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

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‾ has been found to decrease sharply with increasing Bingham number Bn, but subsequently Nu‾ approaches asymptotically to a value of unity, which is indicative of conduction-driven transport. It has also been found that Nu‾ increases with increasing values of Prandtl and Reynolds numbers for both Newtonian (i.e. Bn = 0) and Bingham fluids. In contrast, Nu‾ decreases with increasing Ri for both Newtonian and Bingham fluids for small values of Bingham number, whereas Nu‾ remains insensitive to the variation of Ri for large values of Bingham number. The variation of torque coefficient CT, which gives a quantitative measure of power consumption, has also been investigated. The torque coefficient CT has been found to increase with increasing Bn whereas it decreases with increasing Re. It has also been found that CT 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 CT. However, in the case of mixed convection CT increases with increasing Pr. The simulation data has been used in conjunction with a detailed scaling analysis to propose a correlation for Nu‾ for the range of Re,Ri and Pr considered here.