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Shock Structure and Temperature Overshoot in Macroscopic Multi-temperature Model of Binary Mixtures

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From Particle Systems to Partial Differential Equations II

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 129))

Abstract

The present study deals with the shock wave profiles in the macroscopic multi-temperature model of binary gaseous mixtures. For that purpose we adopt the hyperbolic model developed within the framework of extended thermodynamics. It is assumed that the mass difference between the constituents has the most prominent influence on the shock structure. Simplicity of the model enables systematic analysis of the results, using a large set of values for parameters, with special regard to the temperature overshoot (TO) of the heavier constituent. We found that TO varies non-monotonically with mass ratio of the constituents. In the context of the previous research, the influence of the different types of dissipation on the shock structure is considered by extending the original hyperbolic system with diffusion terms. It has been observed that TO continued to exist even in the presence of additional dissipative mechanisms.

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Acknowledgments

This work was supported by the Ministry of Education and Science, Republic of Serbia, through the project Mechanics of nonlinear and dissipative systems—contemporary models, analysis and applications, Project No. ON174016.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića, Novi Sad, Serbia

    Damir Madjarević

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  1. Damir Madjarević
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Correspondence to Damir Madjarević .

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Editors and Affiliations

  1. Centre of Mathematics, University of Minho, Braga, Portugal

    Patrícia Gonçalves

  2. Centre of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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Madjarević, D. (2015). Shock Structure and Temperature Overshoot in Macroscopic Multi-temperature Model of Binary Mixtures. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations II. Springer Proceedings in Mathematics & Statistics, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-319-16637-7_9

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