Natural convection heat transfer from two vertically aligned circular cylinders in power-law fluids

Abstract

In this work, laminar natural convection in power-law liquids from a pair of vertically aligned heated cylinders has been studied numerically over the following ranges of conditions: Prandtl number (0.72⩽Pr⩽102), Grashof number (10⩽Gr⩽104), power-law index (0.3⩽n⩽1.5) thereby embracing both shear-thinning and shear-thickening fluid behaviour and the center-to-center gap between the two cylinders was varied over the range (2⩽(S/D)⩽20). The heat transfer characteristics of the lower cylinder are little influenced by the presence of the upper heated cylinder in line with the previous studies. On the other hand, the average Nusselt number for the upper cylinder could be higher or lower than that of the lower cylinder depending upon the value of (S/D), Grashof number and power-law index. Overall, all else being equal, shear-thinning behaviour can enhance heat transfer by up to 100% whereas shear-thickening has adverse influence on the rate of heat transfer. The present results on Nusselt number and drag coefficient have been correlated using simple analytical forms which permit the estimation of these parameters for the two cylinders in a new application with acceptable levels of accuracy. In addition to the overall heat transfer characteristics, the detailed structure of the velocity and temperature fields is visualised in terms of the streamline and isotherm contours over the preceding ranges of parameters.