Heat Transfer in Non-Newtonian Laminar Impinging Jets

Numerical results are presented for laminar impinging flow and heat transfer with a non-Newtonian inelastic fluid in a planar two dimensional geometry. Bifurcation diagrams are computed to characterize flow separation and reattachment in steady flow. For a range of rheological parameters calculations show that the dimensionless wall jet heat transfer rate Q may be correlated as $RP1.3$ where R_P is the reattachment coordinate of the primary vortex scaled with the jet half-width, thus quantifying the extent of enhancement with shear thinning. For Re = 200 the unsteady time periodic flow is computed for both fluids and employed in the heat transfer calculations. The Newtonian flow Nusselt numbers at the stagnation point and in the wall jet region, although periodic, show an oscillation in magnitude less than 10% of the mean and time averages similar to steady flow. For the shear thinning fluid the wall jet Nusselt number displays an oscillation amplitude of about half the mean value, and the Nusselt number profile shows considerably improved uniformity over a length scale extending several nozzle widths into the wall jet region. However, unlike steady flow, heat transfer rates are not significantly increased in the oscillatory flow regime.