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Where: τ = VQ This system can be solved if we have an expression for the methanol crossover flux. Methanol is transported through the membrane by convection and diffusion. dCM N = −DM CH 3OH +CM v where v is the convective flow velocity. CH 3OH CH 3OH dz CH 3OH Sundmacher et al [1] gives an expression for v. It was deduced from Schlogl’s expression for v and the Nernst-Plank equation for proton transport through the membrane: iCell +CM .kP .dP kφF H+μdzkdP dPP−P v=. −P. where =A C μDMkμdz dzdM H++CM.φ R.T H+ μ Knowing an expression for v, the previous equation can be solved analytically. DM Pe.exp(Pe) v.dM N = CH3OH .C . where Pe= isthePecletnumber CH3OH dM CH3OH exp(Pe)−1 DM CH 3OH A code was written on Matlab (See Appendix) to solve these equations in which operating conditions were given. To be consistent with experimental data, this code computes the cell current density for a given cell voltage. In order to do this, the current density should be expressed as a function of the cell voltage and anode and cathode over potential. i = − κ M (U − U 0 + η − η ) Cell dM A C - 67 -PDF Image | Direct Methanol Fuel Cell (DMFC) Performance
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