Kinetic theory based numerical scheme such as direct simulation Monte Carlo (DSMC) and information preservation (IP) schemes properly solve micro-nano flow problems in transition and free molecular regimes. However, the high computational cost of these methods encourages the researchers toward extending the applicability of the continuumbased equations beyond the slip flow regime. In addition to correct velocity profile, the continuum-based equations should predict accurate mass flow rate magnitude. The secondorder velocity slip models derived from the kinetic theory provide accurate velocity profiles up to Kn=0.5; however, they yield erroneous mass flow rate magnitudes because the basic Navier-Stokes equations are invalid for transition regime calculation. To remedy this shortcoming, the rarefaction effects must be considered on dynamic viscosity, i.e., μ=μ(Kn), in order to achieve correct mass flow rate magnitude despite using the kinetic-based slip model. Using shear stress distribution of IP simulations, we develop an analytical formula for dynamic viscosity for the early transition regime and use it to modify the continuumbased equations to improve more accurate mass flowrate magnitudes. Before using the IP results, we compare the accuracy of IP solution with the standard DSMC, the linearized Boltzmann and the continuum-based analytical solutions. Using the viscosity coefficient obtained from IP, the analytical expression for the mass flow rate is derived. We show that it provide accurate solutions for mass flow rate for the region of 0.1<Kn<0.5.

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