Laminar mixed convection of power-law fluids in cylindrical enclosures with heated rotating top wall

Abstract

Laminar mixed convection of inelastic non-Newtonian fluids obeying a power law model in a cylindrical enclosure with a heated rotating top cover has been investigated numerically in this study. The steadystate axisymmetric simulations have been carried out for a range of different nominal Reynolds, Prandtl, Richardson numbers (i.e. 500 <= Re <= 2000; 10 <= Pr <= 500 and 0 <= Ri <= 1) and power-law index (i.e. 0.6 <= n <= 1.8) for an aspect ratio (height/radius) of unity (i.e. AR = 1.0). It has been found that mean Nusselt number (Nu) over bar increases as Re and Pr increase, whereas (Nu) over bar decreases with increasing values of Ri for shear-thinning (i.e. n < 1), Newtonian (i.e. n = 1) and shear-thickening (i.e. n > 1) fluids. It has also been observed that the variation of Ni with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, (Nu) over bar exhibits a non-monotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with increasing n for small values of Richardson number, whereas (Nu) over bar monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, (Nu) over bar increases with n before reaching a maximum value which is followed by a decreasing trend for all values of Ri considered here. Detailed physical explanations are provided for the influences of Re, Pr, Ri, and n on (Nu) over bar based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for (Nu) over bar for the ranges of Re, Pr, Ri, n considered here. (C) 2018 Elsevier Ltd. All rights reserved.