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In an effort to investigate the suitability of the concept of portable hydrogen production, we examine numerically the combustion of a very rich methanol-air mixture in a micro-gap assembly consisting of multiple counter-current channels of finite length separated by thin solid conducting walls. Within the mathematical framework of the narrow-channel approximation, the problem can be formulated as a one-dimensional model for a single channel with an extra term representing heat transfer from the hot stream products to the fresh reactants in adjacent channels. We show that the heat recirculation enables superadiabatic temperatures inside the reactor and promotes the oxidation of methanol far beyond the conventional rich limit of flammability. The result is a feasible thermal partial oxidation that produces hydrogen without the need for a catalyst. The paper presents an analysis of the model burner performance with detailed gas-phase kinetics in stationary regimes in terms of operating variables such as the equivalence ratio and the gas inflow velocity, and in terms of physical parameters such as the length of the reformer and the conductivity of the wall material. The idealized microreactor predicts maximum hydrogen yield of the order of 60% at equivalence ratios between 3 and 6.