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This article aims to address lubrication effects on multiphase flows. Bi-phase flows are composed of third-grade fluid as the main carrier, while Hafnium and crystal particles of tiny size are used to obtain different suspensions. Fluid dynamics of two-phase flows are analyzed through a steep channel. An external magnetic field is applied on bi-phase flows due to the magnetic susceptibility of the metal. In order to attenuate walls roughness, lubrication effects are also taken into account. The nonlinear ordinary differential equation subject to nonlinear slip boundary conditions is solved analytically with the help of  “Perturbation method . ”  Contribution of the most significant variables and parameter is examined through graphs and different tables. It is inferred that slippery walls and magnetic fields have an opposite impact on the flow. Multiphase flow suspended with Hafnium particles is better than the one crystal particles.

Mathematical modeling of multiphase flows of third-grade fluid with lubrication effects through an inclined channel: analytical treatment