Heat conduction in an undulating heating wire

An undulating electric wire generates internal heat by Joule heating. The surface temperature is maintained constant by forced convection. The heat conduction in the wire is solved by using intrinsic coordinates and a perturbation about the (small) ratio of the wire radius to the minimum radius of curvature of the centerline. For the nonuniformly heated wire undulations cause an increase in total heat transfer in comparison with a straight wire of same length and volume.