Viscoplastic flow in slightly varying channels with wall slip pertaining to a magnetorheological (MR) polishing process

► Analytical fluid dynamics model emulating an MR polishing process was first proposed. ► The bi-viscosity fluid can have a total of 5 flow types based on the fluid velocity. ► The pseudo-core region of the fluid increases with the viscosity ratio and slip. ► The power efficiency increases as the tool's rotational velocity decreases. ► The MRR increases but the WIWNU decreases as the workpiece length ratio decreases.