavpur University, Kolkata-700032, India for his kind help and guidance in writing the application of one-dimensional void material. We also express our sincere thanks to the reviewer for his valuable suggestions for the improvement of the quality of our paper.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700 032, India

    M. Bachher & A. Lahiri

  2. Department of Mathematics, Gobardanga Hindu College, 24 Pgs (N), Gobardanga, 743 273, West Bengal, India

    N. Sarkar

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  1. M. Bachher
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  2. N. Sarkar
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  3. A. Lahiri
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Correspondence to N. Sarkar.

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Bachher, M., Sarkar, N. & Lahiri, A. Fractional order thermoelastic interactions in an infinite porous material due to distributed time-dependent heat sources. Meccanica 50, 2167–2178 (2015). https://doi.org/10.1007/s11012-015-0152-x

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