EFFECT OF CONFINEMENT ON NATURAL CONVECTION IN POWER-LAW FLUIDS FROM A CIRCULAR CYLINDER

In this work, free convection in power-law fluids from an isothermal horizontal cylinder confined between adiabatic vertical walls has been investigated numerically. The coupled governing equations have been solved over wide ranges of conditions such as Rayleigh number (10(3) <= Ra <= 10(6)), Prandtl number (5 <= Pr <= 100), power-law index (0.3 <= n <= 1.5), channel height (5 <= L/D <= 20), and confinement ratio (2 <= W/D <= 10). The flow and heat transfer results have been interpreted in terms of streamlines and isotherm contours, heatlines, vertical velocity profiles, drag coefficient, and local and average Nusselt number. Furthermore, entropy production rates have been computed to evaluate the value of the Bejan number to delineate the individual contributions due to heat transfer and fluid friction. Depending upon the values of the power-law index and buoyancy-induced flow (Gr), the confinement may enhance or deteriorate heat transfer from the cylinder with reference to that from an unconfined cylinder. Overall, for Newtonian fluids, we may obtain up to 50% enhancement in heat transfer for the minimum confinement effect (W/D = 10), at the highest Rayleigh number (Ra = 10(6)), and the shortest channel height (L/D = 5). At high Ra and Pr, shear-thinning viscosity exerts a positive influence on the Nusselt number while a reverse trend is seen for small values of Ra and Pr. The present results have been consolidated via a simple expression for the average Nusselt number as a function of W/D, L/D, n, and the Rayleigh number. In most cases, the overall entropy generation is mainly due to heat transfer, and it draws only a small contribution from fluid flow friction effects.