Convective heat transfer for power law fluids in packed and fluidised beds of spheres

The forced convection heat transfer characteristics for an incompressible and steady flow of power law liquids in fixed and extended beds of spherical particles has been studied numerically. The sphere-sphere hydrodynamic interactions have been accounted for by using a simple cell model. Within the framework of such a cell model, the momentum and energy equations have been solved using a finite difference method to obtain the velocity and temperature fields. Extensive numerical estimates of the local and average Nusselt numbers as functions of the physical, rheological and kinematic variables have been presented and discussed for the two commonly employed thermal boundary conditions. In broad terms, the Nusselt number for power law fluids (both shear-thinning and shear-thickening conditions) normalized with respect to the corresponding value for a Newtonian fluid shows weak additional dependence on the power law flow behaviour index. The shear-thinning behaviour is seen to promote heat transfer and as expected the shear-thickening behaviour impedes heat transfer in fixed and fluidised beds. All in all, the present results encompass wide ranges of conditions as follows: Reynolds number: 1-500; Peclet number: 1-500; bed voidage: 0.4-0.8 and the flow behaviour index: 0.5-1.8 thereby covering extremely shear-thinning and shear-thickening types of fluid behaviours. The paper is concluded by presenting detailed comparisons with the limited analytical and/or experimental results available for liquid-solid mass transfer in such systems.