Mixed convection of power-law fluids in cylindrical enclosures with a cold rotating top cover and a stationary heated bottom wall

Abstract

Steady-state laminar mixed convection in cylinders with a rotating top cold cover and a heated bottom has been numerically analysed for inelastic shear-thinning/shear-thickening fluids by applying power-law model of viscosity. In this analysis, axisymmetric incompressible flow simulations have been conducted for a range of different values of Reynolds, Richardson, Prandtl numbers (i.e. 500 <= Re <= 2000; 0 <= Ri <= 1.0; 10 <= Pr <= 1000) and power-law index (i.e. 0.6 n 1.8) for an aspect ratio (height/radius) of unity (i.e. AR = 1.0). The thermal convective transport has been found to strengthen with increasing Re and Pr, which in turn gives rise to an increase in the mean Nusselt number Nu. By contrast, an increase in Ri leads to a mild increase in Nu for small Richardson number values but Nu becomes insensitive to the changes in Ri for large Richardson numbers within the range of 0 <= Ri <= 1.0 for all values of n considered here. The mean Nusselt number Nu exhibits a nonmonotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with the variation of n. The influences of Ra, Pr and Ri on the mean Nusselt number Nu have been explained in terms of scaling arguments. The scaling relations along with the numerical findings have been utilised to propose a correlation for the mean Nusselt number for the configuration and the parameter range considered here.