Application of Third-Order Constitutive Relations to Poiseuille Flow of a Rarefied Gas

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Abstract
The third-order constitutive relation for the shear stress tensor is applied to Poiseuille flow of rarefied monatomic gases in three geometries: parallel plates, cylindrical tube, and cylindrical annulus. The expressions for subsonic flow rates and velocity profiles in the transition regime are derived on the basis of reasonable boundary conditions for the three geometries. The flow rate shows a minimum as a function of the Kundsen number. One numerical constant which fixes this curve could not be determined theoretically, but experimental data and other independent theories indicate that this constant has the same value for the three geometries.