Magnetohydrodynamic flow in a rectangular tube at high Hartmann number

Asymptotic forms, valid for high Hartmann number M , are obtained for the mean velocity for laminar magnetohydrodynamic flow in a rectangular tube. For a tube with non-conducting walls it is found that, neglecting exponentially damped terms, the mean velocity can be expressed in closed form in terms of tabulated functions. The first three terms of the expansion of the mean velocity in inverse powers of M are in extremely close agreement with a corresponding expansion obtained by Shercliff (1953) using a boundary-layer method. For perfectly conducting walls the first five terms of an expansion in inverse powers of M are obtained.