On the flow of an electrically conducting nonlocal viscous fluid between parallel plates in the presence of a transverse magnetic field in magnetohydrodynamics

A continuum theory is constructed for the flow of an electrically conducting nonlocal viscous fluid between two nonconducting parallel plates. The flow is subject to the influence of a transverse magnetic field. The effects of long range or nonlocal interactions at a material point in the fluid arising from all material points in the rest of the fluid are taken into account by means of a nonlocal influence function. Equations of motion governing the nonlocal viscous flow are derived from localized forms of global balance laws and constitutive equations appropriate for electromagnetically active media. These field equations are analytically solved for the nonlocal velocity and the nonlocal stress fields. The effects of varying the magnetic field strength on the shear stress are investigated. The effects of such variations on the shear stress exerted on the walls of microscopic channels are also determined. Numerical computations are provided for these results.