Free convection from a vertical plate to generalized Newtonian fluids

Abstract

Abstract: Laminar free convective heat transfer to power-law and Bingham plastic fluids from a vertical surface has been studied numerically. New extensive results for streamlines, isotherms, local and surface-averaged Nusselt number presented herein embrace the following ranges of conditions: 0.2 ≤ n ≤ 1; 1 ≤ PrPL ≤ 100; 10 ≤ GrPL ≤ 105 for power-law fluids and 1 ≤ Bn ≤ Bnmax, 10 ≤ PrBP ≤ 100 and 102 ≤ RaBP ≤ 105 for Bingham plastics. The effect of the two thermal conditions on the plate, namely, constant temperature (CWT) and constant heat flux (CHF) has also been investigated. Otherwise, under identical conditions, shear-thinning fluid viscosity facilitates overall heat transfer by up to 80–100% over and above that in Newtonian fluids. On the other hand, Bingham yield stress adversely influences heat transfer due to the formation of unyielded domains thereby leading to changes in temperature gradients on the surface of the plate. Beyond a critical Bingham number, conduction is the sole mode of heat transfer. The values of the average Nusselt number have been consolidated in the form of a modified Rayleigh number for power-law liquids. These results also help delineate the conditions for the onset of convection as well as the limits of the Boundary-layer flow approximation. For Bingham plastics, the average Nusselt number decreases gradually with the increasing ratio of the yield stress and the buoyancy-induced forces approaching the conduction limit at about ∼ 1–2.