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Influence of the Prandtl and Knudsen numbers on heat-transfer process in the problem of planar Poiseuille flow

Influence of the Prandtl and Knudsen numbers on heat-transfer process in the problem of planar... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thermophysics and Aeromechanics Springer Journals

Influence of the Prandtl and Knudsen numbers on heat-transfer process in the problem of planar Poiseuille flow

Thermophysics and Aeromechanics , Volume 19 (2): 8 – Jun 1, 2012

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Publisher
Springer Journals
Copyright
2012 Pleiades Publishing, Ltd.
ISSN
0869-8643
eISSN
1531-8699
DOI
10.1134/S0869864312020035
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Thermophysics and AeromechanicsSpringer Journals

Published: Jun 1, 2012

References