The main goal of the current study is to extend the range of application of the Navier Stokes equations beyond the slip-flow regime by using information preservation (IP) method. In addition to a correct velocity profile, the continuum-based equations should predict accurate mass flow rate and axial pressure distribution. The second-order slip velocity model based on the kinetic theory provides accurate velocity profiles while it gives erroneous mass flow rate. In this study, we use shear stress distribution obtained from an extended IP code to develop analytical formula for dynamic viscosity in the midtransition regime and use it to modify Navier Stokes equations. Using the new viscosity coefficient, analytical expression is derived for mass flow rate in the range of 0.1<Kn<0.5. Comparing with experimental data and analytical solutions, the new model accurately predicts mass flowrate for a much wider range of Knudsen number. Meanwhile, we observe that axial pressure distribution is of the highest sensitivity to the viscosity coefficient and unpredicted by new model at high Knudsen numbers.

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