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This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field. For large time, it is anticipated that higher profiles for velocity and skin friction are seen with fluid phase and an accelerated moving wall.

Hydrodynamic behaviour of velocity of applied magnetic field on unsteady MHD Couette flow of dusty fluid in an annulus