Small-scale superadiabatic combustors with counter-flow heat exchange segments of finite length are studied using irreversible Arrhenius kinetics. First, the complete two-dimensional conservation equations for the gas phase and the solid walls separating the channels are investigated numerically. Next, a simplified one-dimensional model, also known as the narrow-channel approximation, is derived asymptotically and the results are compared with those of the complete model. The main aim of the study is to assess the applicability limits of the simplified model. The analysis shows that this approximation provides valid results beyond its strict limits of validity. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.