Free convection heat transfer from a semi-circular cylinder inside a square enclosure: Orientation effects

Abstract

The numerical investigation has been carried out for the buoyancy driven flow (free convection) from a cylinder of semi-circular cross-section at three orientation angles (i.e., φ=0°,45°and90°) to stagnant power-law fluids inside a square cavity. The coupled governing equations were solved for the given range of the pertinent dimensionless parameters of Rayleigh number (102⩽Ra⩽105), Prandtl number (10⩽Pr⩽100), and power-law index (0.3⩽n⩽1.8). At different orientation angles of the semi-circular cylinders, the numerical results were visualized in terms of velocity and temperature profiles near the cylinder and, gross engineering parameters (e.g., average Nusselt numbers). If all other factors are equal, the rate of heat transfers from a semi-circular cylinder at φ=90° is higher than for the other orientations. The rate of heat transfer can also be increased by increasing the value of Ra and decreasing the value of Pr. In the power-law fluids, the heat transfer rate is always higher in shear-thinning fluids under the same condition. In the end, the average Nusselt number for different orientation angles of the cylinder has been correlated by simple expression.