**Fourier states in a low density
granular gas**

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Vega
Reyes, F^{1}

^{1 }Departamento de Física,
Universidad de Extremadura, Spain

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We describe in detail in this work the properties of the Fourier steady state in a low density granular gas. The system consists of a granular gas enclosed by two infinite parallel thermal walls. Our work is based on the theoretical classification of steady base states described in a recent work [F. Vega Reyes and J. S. Urbach, J. Fluid Mech., in press (2009)]. We show by means of computer simulations that, as we increase wall temperature difference, the temperature profiles transition from positive to negative curvature, passing through an intermediate state with linear temperature profile. We show these transitions occur in the same way for both low (Navier-Stokes regime) and moderate Knudsen number (non-linear regime). We show that the departure from Navier-Stokes hydrodynamics may be characterized with a critical parameter A_th, which we define ad hoc, that is a function of the degree of inelasticity, in strong analogy with the critical shear rate for uniform shear flow in Couette granular flows. The new critical parameter marks the point where the linear temperature occurs, which, as we show, is the point where the reduced time/length scales defined by wall temperature difference and inelasticity are balanced.