We investigate the possibility of heating of the loops and other closed magnetic structures in active regions of the solar corona by the flow of solar wind (plus other flows that may be present) across the magnetic field lines (that are perpendicular to the flow), in a similar manner to a conventional MHD generator. A simple model is formulated which allows us to calculate the typical currents generated by this mechanism. This enables us to make a judgement as to whether the loops in solar active regions can be heated by the proposed mechanism through the associated Ohmic dissipation. It is shown that even if the heating region width is of the order of a few proton Larmor radii (this effectively means that a loop is represented by n...