Numerical investigation of microwave heating and scale-up challenges in dielectric reactor systems

Microwave (MW) heating provides selective and volumetric energy delivery for endothermic catalytic processes, enhancing both catalytic activity and energy efficiency. However, its practical deployment remains constrained by shallow penetration depth, non-uniform temperature fields, and scale-up limitations. In this study, an electromagnetic–thermal coupled model was developed for a dielectric packed-bed reactor and validated against temperature measurements at twenty-four axial and radial locations within a waveguide-based MW system, showing reasonable agreement with experiments, with a mean absolute percentage error (MAPE) of about 10% and coefficients of determination (R 2 ) reaching up to 0.74. Heating performance was evaluated using the coefficient of variation of temperature (COV T ) and the microwave energy efficiency ( η ) for effective power utilization. The results indicate that penetration-depth-driven attenuation and cavity geometry collectively govern axial and radial temperature gradients. Reactor height was identified as the dominant geometric parameter, exhibiting a confined design window where both low COV T and high average temperatures were achieved, while further increase in height reduces heating uniformity and overall performance due to cumulative axial attenuation. Reactor diameter further exhibited a non-monotonic trend resulting from the interplay between dielectric attenuation and the spatial redistribution of absorbed microwave energy. These findings demonstrate that linear geometric enlargement is fundamentally limited by electromagnetic field behavior and provide a predictive framework for designing MW-assisted catalytic reactors with improved temperature uniformity, energy efficiency, and scalability. Within the investigated reactor-size combinations, the overall heating performance was quantified in terms of temperature uniformity and energy efficiency, average temperatures in the range of 390–910 °C, COV T values of 0.09–0.14, and microwave energy efficiencies of 43–50%.