Momentum and heat transfer from an asymmetrically confined rotating cylinder in a power-law fluid

In the present study, the momentum and heat transfer aspects from an isothermally rotating cylinder immersed in a power-law fluid, confined symmetrically and asymmetrically between two parallel walls are considered. The governing equations are solved numerically for the rotational Reynolds number ( 10 − 3 ≤ R e ≤ 40 ) , Prandtl number ( 1 ≤ P r ≤ 100 ) , power-law index ( 0.02 ≤ n ≤ 1 ) , blockage ratio ( 10 − 3 ≤ β ≤ 0.9999 ) and asymmetry ratio ( 10 − 4 ≤ γ ≤ 1 ) to elucidate the role of these parameters on the momentum and heat transfer characteristics. The results reported herein pertain to the two dimensional, steady, incompressible power-law fluid in the laminar flow region. The numerical strategy and method used here are validated by comparing the present results with some of the available experimental and numerical studies, showing good agreements. As far as can be ascertained, it is the first systematic numerical study of a rotating cylinder immersed in power-law fluids elucidating the complex interplay between the rheological and kinematic parameters. The flow field is visualized by plotting the streamlines and, hydrodynamic forces and torque acting on the rotating cylinder are computed. The numerical results are supplemented by a lubrication approximation analysis relevant to highly confined cases, i.e., large values of β. In this case, when confinement increases, the asymptotic scaling of the torque is given by e − 1 / 2 where e denotes the non-dimensional gap between the cylinder surface and the nearest wall. The heat transfer characteristics are presented in terms of the isotherm contours, and the local and average Nusselt numbers as functions of the aforementioned governing parameters. The rate of heat transfer exhibits a positive dependence on the Reynolds number, Prandtl number, confinement and the degree of asymmetry while the shear-thinning behavior decreases the rate of heat transfer above the corresponding value in Newtonian fluids. Finally, the present results are consolidated by fitting them in the form of a predictive correlation for the average Nusselt number for different blockage ratios studied herein.