Electrorheological and magnetorheological duct flow in shear-flow mode using Herschel-Bulkley constitutive model

A quasi-steady duct flow through a parallel plate model for electrorheological (ER) and magnetorheological (MR) fluids under shear-flow mode is investigated mathematically. To do so Herschel-Bulkley power law constitutive model for ER and MR fluid is adopted to account for postyield shear thinning or shear thickening conditions as indicated in recent research. This approach is selected in order to obtain a more flexible representation of ER or MR postyield behavior rather than using the mostly adopted Bingham plastic model. This will lead to developing a theoretical method for prediction of ER or MR force characteristics.