H imposed magnetic field; α the angle between 0 H and y -axis; z v , * z z V -component of fluid velocity and dimensional form u dimensionless z -component of fluid velocity; B dimensionless z -component of magnetic induction; a half channel width; σ conductivity; η fluid dynamic viscosity; µ permeability; ρ fluid density; , p p ∇ fluid pressure and pressure gradient; k coefficient of p ∇ ; Z B , * z z Hartmann number Multiplied sin ; α y M Hartmann number Multiplied cos ; α Eelectric field; j current density vector; V fluid velocity vector; H imposed magnetic field; B magnetic induction.