A Numercial Investigation of the Skin Friction Coefficient and Nusselt Number in a Laminar Wall Jet That Evolves From a Parabolic Velocity Profile to its Self-Similar Behavior

Abstract

A finite volume numerical approach is used to study the steady, laminar, plane wall jet that evolves from a parabolic velocity profile with uniform temperature to its self-similar behavior downstream of the jet exit. A variety of Reynolds numbers ranging between 50 and 250 is considered in this numerical investigation. The working fluids are air and water with constant physical properties corresponding to Prandtl number of 0.712 and 7 at ambient conditions. In these types of flows, a developing region over which the flow converges to its self-similar behavior is observed in the vicinity of the jet exit. The location of the dimensionless virtual origin, which is of main importance in determining the flow field in the self-similar region, is carefully studied and correlated as a function of Reynolds number. The local skin friction coefficient is observed to converge to the analytical self-similar solution at downstream locations. Given that an analytical solution for the thermal behavior of this problem doesn’t exist in either the developing or self-similar regions, the thermal solution of this problem is studied for isothermal and uniform heat flux boundary conditions at the wall. The idea of a dimensionless thermal virtual origin is introduced and correlated as a function of Reynolds number. The Nusselt number dependence on Prandtl number, Reynolds number and the downstream location are obtained for both thermal boundary conditions at the wall.