The present study addresses corrosion of RAFM steel in the flowing eutectic alloy PbLi in a special case of the 1-D magnetohydrodynamic Hartmann flow, where the liquid metal flows in a wall-normal magnetic field. For this flow, the effect of a magnetic field on corrosion and transport of corrosion products are studied analytically, using a self-similar mass transfer model, and numerically. The results are presented in the form of the dimensionless mass transfer coefficient (the Sherwood number, Sh) as a function of dimensionless flow parameters, the Reynolds (Re) and the Hartmann (Ha) numbers. In turbulent flows, Sh decreases as Ha increases due to turbulence suppression by a magnetic field. In laminar flows, Sh slightly increases with the magnetic field due to formation of steep velocity gradients at the Hartmann wall. The obtained results are then applied to analysis of corrosion for a family of PbLi blankets.