Development length in planar channel flows of newtonian fluids under the influence of wall slip

Abstract

This technical brief presents a numerical study regarding the required development length ðL ¼ Lfd=HÞ to reach fully developed flow conditions at the entrance of a planar channel for Newtonian fluids under the influence of slip boundary conditions. The linear Navier slip law is used with the dimensionless slip coefficient kl ¼ klðl=HÞ, varying in the range 0 < kl 1. The simulations were carried out for low Reynolds number flows in the range 0 < Re 100, making use of a rigorous mesh refinement with an accuracy error below 1%. The development length is found to be a nonmonotonic function of the slip velocity coefficient, increasing up to kl 0:1 0:4 (depending on Re) and decreasing for higher kl. We present a new nonlinear relationship between L, Re, and kl that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and kl up to 1.