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Some Linear Effects of Rotation on the Heat Transfer Problem in Rarefied Gases and Rarefied Gas Mixtures

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Abstract

The linearized field equations of extended thermodynamics for rarefied monatomic gases and gas mixtures are used to describe two different stationary processes. The aim of the paper is to study the linear effects predicted for such phenomena. Comparison between classical and extended theory and between the solutions for a single gas and a gas mixture will be also presented.

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Notes

  1. Only in one case, which in this paper is only recalled but not explicitly calculated, it was not possible to determine the explicit solutions.

  2. The exponential integral function is the integral defined as \(\mathrm{Ei} ( x ) =-\int_{-x}^{+\infty }\frac{e^{-t}}{t}\mathrm{d}t\).

  3. We recall that the modified Bessel functions of the first and second kind I n and K n are the solutions y(z) of the differential equation z 2 y′′+zy′−(z 2+n 2)y=0.

  4. The boundary conditions for the temperatures can be used only to integrate system (10)2,4,6,7 and (11)1,3,4,6.

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Acknowledgements

This paper was supported by GNFM-INdAM and by University of Bologna Farb Project 2012 “Termodinamica Estesa dei Processi di Non Equilibrio dalla Macro-alla Nano-Scala”.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Messina, V.le F. D’Alcontres 31, 98166, Messina, Italy

    Elvira Barbera

  2. Department of Mathematics, University of Bologna, via Saragozza 8, 40123, Bologna, Italy

    Francesca Brini

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  1. Elvira Barbera
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  2. Francesca Brini
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Correspondence to Elvira Barbera.

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Barbera, E., Brini, F. Some Linear Effects of Rotation on the Heat Transfer Problem in Rarefied Gases and Rarefied Gas Mixtures. Acta Appl Math 132, 51–62 (2014). https://doi.org/10.1007/s10440-014-9890-3

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  • DOI: https://doi.org/10.1007/s10440-014-9890-3

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