Monte Carlo simulation of a hard-sphere gas in the planar Fourier flow with a gravity field

Abstract

By means of the Direct Simulation Monte Carlo (DSMC) method, the Boltzmann equation is numerically solved for a gas of hard spheres enclosed between two parallel plates kept at different temperatures and subject to the action of a gravity field normal to the plates. The profiles of pressure, density, temperature and heat flux are seen to be quite sensitive to the value of the gravity acceleration g. If the gravity field and the heat flux are parallel (g > 0), the magnitudes of both the temperature gradient and the heat flux are smaller than in the opposite case (g < 0). When considering the actual heat flux relative to the value predicted by the Fourier law, it is seen that, if g > 0, the ratio increases as the reduced local field strength increases, while the opposite happens if g < 0. The simulation results are compared with theoretical predictions for Maxwell molecules.