This paper addresses liquid-metal flow under a strong, fringing, decreasing magnetic field in an insulating circular pipe by a full resolution of the magnetohydrodynamic (MHD) equations. The aims of the paper are first to provide a detailed description of the flow and second to perform a study of the restrictions related to the approximate numerical techniques commonly used in the nuclear fusion field, namely, the so-called core flow approximation based on asymptotic methods. Finally, a comparison between full MHD solutions obtained under conducting and insulating circular pipe walls, at similar MHD conditions, is provided. The current results show that the role of inertia is clearly more important under electrically insulating ducts because no net braking MHD forces are present in such configurations. This fact adversely affects the accuracy of asymptotic method results. From a phenomenological point of view, the effects of wall conductivity are found to be very important. For instance, when insulating walls are present, the intensity of the generated near-wall jets is three times larger than that found in conducting configurations. As a result, the shear effects and the triggering of turbulence in the downstream area are clearly enhanced.