Development of analytical and numerical solutions for direct ethanol fuel cells

This paper presents an analytical solution to calculate the mole fraction of the major species involved in the oxidation of ethanol on the anode side, and the reduction of oxygen on the cathode side of a direct ethanol full cell. The equations of the species are solved using two mathematical tools: Separation of variables and Laplace transform. The solutions obtained with the two methods are equivalent and describe the mole fraction of chemical species. The results obtained with the analytical solution were compared with the data obtained with the two-dimensional model, solved numerically with the finite difference method in space and Runge-Kutta method in time. The results of mole fraction of the species obtained through the analytical solution are used to calculate, at a lower cost, the overpotential losses and the direct ethanol fuel cell voltage. The results obtained are in accordance with the experimental data found in the literature for the catalysts Pt-Re-Sn/t-MWCNTs and Pt-Re-Sn/MCN.