Class of dilute granular Couette flows with uniform heat flux

TL;DR

This paper characterizes a special class of steady dilute granular Couette flows with uniform heat flux, where viscous heating balances inelastic cooling, supported by theoretical and computational analyses showing good agreement.

Contribution

It extends the understanding of the LTu class of flows by providing theoretical and simulation evidence for their properties and behavior under various conditions.

Findings

Good agreement between theory and simulations for rheological properties.

Theoretical methods accurately predict heat flux coefficients.

LTu flows include Fourier and simple shear flows as special cases.

Abstract

In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad's moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad's method, the agreement being only qualitative in the case of the kinetic model.