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Fractional-order generalized thermoelastic diffusion theory

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Abstract

The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by a sequence of incomplete differential equations, particularly by a fractional equation, a generalized variational principle is obtained for the unified theory using a semi-inverse method. In numerical implementation, the dynamic response of a semi-infinite medium with one end subjected to a thermal shock and a chemical potential shock is investigated using the Laplace transform. Numerical results, i.e., non-dimensional temperature, chemical potential, and displacement, are presented graphically. The influence of the fractional order parameter on them is evaluated and discussed.

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Authors and Affiliations

  1. School of Civil Engineering, Tianjin University, Tianjin, 300072, China

    Chunbao Xiong & Yanbo Niu

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  1. Chunbao Xiong
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  2. Yanbo Niu
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Correspondence to Yanbo Niu.

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Xiong, C., Niu, Y. Fractional-order generalized thermoelastic diffusion theory. Appl. Math. Mech.-Engl. Ed. 38, 1091–1108 (2017). https://doi.org/10.1007/s10483-017-2230-9

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  • DOI: https://doi.org/10.1007/s10483-017-2230-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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