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Generalized magneto-thermoviscoelasticity in a perfectly conducting thermodiffusive medium with a spherical cavity

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Abstract

In this work, the effects of viscosity and diffusion on thermoelastic interactions in an infinite medium with a spherical cavity are studied. The formulation is applied to the generalized thermoelasticity based on the theory of generalized thermoelastic diffusion with one relaxation time. The surface of the spherical cavity is taken to be traction free and subjected to both heating and external constant magnetic field. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain obtained numerically using a method based on Fourier expansion techniques. The temperature, displacement, stress, concentration as well as the chemical potential are obtained and represented graphically. Comparisons are made within the theory in the presence and absence of viscosity and diffusion.

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Acknowledgements

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. 142/130/1433. The authors acknowledge with thanks DSR technical and financial support.

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Authors and Affiliations

  1. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia.

    ASHRAF M ZENKOUR & EBRAHEEM O ALZAHRANI

  2. Department of Mathematics, Kafrelsheikh University, Kafr El-Sheikh, 33516, Egypt.

    ASHRAF M ZENKOUR

  3. Department of Mathematics, Mansoura University, Mansoura, 35516, Egypt.

    AHMED E ABOUELREGAL

  4. Department of Mathematics, College of Science and Arts, Aljouf University, El-Qurayat, Saudi Arabia.

    AHMED E ABOUELREGAL

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  1. ASHRAF M ZENKOUR
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  2. EBRAHEEM O ALZAHRANI
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  3. AHMED E ABOUELREGAL
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Correspondence to ASHRAF M ZENKOUR.

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ZENKOUR, A.M., ALZAHRANI, E.O. & ABOUELREGAL, A.E. Generalized magneto-thermoviscoelasticity in a perfectly conducting thermodiffusive medium with a spherical cavity. J Earth Syst Sci 124, 1709–1719 (2015). https://doi.org/10.1007/s12040-015-0628-z

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  • DOI: https://doi.org/10.1007/s12040-015-0628-z

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