Magnetohydrodynamic laminar flow between porous disks

The steady two-dimensional laminar flow of an incompressible conducting fluid between two parallel circular disks in the presence of a transverse magnetic field is investigated. A solution is obtained by perturbing the creeping flow solution and it is valid only for small suction or injection Reynolds numbers. Expressions for velocity, induced magnetic field, pressure, and shear stress distribution are determined and are compared with the creeping flow and hydrodynamic solutions. It is found that the overall effect of the magnetic field on the flow is the same as that in the Hartmann flow.Nomenclature stream function - 2h channel width - z, r axial and radial coordinates - radius of the disk - U _r radial component of velocity - U _r average velocity in the radial direction, U _r d - U _z axial component of velocity - U ₀ injection or suction velocity - dimensionless axial coordinate, z/h - f() function defined in (8) - density - coefficient of kinematic viscosity - electrical conductivity - magnetic permeability - H ₀ impressed magnetic field - h _r induced magnetic field, H _r /H ₀ - M Hartmann number, H ₀ h(/)^1/2 - R Reynolds number, U ₀ h/ - R _m magnetic Reynolds number, U ₀ r - A constant defined in (15) - K constant defined in (27) - C ₂ constant defined in (26) - p pressure - C _p pressure coefficient - C _f skin friction coefficient