Monte Carlo simulation of the Boltzmann equation for steady Fourier flow

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Abstract
The planar Fourier flow for a dilute gas of hard spheres is studied by means of the direct-simulation Monte Carlo method to solve the Boltzmann equation. Two different types of boundary conditions are considered. In the conventional conditions, the gas can be seen as enclosed between two baths at equilibrium at wall temperatures. In the alternative conditions, both baths are out of equilibrium in states close to the one of the actual gas. It is shown that these alternative conditions are more appropriate to analyze bulk transport properties, as they reduce the boundary effects. The deviation of the heat flux from the Fourier law is small, even for large thermal gradients. In addition, the velocity distribution function is obtained and compared with the exact solution of the Bhatnagar-Gross-Krook model.