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Hydrodynamics of Inelastic Maxwell Models

Published online by Cambridge University Press:  18 July 2011

V. Garzó  and
A. Santos
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Abstract

An overview of recent results pertaining to the hydrodynamic description (both Newtonianand non-Newtonian) of granular gases described by the Boltzmann equation for inelasticMaxwell models is presented. The use of this mathematical model allows us to get exactresults for different problems. First, the Navier–Stokes constitutive equations withexplicit expressions for the corresponding transport coefficients are derived by applyingthe Chapman–Enskog method to inelastic gases. Second, the non-Newtonian rheologicalproperties in the uniform shear flow (USF) are obtained in the steady state as well as inthe transient unsteady regime. Next, an exact solution for a special class of Couetteflows characterized by a uniform heat flux is worked out. This solution shares the samerheological properties as the USF and, additionally, two generalized transportcoefficients associated with the heat flux vector can be identified. Finally, the problemof small spatial perturbations of the USF is analyzed with a Chapman–Enskog-like methodand generalized (tensorial) transport coefficients are obtained.

Keywords

kinetic theoryBoltzmann equationgranular gasesinelastic Maxwell modelstransport coefficientshydrodynamics

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Type
Research Article
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Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 37 - 76
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© EDP Sciences, 2011

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