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The unsteady MHD Hartmann flow of an incompressible Casson nanofluid bounded by two stationery parallel horizontal plates in a porous medium is studied with heat and mass transfer. A non-Darcy model that obeys the Forchheimer extension is assumed for the characteristics of the porous medium. A uniform and constant pressure gradient is applied in the axial direction whereas a uniform suction and injection are applied in the direction normal to the plates. The two plates are kept at constant and different temperatures and the viscous and porous dissipations are not ignored in the energy equation. Moreover, the concentration of the nanoparticles at the lower plate level differs from that at the upper one, while, both are kept constants. The system of momentum, heat and concentration equations is solved numerically using the finite difference scheme under the appropriate initial and boundary conditions. The effects of the Hall current, the porosity of the medium, inertial damping force, the uniform (suction/ injection) velocity, the non-Newtonian Casson parameter, Hartmann number, Eckert number, Prandtl number, Lewis number, Brownian motion parameter and thermophoretic parameter on the fluid velocity, temperature and nanoparticles concentration distributions are investigated

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