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Fractional Thermoelasticity

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Encyclopedia of Thermal Stresses

Overview

The conventional thermoelasticity is based on the principles of the classical theory of heat conductivity, specifically on the classical Fourier law, which relates the heat flux vector to the temperature gradient. In combination with the balance equation, the Fourier law leads to the parabolic heat conduction equation. Nonclassical theories, in which the Fourier law and the standard heat conduction equations are replaced by more general equations, constantly attract the attention of the researchers.

It should be noted that the Fourier law is a phenomenological law which states the proportionality of the flux to the gradient of the transported quantity. It is met in several physical contexts with different names, e.g., the Fick law in the theory of diffusion and the Darcy law in the theory of fluid flow through a porous medium.

The time- and space-nonlocal dependences between the heat flux vector and the temperature gradient with power kernels can be interpreted in terms of...

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Długosz University, al. Armii Krajowej 13/15, 42-200, Częstochowa, Poland

    Yuriy Povstenko

  2. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    Yuriy Povstenko

Authors
  1. Yuriy Povstenko
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Correspondence to Yuriy Povstenko .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY, USA

    Richard B. Hetnarski

  2. Naples, FL, USA

    Richard B. Hetnarski

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Povstenko, Y. (2014). Fractional Thermoelasticity. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_612

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