Influence of the Prandtl and Knudsen numbers on heat-transfer process in the problem of planar Poiseuille flow
V.N. Popov, D.A. Rudny
Northern (Arctic) Federal University
popov.vasily@pomorsu.ru
Keywords: Boltzmann equation, model kinetic equations, models of boundary conditions, gas flow in planar channel, Prandtl number, Knudsen number
Pages: 193-200
Abstract
The analytic solution (in the form of the Neumann series) has been derived for the problem of computing the heat flux in a planar channel in the presence of a pressure gradient parallel with the walls (in the problem of planar Poiseuille flow) within the framework of the kinetic approach for arbitrary values of the Prandtl number. The ellipsoidal-statistical model of the Boltzmann kinetic equation is used as the governing equation, and the model of diffuse reflection is used as the boundary condition. The conducted numerical analysis of final expressions obtained in the present work showed a substantial dependence of the heat flux on the value of the Prandtl number of gas for channels whose thickness is comparable with the mean free path of gas molecules.
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