Development length in planar channel flows of inelastic non-Newtonian fluids

This work presents a numerical study on the development length (L=L/H) required to reach fully-developed flow conditions at the entrance of a planar channel for inelastic non-Newtonian fluids modeled by the Sisko model. The simulations were carried out for low Reynolds number flows in the range 0 < Re ≤ 100, for a power law index, n, in the range 1/3 ≤ n ≤ 1 and for a dimensionless infinite viscosity, μ¯∞, varying in the range 0≤μ¯∞≤0.1. A new non-linear relationship between L and Re was derived, taking into account the different values of n and μ¯∞. Moreover, new exact solutions are presented for the velocity profile under fully developed flow conditions (for specific values of n).