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The present study was conducted to model the fuel cells with the aim of energy production and wastewater treatment. In the present study, the obtained equations for the model were solved using numerical methods in MATLAB software. First, the series of ordinary differential equations (ODE) for CB were solved in the time interval of tn and tn+Δt. The new CB values obtained in each step were used to obtain other new CB values in the time interval of tn to tn+Δt, and CL concentration values at a time of tn were used to calculate rL and CE rates to obtain rE. Non-linear methods were used to solve partial differential equations (PDE). The geometry of the microbial fuel cell including the volume and surface area of the anode, operating conditions including pH, biomass concentration, and initial concentrations of substrate and medium, and parameters related to the electrical circuit including external resistance and cathode potential was directly adapted from the article by Delaney et al. Some kinetic parameters such as the rate constant for the reduction of thionine and its standard potential had been also calculated in another article by Roller et al. The results showed that by combining the current intensity-time curves obtained from the study by Delaney et al, a total value of 12.6 C was obtained. It means that only 74.8 C was the result of glucose oxidation. Using these data, the value of YQ=0.37, and accordingly the real value of glucose efficiency on Ys=0.22 mol.mol- was obtained. These values provide a better fit of current intensity-time and electric charge-time curves to experimental data.
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