Small gears are an integral part of the transmission of power and other devices in the small machines which are employed in aerospace, automotive and medical industries etc. Nanofinishing of small gear is a difficult task due to the complexity in its geometry. The modern hybrid approach for the development of nano-scale surface finishing is magnetorheological abrasive flow finishing (MRAFF) method. These surfaces decrease friction among meshing components to improve the their service life. A model for simulating the effects of the MRAFF method was built in the current research study by using FEA based software i.e. (COMSOLÒ Multiphysics). Computational fluid dynamic (CFD) analysis of MR fluid in the 2D computational domain is conducted to see the effects of different process variables on the fluid flow properties (shear rate, shear stress, velocity profile) while finishing the gear component. To analyze the forces acting in the MRAFF method, a viscosity model for the magnetorheological polishing (MRP) fluid flow around a complex component (small steel gear) in external magnetic field is identified and simulated. The magnetic field significantly affects process efficiency by regulating the MR fluid viscosity. The surface finish achieved at various positions on the workpiece surface is consistent throughout the finishing of the gear component.