Rarefied MHD laminar radial channel flow

The steady axisymmetrical laminar flow of slightly rarefied electrically conducting gas between two circular parallel disks in the presence of a transverse magnetic field is analytically investigated. A solution is obtained by expanding the velocity and the pressure distribution in terms of a power series of 1/r. The effect of rare-faction is taken to be manifested by slip of the velocity at the boundary. Velocity, induced magnetic field, pressure and shear stress distributions are determined and compared with the case of no rarefaction.Nomenclature b outer radius of channel - C _f skin friction coefficient, _w /(Q ²/t ⁴) - H ₀ impressed magnetic field - H _r ^* induced magnetic field in the radial direction - H _r induced dimensionless magnetic field in the radial direction, H _r ^* /H ₀ - M Hartmann number, H ₀ t(/)^1/2 - P dimensionless static pressure, P*t ⁴/Q ² - P* static pressure - P _b dimensionless pressure at outer radius of channel - P ₀ reference dimensionless pressure - Q source discharge - R gas constant - Rm magnetic Reynolds number, Q/t - Re Reynolds number, Q/t - 2t channel width - T absolute gas temperature - u dimensionless radial component of the velocity, u*t ²/Q - u* radial component of the velocity - w dimensionless axial component of the velocity, w*t ²/Q - w* axial component of the velocity - z, r dimensionless axial and radial directions, z*/t and r*/t, respectively - z*, r* axial and radial direction, respectively - molecular mean free path - magnetic permeability - coefficient of kinematic viscosity - density - electrical conductivity