## Surface Effect on Flow of Magnetorheological Fluids: Featuring Modified Mason Number

This Chapter presents a new unified approach for the flow analysis of magneto-rheological (MR) fluids through channels without using the shear yield stress property of MR fluids. For modeling of MR fluid flow behavior, customarily, a constitutive model, such as a Bingham Plastic or Herschelâ€“Bulkley model, is utilized, both of which depend on the definition of a shear yield stress. However, if the material and geometric characteristic of the wall surface change, different shear yield stress values are obtained. An extensive experimental study is conducted to investigate the relationship between the pressure drop, which is directly proportional to the shear stress, of MR fluids as a function of the applied magnetic field strength, volumetric flow rate, and surface roughness, without utilizing the concept of shear yield stress. This chapter will demonstrate that the shear yield stress is not unique; thus, it is not a material property. The shear yield stress is a system property. A unified method is developed in order to determine the non-dimensional friction factor, which is defined as normalized shear stress, in terms of a modified dimensionless Mason number and dimensionless surface morphology parameters. The modified Mason number incorporates surface morphology effects and surface-independent MR fluid properties. For a given surface morphology, the developed unified method can estimate the friction factor of MR fluid flow with a single curve, similar to a Moody diagram for Newtonian fluids, for all flow rates and magnetic fields that are considered in this chapter, without using a shear yield stress.