An apparatus for use in direct resistance heating of a molten glass-carrying vessel, such as a finer or connecting pipe, is provided. The apparatus comprises a flange comprises a plurality of electrically-conductive rings that include an inner ring joined to the vessel's exterior wall during use of the flange and an outer ring that receives electric current during use of the flange. The innermost ring comprises a high-temperature resistant metal preferably comprising at least 80% platinum, and the outermost ring preferably comprising at least 99.0% nickel. This combination of materials both increases the reliability of the flange and reduces its cost. Either one or both of the width or thickness of one or both of the inner or outer rings varies as a function of angular position relative to the vessel. The width and/or thickness of the inner and the outer rings with relation to each other produces a uniform current distribution in the flange and the vessel.