Natural Convection of Power-Law Fluids Inside an Internally Finned Horizontal Annulus

In the present study, laminar natural convection of power-law fluid confined between two horizontal concentric cylinders with two radial fins attached to the inner cylinder is studied. Governing equations are solved using the finite element method. The computations are carried out for various Rayleigh numbers, fin lengths, fin inclination angles and Prandtl numbers for both shear-thickening and shear-thinning fluids, and their effects on average equivalent thermal conductivity (keq) are investigated. The results indicate that as we move from shear-thinning fluids to shear-thickening fluids, isotherm’s density decreases near the cylinders and at the same time, the thermal boundary layer thickness near the cylinders and fins increases, which results in reduction of the heat transfer rate. Net convective heat transfer for the shear-thinning fluids decreases as fin length ratio Lf increases. Also, it is shown that for shear-thickening fluids, fins orientation does not have significant effects on keq, similar to Newtonian fluids. But for shear-thinning non-Newtonian fluids, an increase in keq can be observed for fins inclination angle larger than about 50°.