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Analytical solutions for heat diffusion beyond Fourier law

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  • Zhukovsky, K.V.
  • Srivastava, H.M.

Abstract

We obtain solutions for differential equations, describing a broad range of physical problems by the operational method with recourse to inverse differential operators, integral transforms and operational exponent. Generalized families of orthogonal polynomials and special functions are also employed with recourse to their operational definitions. The evolutional type problems for heat transfer in various heat conduction models are studied. Exact analytical solutions for Guyer–Krumhansl hyperbolic heat equation are obtained and compared with those of Fourier and Cattaneo equations. Modelling heat pulse propagation from a laser source is performed in the framework of Fourier, Cattaneo and Guyer–Krumhansl heat transfer models. Compliance of obtained solutions with the maximum principle is studied.

Suggested Citation

  • Zhukovsky, K.V. & Srivastava, H.M., 2017. "Analytical solutions for heat diffusion beyond Fourier law," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 423-437.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:423-437
    DOI: 10.1016/j.amc.2016.08.038
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    References listed on IDEAS

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    1. Allon I. Hochbaum & Renkun Chen & Raul Diaz Delgado & Wenjie Liang & Erik C. Garnett & Mark Najarian & Arun Majumdar & Peidong Yang, 2008. "Enhanced thermoelectric performance of rough silicon nanowires," Nature, Nature, vol. 451(7175), pages 163-167, January.
    2. Jens Baringhaus & Ming Ruan & Frederik Edler & Antonio Tejeda & Muriel Sicot & Amina Taleb-Ibrahimi & An-Ping Li & Zhigang Jiang & Edward H. Conrad & Claire Berger & Christoph Tegenkamp & Walt A. de H, 2014. "Exceptional ballistic transport in epitaxial graphene nanoribbons," Nature, Nature, vol. 506(7488), pages 349-354, February.
    3. Akram I. Boukai & Yuri Bunimovich & Jamil Tahir-Kheli & Jen-Kan Yu & William A. Goddard III & James R. Heath, 2008. "Silicon nanowires as efficient thermoelectric materials," Nature, Nature, vol. 451(7175), pages 168-171, January.
    4. H. M. Srivastava & K. V. Zhukovsky, 2016. "Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 573-629, Springer.
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