Effects of the induced magnetic field on the magnetohydrodynamic channel flow

The effects of a nonuniform magnetic field on magnetohydrodynamic (MHD) channel flow between two parallel plates of infinite extent are investigated. Influence of the induced magnetic field, such that the magnetic Reynolds number is less than unity but greater than zero, is included. The goal is to use the MHD effects to reduce the amount of heat transfer from the fluid to the channel walls. Expressions for distortion in the magnetic and flow fields are obtained. A solution is then obtained using the perturbation theory in the expansion of the field components in a double-power series in R
m
and
I
. The pressure gradient along the channel wall is examined. A criterion is developed under which R
m
must be taken into account in determining the heat transfer between the fluid and the channel walls.