Numerical simulation of laminar flow of water-based magneto-rheological fluids in microtubes with wall roughness effect

Fully developed laminar flows of water-based magneto-rheological (MR) fluids in microtubes at various Reynolds and Hedsrom numbers have been numerically simulated using finite difference method. The Bingham plastic constitutive model has been used to represent the flow behavior of MR fluids. The combined effects of wall roughness and shear yield stress on the flow characteristics of MR fluids, which are considered to be homogeneous by assuming the small particles with low concentration in the water, through microtubes have been numerically investigated. The effect of wall roughness on the flow behavior has been taken into account by incorporating a roughness–viscosity model based on the variation of the MR fluid apparent viscosity across the tube. Significant departures from the conventional laminar flow theory have been acquired for the microtube flows considered.