Numerical Investigation of Power-law Fluid Flow and Heat Transfer around a Rotating Patterned Cylinder in Laminar Flow Regime

Abstract

The present numerical investigation studies the momentum and heat transfer phenomena from a heated rotating patterned cylinder in a laminar flow regime. A sinusoidal surface topography and power-law fluid are considered to account for the surface pattern and fluid behavior. The range of parameters considered for the present study are pattern frequency, 𝜔 = 5 and 11 pattern amplitude, 𝛿 = 0.01 and 0.1 Reynolds number 5 ≤ 𝑅𝑒 ≤ 150; power-law index 0.4 ≤ 𝑛 ≤ 1.6 Prandtl number 1 ≤ 𝑃𝑟 ≤ 100 and rotational speed 0.5 ≤ 𝛼 ≤ 2. The study aims to determine the degree to which various macroscopic parameters, such as the drag and lift coefficients and the average Nusselt number, vary in relation to the Reynolds number, rotating speed, power-law index, and Prandtl number. The sliding mesh method is employed to handle the dynamic interface between solid and fluid. The streamlines, vorticity, and isotherm contours are drawn to visualize the flow and temperature field around the patterned cylinder. For a non-rotating patterned cylinder, small recirculation zones are observed over the trough, which are absent in circular cylinders. The size of these recirculation regions increase on increase in the power-law index and Reynolds number. When adding rotation to the cylinder, these recirculation zones move away from the cylinder and appear over the crest. When increasing the rotating speed of the cylinder, the front detached vortices disappear. In case of vortex shedding, a significant decrease in the frequency of vortex shedding occurs when adding topographical patterns. It is observed that, with an increase in rotational speed, vortex shedding can be suppressed for all fluid conditions considered here. The drag force acting on the patterned cylinder is seen to be reduced in comparison with a smooth circular cylinder. A significant reduction in drag can be achieved by choosing a suitable value of pattern frequency (𝜔) and amplitude (𝛿). Higher values of surface patterns (𝜔 = 11, 𝛿 = 0.1) result a significant amount of drag reduction at a higher rotating speed. The behavior of the fluid has a considerable influence on the reduction of drag. It has been observed that shear-thickening fluid significantly contributes to drag reduction. The pattern frequency and amplitude significantly influence the average Nusselt number. With an increase in pattern frequency and amplitude, a progressive decrease in the average Nusselt number is observed. The shear-thinning fluid behavior helps to dissipate the heat from the cylinder to the surrounding fluid. Conversely, shear-thickening fluid behavior exhibits the opposite trend. Also, two correlations are provided to show the relationship between the average Nusselt number, the Prandtl number, the Reynolds number, the rotating speed, and the power-law index.