Physica A 160 (1989) 395-408 North-Holland, Amsterdam PLANE POISEUILLE FLOW: NEAR CONTINUUM RESULTS FOR A RIGID SPHERE GAS S.K. LOYALKA and K.A. HICKEY Nuclear Engineering Program and Particulate Systems Research Center, University of Missouri-Columbia, Columbia, MO 65211, USA Received 17 January 1989 Revised manuscript received 16 May 1989 In Poiseuille flow between two parallel plates, the bulk flow is characterized by the Burnett distribution. We report explicit a'esuhs for this distribution by solving numerically the relevapt integral equations for a rigid sphere gas in the context of the linearized Boltzmann equation. Then, we use this distribution together with the Chapman-Enskog distribution to obtain asymptotic results (near-continuum) for mass and heat fluxes corresponding to planar thermal transpiration and mechanocaloric effects. I. Introduction It has been recognized for some time [1, 2] that in Poiseuille flow between parallel plates, the bulk (hydrodynamic or generalized hydrodynamic) flow is characterized by the Burnett distribution. Explicit results for this distribution were reported for several model equations and Maxwell molecules in an earlier paper [2], but since the problem of Poiseuille flow is of basic interest, it is important to consider the Boltzmann equation with more realistic intermolecu- lar interactions. The purpose of this paper is to report results for the Burnett distribution for a rigid sphere gas, and then to discuss its use in the calculation of flow rates. We begin with the n_, ........ " ~nu--" .,. _ ..o,. ,.. +hn, ~.~ Doltzmann equation, tl~en reduce the ta~, ~.v tl,at vt solving three linear integral equations. Thc first of these is the Chapman- Enskog equation for viscosity, which in fact was solved earlier by Pekeris and Alterman [3] via conversion to a differential equation of the fourth order. We solve the integral equation directly to the same accuracy as that of Pekeris and Alterman by using finite element analysis with Neumann series [5] and also collocation i6.7]. We then use these techniques to solve the other two integral equations. 0378-4371/89/$03.50 (~ Elsevier Science Publisher~ B.V. (North-Holland Pl:ysics Publishing Division)