The skin friction and heat transfer in a laminar plane wall jet that evolves from a uniform velocity to its self-similar behavior

Abstract

The plane, steady, laminar wall jet with a uniform velocity and temperature profiles at the jet exit is numerically investigated using a two-dimensional finite volume approach for a variety of Reynolds numbers and Prandtl number of 0.712 and 7. Between the jet exit and the downstream self-similar behavior, the flow exhibits a developing region that is not self-similar. The location of the dimensionless virtual origin is carefully investigated and expressed as a function of Reynolds number. The local skin friction coefficient is observed to converge to the analytical self-similar solution at downstream locations. Since no analytical solution exists for the temperature field in either the developing or self-similar regions of this problem, the thermal solution is investigated for both isothermal and isoflux boundary conditions at the wall. The local and overall skin friction coefficients, in addition to the local and overall Nusselt numbers, are reported as a function of Reynolds number, Prandtl number and the dimensionless location downstream of the jet exit.