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 steady-state 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‾ increases as Re and Pr increase, whereas Nu‾ 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 Nu‾ with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, Nu‾ 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‾ monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, Nu‾ 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‾ based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for Nu‾ for the ranges of Re,Pr,Ri,n considered here.