Steady flow of Newtonian and dilatant fluids over an array of long circular cylinders

Abstract

Field equations for the steady flow of power-law dilatant fluids normal to an array of long circular cylinders have been solved numerically using the finite difference method. The cylinder-cylinder interactions have been simulated using the two widely used concentric cylindrical cell models, namely, the Free surface and Zero vorticity cell models. Extensive theoretical results on the individual components of flow resistance arising from pressure and shear forces are presented for a range of physical and kinematic conditions. Furthermore, information on the variation of vorticity and power-law viscosity is also presented to provide some physical insights into the nature of the flow field. The results presented herein encompass the following ranges of physical and kinematic conditions: ε = 0.5 and 0.9; Re = 0.1, 1 and 10 and 1 ≤ n ≤ 1.8. An excellent match between theory and experiments for Newtonian fluids demonstrates the utility of this simple approach to the modeling of momentum transfer in fibrous beds and tubular heat exchangers. However, no suitable experimental results are available for dilatant fluids in these systems.