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Published on: December 27, 2012
Internal energy in compressible Poiseuille flow
Konrad Gizynski1, Karol Makuch1, Jan Paczesny1
1Institute of Physical Chemistry, Polish Academy of Sciences Kasprzaka 44/52, 01-224 Warsaw, Poland.
Abstract:
We analyze a compressible Poiseuille flow of ideal gas in a plane channel. We provide the form of internal energy U for a nonequilibrium stationary state that includes viscous dissipation and pressure work. We demonstrate that U depends strongly on the ratio Δp/p_{0}, where Δp is the pressure difference between inlet and outlet and p_{0} is the outlet's pressure. In addition, U depends on two other variables: the channel aspect ratio and the parameter equivalent to Reynolds number. The stored internal energy, ΔU=U-U_{0}, is small compared to the internal energy U_{0} of the equilibrium state for a moderate range of values of Δp/p_{0}. However, ΔU can become large for big Δp or close to vacuum conditions at the outlet (p_{0}≈0Pa).
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