Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip

This technical brief presents a numerical study regarding the required development length $(L=Lfd/H)$ 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 $k¯l=kl(μ/H)$⁠, varying in the range $0<k¯l≤1$⁠. 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 $k¯l≈0.1-0.4$ (depending on Re) and decreasing for higher $k¯l$⁠. We present a new nonlinear relationship between $L$⁠, Re, and $k¯l$ that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and $k¯l$ up to 1.