An experimental and theoretical study was conducted on excess enthalpy flames stabilized in a radial multi-channel as a model cylindrical radial-flow porous medium burner. In experiments, the flame position and burning velocity were directly measured under various mixture conditions. The result showed that the multi-channel flames had excess burning velocities due to heat recirculation via the channel walls. As the flow rate reduced, its radial position decreased with a linear-to-nonlinear transition and it was extinguished at its minimum radial position. To elucidate the mechanisms behind these behaviors, a theoretical analysis was conducted. From the rotational symmetry, the multi-channel was simplified to a slightly-diverging adiabatic channel. After assuming a one-dimensional far-field stabilized flame, the entire region was divided into the classical flame zone and outer regions and then asymptotic solutions were obtained. The result indicated the existence of a turning-point flame behavior with two different branches, one of which qualitatively agreed with our experimental results. Detailed examination showed that there are three different stabilization mechanisms, i.e., the flow divergence, the heat recirculation and an enhanced heat diffusion. The heat recirculation is a long-range gas-solid interaction leading to the excess-enthalpy burning, whereas the enhanced heat diffusion is a short-range flame-solid interaction dispersing heat from the flame zone to the neighboring regions and so suppressing the excessive burning. The competition between these two is believed to cause the transition behavior of flames prior to extinction in our multi-channel and further in cylindrical porous media. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.