Microfluidic fuel cells (MFCs) are effective energy conversion devices in microscales due to their simplicity and high energy density as they are based on laminar co-flow of reactants in microchannels without a separator. However, fuel utilization at practical flow rates remains as one of the important challenges. In this study, a two-dimensional (2D) model is developed based on Brinkman equations for flow, Fick's law for mass transport and Butler-Volmer equations for reaction kinetics to study MFCs and address the effects of geometric and operation parameters on the performance and fuel utilization. Commercial finite-element software, COMSOL, is used to solve coupled equations and to analyze the performance of MFCs for different Peclet numbers, concentrations of reactants and geometric variables. According to simulation results, the 2D model compares very well with the three-dimensional model based on Navier-Stokes equations and with the experimental data reported in the literature. Moreover, the model is used for the analysis of the proposed branched-channel design of microfluidic cells that improves the fuel utilization and power output of the MFC. (C) 2019 Elsevier Ltd. All rights reserved.