Recently, there has been a research trend towards clean energy sources such as fuel cells, owing to their high efficiency and close-to-zero emissions. However, the efficiency level depends on the design, and physical experiments are time-consuming requiring expensive materials; therefore, a realistic numerical simulation is crucial to test different designs and conditions. In this paper, the fluid dynamics and electrochemical reactions in direct methanol fuel cells (DMFC) are mathematically modeled and numerically simulated using computational fluid dynamics (CFD) techniques within the OpenFOAM software. The profiles of temperature, reactants, and products flow through the anodic and cathodic chambers of DMFC are derived from the equations of continuity, momentum, species transport, and electrochemical reactions are simulated to study two flow field geometries of a DMFC, parallel channels, and a serpentine channel. A methodology to obtain the crossover current density is presented, and its effect is evaluated on the DMFC behavior. The accuracy and confidence of the results are validated with a case reported in the literature.