2009
DOI: 10.1140/epjst/e2010-01199-9
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An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

Abstract: In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution α, so that the only free parameter… Show more

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Cited by 8 publications
(17 citation statements)
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“…Thus, the reliability of IMM as a prototype model for granular flows can be considered more robust in driven states than in the case of undriven states. This conclusion agrees with the results derived in the case of the simple shear flow problem [26] and more complex shear-induced laminar flows [40]. In this context, the search for exact solutions for driven IMM, and comparison with computer simulations or experiments, can be considered as an interesting problem in the near future.…”
Section: Discussionsupporting
confidence: 88%
“…Thus, the reliability of IMM as a prototype model for granular flows can be considered more robust in driven states than in the case of undriven states. This conclusion agrees with the results derived in the case of the simple shear flow problem [26] and more complex shear-induced laminar flows [40]. In this context, the search for exact solutions for driven IMM, and comparison with computer simulations or experiments, can be considered as an interesting problem in the near future.…”
Section: Discussionsupporting
confidence: 88%
“…This class of Couette flows has been observed in computer simulations of IHS and studied theoretically by means of Grad's approximate method and a simple kinetic model [81,82]. Interestingly, an exact solution of the Boltzmann equation for IMM supports this class of Couette flows with uniform heat flux [75].…”
Section: Couette Flow With Uniform Heat Flux Ltu Flowmentioning
confidence: 73%
“…As will be seen, the consistency of the profiles (6.5) is possible only if a takes a certain particular value for each coefficient of restitution α. In contrast, the reduced thermal gradient ǫ will remain free and so independent of α [75]. From Eqs.…”
Section: Couette Flow With Uniform Heat Flux Ltu Flowmentioning
confidence: 93%
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“…First, they have shown a good agreement with computer simulations in previous works on Couette granular gas flows in the particular case ∂ y (T 1/2 ∂ y T ) < 0 (Tij et al 2001). In addition, there exists a special class of flows, including both elastic and inelastic flows Santos et al 2009;Vega Reyes et al 2010, 2011a, characterized by ∂ y (T 1/2 ∂ y T ) = 0. This special class defines a surface in the three-parameter space conformed by inelasticity (represented by the coefficient of normal restitution α), reduced shear rate and thermal gradient, as shown in figure 2.…”
Section: Introductionmentioning
confidence: 99%