Inertial perturbations to inertialess MHD flows in insulating, rectangular ducts with small divergences

The perturbations of certain MHD duct flows is treated, for which inertial effects are small due to the presence of strong magnetic fields; such a study is useful with regard to the liquid-lithium cooling blankets for future fusion reactors. Separate analyses are presented for intermediate slopes, where 1 is much greater than the slope of the divergence, which is much greater than 1/the square root of the Hartmann number, and for small slopes, with the slope of divergence equal to 0(1/the square root of the Hartmann number). It is found that far downstream, inertial perturbations become algebraically small compared to inertialess solutions; in addition, inertial effects do not accumulate over long duct lengths in such a way that inertial perturbations become comparable to inertialess solutions.