Thirdhyphen;Order Constitutive Equations and Transport in Rarefied Gases

摘要

A description of transport of either heat, momentum, or mass in the transition regime is based upon thirdhyphen;order constitutive equations for the fluxes. The onehyphen;dimensional steadyhyphen;state equation which governs the dependent variableP*(either dimensionless temperature, velocity, or concentration) as a function of distancex*is the linearized fourthhyphen;order differential equationN2lpar;d4P*sol;dx*4rpar; plus; lpar;d2P*sol;dx*2rpar;equals;0,whereNis proportional to the Knudsen number. A solution is proposed based on reasonable boundary conditions for parallel plate geometry. Expressions are derived for the profile ofP*, the slip or jump ofP*at a wall, the effective transport coefficient, and the flux. The expressions have the proper limits for the continuum and free molecule regimes, and compare well with other theories for the transition regime and with subsonic experimental data.