Third-Order Constitutive Equations and Transport in Rarefied Gases

Publisher Website
Google Scholar
Abstract
A description of transport of either heat, momentum, or mass in the transition regime is based upon third-order constitutive equations for the fluxes. The one-dimensional steady-state equation which governs the dependent variable P* (either dimensionless temperature, velocity, or concentration) as a function of distance x* is the linearized fourth-order differential equationN2(d4P*/dx*4) + (d2P*/dx*2)=0,where N is proportional to the Knudsen number. A solution is proposed based on reasonable boundary conditions for parallel plate geometry. Expressions are derived for the profile of P*, the slip or jump of P* 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.