Stable combustion in a heated tube, with a radius on the order of the flame thickness, is investigated experimentally and numerically. The downstream portion of the tube is heated by an external heat source resulting in a steady, axially varying temperature gradient along the tube wall. Strongly burning, axisymmetric methane/air flames are stabilized inside this wall temperature profile which are observed to be "flat" for sufficiently small tube dimensions. The position of these flames is dictated by a competition between the energy required to preheat the reactants, that released by combustion, and the heat lost to the wall. To model such flames, an extension to the standard 1-D, volumetric flame formulation is proposed to solve for wall/gas heat transfer by employing a thermal boundary layer. The boundary layer utilizes a non-linear, radially-varying heat source to account for combustion and captures the effect of enhanced interfacial heat transfer inside the reaction zone. The proposed numerical model gives improved quantitative predictions for flame stabilization position than approaches which neglect the effect of heat release by modeling heat transfer with Newton's law of cooling and a local Nusselt number. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.