Numerical investigation of mixed convection of Bingham fluids in cylindrical enclosures with heated rotating top wall

Abstract

The steady-state laminar mixed convection of yield stress fluids obeying the Bingham model in a cylindrical enclosure with a heated rotating top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Yield stress effects on heat and momentum transport have been investigated for an aspect ratio (height/radius) of unity (i.e. AR = 1) for a range of different values of nominal Prandtl, Richardson and Reynolds numbers given by 10 <= Pr <= 500, 0 <= Ri <= 1 and 100 <= Re <= 3000. The mean Nusselt number (Nu) over bar has been found to decrease sharply with increasing Bingham number Bn, but subsequently (Nu) over bar approaches asymptotically to a value of unity, which is indicative of conduction driven transport. It has also been found that (Nu) over bar increases with increasing values of Prandtl and Reynolds numbers for both Newtonian (i.e. Bn = 0) and Bingham fluids. In contrast, (Nu) over bar decreases with increasing Ri for both Newtonian and Bingham fluids for small values of Bingham number, whereas (Nu) over bar remains insensitive to the variation of Ri for large values of Bingham number. The variation of torque coefficient C-T, which gives a quantitative measure of power consumption, has also been investigated. The torque coefficient C-T has been found to increase with increasing Bn whereas it decreases with increasing Re. It has also been found that C-T decreases slightly with increasing Ri for small values of Bn, whereas it becomes insensitive to the variation of Ri for large Bingham numbers. For the fully forced convection (Ri = 0) case, Pr does not have a significant influence on C-T. However, in the case of mixed convection C-T increases with increasing Pr. The simulation data has been used in conjunction with a detailed scaling analysis to propose a correlation for (Nu) over bar for the range of Re, Ri and Pr considered here. (C) 2017 Elsevier Ltd. All rights reserved.