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An energy balance analysis has been performed for a confined cylindrical arc column heated inductively by high-frequency fields. The analysis includes the convective energy transport due to a radial inflow in addition to the radiative and conductive transport considered in the Ellenbaas-Heller equation. The resulting non-linear, two-point boundary value equations were solved numerically. Calculations were performed for an argon arc operating at atmospheric pressure using experimentally determined transport properties. Temperature profiles were found to be in better agreement with measured values, when radial inflow was included. There was no indication that the arc attained some natural diameter based on a specific plasma radius to skin depth ratio.