Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

Abstract

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.