In order to overcome the apparent limitations of large-scale microwave processing, a microwave heating system with a screw propeller was utilized for biodiesel synthesis. To elucidate the heating dynamics and reaction process in the reactor, a comprehensive physics-based model was developed. A step-by-step algorithm based on implicit function, level set methods, and Arbitrary Lagrangian-Eulerian Formulation (ALE) machinery was proposed to compute the microwave heating process with chemical reaction and stirring. Material properties applied in the simulation were expressed as bivariate functions of the reaction solution's component and temperature. The temperature and reactant concentration of the microwave reactor outlet were measured and compared to simulation results to validate the simulation model. By using the proposed model, the heating process with different rotating speeds, material composition (Teflon and metal), pitch, and blade widths of the screw propeller and inlet velocities were also calculated to determine their effect on the temperature distribution of the reactor. (C) 2019 Elsevier Ltd. All rights reserved.