Heat flux vector in highly inhomogeneous nonequilibrium fluids

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Abstract
We develop a simple, efficient, and general statistical mechanical technique, based upon the previously developed method of planes (MOP) technique of calculating the pressure tensor, in order to calculate the heat flux vector of an atomic fluid. The method is applied to the case of Poiseuille flow through a narrow channel and is compared to the corresponding Irving-Kirkwood heat flux vector, using the first approximation (IK1). Our exact MOP method is shown to be more efficient than the approximate IK1 approach. Additionally, for the special case of planar Poiseuille flow, we derive an alternative mesoscopic expression by integrating the energy continuity equation. This mesoscopic calculation is shown to be extremely efficient and is in excellent numerical agreement with the MOP.