Forced convection from a sphere to power-law fluids in a tapered tube

Abstract

The Poiseuille flow of power-law fluids past a heated sphere in a tapered tube is studied over the following ranges: Blockage ratio, BR (0.1 to 0.5), Separation ratio, SR (0.1 to 0.7), taper angle, α (1o to 20o), Reynolds number, Re (1 to 100), Prandtl number, Pr (10 to 100), and the power law index, n (0.2 to 1). The hydrodynamic force exerted on the sphere is expressed using the total drag coefficient and its pressure component. Both exhibit the expected inverse dependence on Re while it bears a positive dependence on n, SR and BR. The normalized drag for a confined sphere also exhibits a complex functional relationship with each of these parameters. The normalized drag is significantly influenced by the taper angle. In general, SR, BR and α delay the boundary layer separation and hence, stabilize the flow. Similarly, the heat transfer characteristics are described in terms of isotherms, local and surface average Nusselt number. The Nusselt number shows a positive relationship both with SR and BR. The taper angle exerts only a weak effect on the Nusselt number. The heat transfer coefficient is augmented up to 59% in shear-thinning fluids above that in a Newtonian fluid.