On the presumption that an axial-radial flow pattern (AR) can contribute to a more even distribution of fresh syngas over the catalyst bed, in this study, effects of AR pattern in a mega methanol plate reactor are studied, and the corresponding results are compared with that of fully axial (APR) or radial (RPR) ones. For this purpose, a two-dimensional mathematical model is developed for the AR, while this is one-dimensional for APR and RPR. Afterward, partial differential equations are solved with orthogonal collocation of finite elements method, and the modeling results are compared with industrial data, indicating a good agreement. Besides, the AR reactor is optimized (OAR) using differential evolution (DE) method in order to maximize methanol production. Results demonstrate that the AR can promote methanol production up to 6 and 3% relative to the APR and RPR, respectively. Moreover, in the OAR, 2% and 14 degrees C increase in the feed flow rate and temperature, correspondingly, results in 3.5% improvement in the methanol production. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.