A Note on Heat Transfer Enhancement in Laminar Impinging Flows With Shear Thinning Inelastic Fluids

A recent article presented axisymmetric numerical calculations showing substantial heat transfer enhancement in a laminar impinging flow with shear thinning inelastic fluids. This paper compares enhancement in planar and axisymmetric geometries and presents empirical dependencies correlating heat transfer rates to fluid rheology. The parametric correlation is expressed in the form $∼ ReGp$⁠. Re_G is a generalized Reynolds number based on the reference strain rate and fluid rheology, and it is larger than the Newtonian Reynolds number for the same mean nozzle velocity and flow geometry. The value of p > 0 is estimated from the numerical data for weak and strong shear thinning. Within the impinging zone spanning the nozzle cross section, the value of p is essentially similar for both geometries, but in the wall jet the planar flow shows a somewhat larger value. The total heat transfer rate in the planar wall jet may be two to ten times larger for a shear thinning fluid. This is because in shear thinning flow, the primary separation vortex is able to maintain the Nusselt number at a higher average value over a significantly longer length scale in the streamwise direction.