The effects of bottom wall heating on mixed convection of yield stress fluids in cylindrical enclosures with a rotating end wall

Abstract

Steady-state laminar mixed convection of Bingham fluids in cylindrical enclosures with a rotating top cover has been numerically analysed for the configuration where the bottom cover is kept at a higher temperature than the rotating top cover. The numerical investigations have been carried out based on steady-state axisymmetric incompressible flow simulations for a range of different values Reynolds, Richardson, and Prandtl number given by 500 <= Re 3000, 0 <= Ri <= 1 and 10 <= Pr <= 500 respectively. The aspect ratio (i.e. height: radius = AR = H/R) of the cylindrical container is considered to be unity (i.e. AR = H/R = 1). The mean Nusselt number (Nu) over bar has been found to decrease sharply with increasing Bn owing to flow resistance arising from yield stress, but subsequently (Nu) over bar asymptotically approaches a value of unity, which is indicative of a conduction-driven transport. In addition, the mean Nusselt number (Nu) over bar has been found to increase with increasing Reynolds number due to the strengthening of advective transport. However, the mean Nusselt number (Nu) over bar exhibits a non-monotonic trend (i.e. increases with increasing Ri for small values of Richardson number before showing a weak decreasing trend) with increasing Ri for Newtonian fluid (i.e. Bn = 0), whereas (Nu) over bar increases with increasing Ri for small values of Richardson number before becoming a weak function of Ri for Bingham fluids. A step change in the mean Nusselt number has also been observed with an increase in Richardson number for some Bingham number values due to a change in flow pattern. The influences of Prandtl, Reynolds, Richardson, and Bingham numbers on the mean Nusselt number have been explained in detail based on both physical and scaling arguments. The simulation data and scaling relations have been utilised to propose a correlation for the mean Nusselt number, which has been shown to capture the numerical findings satisfactorily for the parameter range considered here. 2018 Elsevier Ltd. All rights reserved.