Bird's direct simulation Monte Carlo method is used to compute the molecular velocity distribution of a gas with heat flow. At continuum nonequilibrium conditions (small heat flux), Chapman-Enskog behavior is obtained for inverse-power-law molecules (hard-sphere through Maxwell): the Sonine-polynomial coefficients away from walls (i.e., the normal solution) agree with theory. At noncontinuum nonequilibrium conditions (large heat flux), these coefficients differ systematically from their continuum values as the local Knudsen number (nondimensional heat flux) is increased.
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Gallis et al. (2004) studied this question.
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