Momentum and Heat Transfer Phenomena for Power–Law Liquids in Assemblages of Solid Spheres of Moderate to Large Void Fractions

Abstract

This work extends our previously reported results for the flow of and heat transfer from expanded beds of solid spheres to power–law fluids by using a modified and more accurate numerical solution procedure. Extensive results have been obtained to elucidate the effects of the Reynolds number (Re), the Prandtl number (Pr), the power–law index (n), and the bed voidage (ε) on the flow and heat transfer behavior of assemblages of solid spheres in the range of parameters: 1 ≤ Re ≤ 200, 1 ≤ Pr ≤ 1000, 0.6 ≤n ≤ 1.6, and 0.7 ≤ε ≤ 0.999999. The large values of bed voidage are included here to examine the behavior in the limit of an isolated sphere. As compared to Newtonian fluids, for fixed values of the Reynolds number and the voidage, the total drag coefficient decreases and the average Nusselt number increases for shear thinning fluids (n < 1); whereas, for shear thickening fluids (n > 1), the opposite behavior is observed. The drag results corresponding to bed voidage, ε = 0.99999, are very close to that of a single sphere; whereas, the heat transfer results approach this limit at ε = 0.999. Based on the present numerical results, simple correlations for drag coefficient and average Nusselt number are proposed which can be used to calculate the pressure drop for the flow of a power–law fluid through a bed of particles, or rate of sedimentation in hindered settling and the rate of heat transfer in assemblages of solid spheres in a new application. Broadly speaking, all else being equal, shear-thinning behavior promotes heat transfer, whereas shear-thickening behavior impedes it.