Aaron Morris

Despite its general application, the Fourier's law of heat conduction is not always valid in dilute gases. One of the physical shortcomings of Fourier's law is the mismatch at the boundary; the temperature gradient in the Knudsen layer diverges in the boundary, but the heat flux does not. In this paper, we propose a more generalized constitutive relation for the heat flux to match the heat flux with the hydrodynamics in a rarefied granular gas. The proposed modified heat flux relation is then used to derive analytical solutions for the hydrodynamics of a granular gas bounded by equal and unequal temperature walls. The analytical solutions are then compared to direct simulation Monte Carlo simulations.