Heat transfer in a gas between parallel plates: Moment method and molecular dynamics

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Abstract
We present here a comparison between measurements made in numerical experiments and approximate solutions to the Boltzmann equation for a dilute gas in a finite geometry and subjected to a temperature gradient. We first briefly recall a moment method that has been developed to solve the stationary state for the Boltzmann equation with boundary conditions independently of any small gradient expansions and we then apply it to the case of a temperature gradient within the so-called four- and six-moment approximations. These solutions are then compared to the results obtained by nonequilibrium molecular dynamics simulations of a dilute gas enclosed between parallel plates held at different temperatures: Local measurements of the moments of the one-particle distribution function, related to the densities, the temperature, and the fluxes, are reported for various Knudsen numbers and for various temperature gradients.