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Shock-induced molar concentration wave propagation and coupled non-Fick diffusion–elasticity analysis using an analytical method

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Abstract

In this article, an analytical method for dynamic and transient analysis of coupled non-Fick diffusion–elasticity is presented. The governing equations of the problem are transferred to the frequency domain using Laplace transform technique. The unknown parameters are then obtained in the series form using the presented analytical method. By employing the fast Laplace inverse technique, the unknown parameters are determined in time domain. It is concluded that the presented analytical method has a high capability for wave propagation analysis in mass transfer and elastic wave propagation problems. The propagation of wave fronts for displacements and molar concentration are studied in detail. It is shown that both molar concentration and elastic wave are propagated in the domain with finite speeds in the non-Fick theory of diffusion.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

    Seyed Amin Hosseini

  2. Department of Mechanical Engineering, Lean Production Engineering Research Center, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

    Mohammad Hossein Abolbashari

  3. Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

    Seyed Mahmoud Hosseini

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  1. Seyed Amin Hosseini
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  2. Mohammad Hossein Abolbashari
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  3. Seyed Mahmoud Hosseini
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Correspondence to Seyed Mahmoud Hosseini.

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Hosseini, S.A., Abolbashari, M.H. & Hosseini, S.M. Shock-induced molar concentration wave propagation and coupled non-Fick diffusion–elasticity analysis using an analytical method. Acta Mech 225, 3591–3599 (2014). https://doi.org/10.1007/s00707-014-1161-x

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  • DOI: https://doi.org/10.1007/s00707-014-1161-x

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