Numerical investigation of effect of surface pattern and rotation on power-law fluid flow and heat transfer around a cylinder in laminar flow regime

We have studied the effect of surface topography, fluid behavior, and rotation on fluid flow and heat transfer phenomena over a cylinder. In this study, we have incorporated a sinusoidal surface topography to account for the impact of surface patterns and a power-law model to include fluid behavior. The governing equations are solved numerically for a range of pattern frequency ( ω = 5 and 11 ) , pattern amplitude ( δ = 0.01 and 0.1 ), power-law index ( 0.4 ≤ n ≤ 1.6 ) , Prandtl number ( 1 ≤ P r ≤ 100 ) , rotational speed ( 0.5 ≤ α ≤ 2 ), and Reynolds number ( 5 ≤ R e ≤ 40 ). In particular, the study aims to determine the degree to which various macroscopic parameters, such as the drag and lift coefficients, the average Nusselt number in relation to the Reynolds number, the Prandtl number, the rotating speed, and the power-law index, vary. In this range of Reynolds number, the flow around a circular cylinder is steady, with two symmetric vortices in the rear side. The sliding mesh method is used to deal with dynamic interface between solid and fluid. The streamlines are drawn to visualize the flow 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 increases on increase in Reynolds number and power-law index. On adding rotation to the cylinder, these recirculation zones move away from the cylinder and appear over the crest. On increasing the rotating speed of the cylinder, the frontal vortices disappear. The enveloping vortex gets larger with increase in rotating speed and power-law index. The size of the rear detached vortex increases with power-law index and Reynolds number and decreases with rotating speed. It is observed that the results are contrasted with the previous studies on smooth circular cylinder. The drag force acting on the patterned cylinder is seen to be reduced. Compared to a circular cylinder, a significant reduction in drag can be achieved by choosing suitable value of pattern frequency ( ω ) and amplitude ( δ ). Overall, there is a decrease in the amount of drag reduction as the Reynolds number increases. 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 the enhancement of drag reduction. For a higher value of pattern frequency and amplitude ( ω = 11 , δ = 0.1 ), the drag force reduces significantly for Newtonian and shear-thickening fluids at higher rotating speed ( α = 2 ). Also, the pattern frequency and amplitude substantially impact the average Nusselt number. On increase in pattern frequency and amplitude, a progressive decrease in the average Nusselt number is observed. Compared to shear-thinning and Newtonian fluid, shear-thickening fluid exhibits a greater reduction in average Nusselt number. One correlation is provided at the end to show the relationship between the average Nusselt number, the Prandtl number, the Reynolds number, the rotating speed, and the power-law index.