Ferrofluid flow past a vertically reciprocating disk: The BEK family of rotating flows

Abstract

The phenomenon of rotating flow across a disk holds significant importance in diverse fields, including advancements in aerodynamics, turbo-machinery design, blood flow analysis, oceanography, and meteorology. The current study aims to investigate the rotating family of flows, i.e., the Bodewadt, Ekman, and von Karman (BEK) ferrofluid flow past a vertically reciprocating and rotating disk. A similarity transformation reduces the governing momentum and energy equations to a set of coupled nonlinear ordinary differential equations, solved numerically using the bvp5c solver in MATLAB. Graphical visualizations of velocity components, streamlines, isotherms, and temperature fields are presented to illustrate the physical trends. The findings reveal that the radial velocity of the ferrofluid is a decreasing function of both the ferromagnetic interaction parameter and downward reciprocation, whereas the tangential velocity exhibits a direct relationship with these parameters. Notably, in Ekman flow, the radial velocity increases near the geostrophic region, where the Coriolis and pressure gradient forces reach equilibrium, underscoring the balance of rotational and pressure-driven effects. The analysis of thermal behavior indicates that temperature profiles escalate with thermal conductivity and upward reciprocation, while they decline with increasing Prandtl number, demonstrating the superior cooling efficiency of hydrocarbon-based ferrofluid (C1-20B). Hydrocarbon-based ferrofluid exhibits a higher surface heat transfer rate than water-based and fluorocarbon-based ferrofluids. These findings underline the potential of ferrofluids for electronic cooling, compact heat sink design, and improved drilling efficiency in oil and mineral extraction.