Numerical Simulation and Modeling of Laminar Developing Flow in Channels and Tubes With Slip

Abstract

Analytical solutions for slip flows in the hydrodynamic entrance region of tubes and channels are examined. These solutions employ a linearized axial momentum equation using Targ's method. The momentum equation is subjected to a first order Navier slip boundary condition. The accuracy of these solutions is examined using computational fluid dynamics (CFD) simulations. CFD simulations utilized the full Navier–Stokes equations, so that the implications of the approximate linearized axial momentum equation could be fully assessed. Results are presented in terms of the dimensionless mean wall shear stress, τ⋆, as a function of local dimensionless axial coordinate, ξ, and relative slip parameter, β. These solutions can be applied to either rarefied gas flows when compressibility effects are small or apparent liquid slip over hydrophobic and superhydrophobic surfaces. It has been found that, under slip conditions, the minimum Reynolds number should be ReDh>100 in order for the approximate linearized solution to remain valid.