An Innovative Approach to Predict the Diffusion Rate of Reactant’s Effects on the Performance of the Polymer Electrolyte Membrane Fuel Cell

As the analytical solution can provide much more accurate and reliable results in a short time, in the present study, an innovative analytical approach based on the perturbation method is proposed. The governing equations, which consist of continuity, momentum, species, and energy equations, are solved analytically by using the regular perturbation method. The perturbation parameter is the function of the penetration (diffusion) velocity. At first, the momentum and continuity equations are coupled together and solved analytically to find the velocity distribution. In the polymer electrolyte membrane fuel cell (PEMFC), the penetration velocity can be increased by increasing the gas diffusion layer (GDL) porosity and the operating pressure of the PEMFC. The solution showed that by increasing the perturbation parameter from 0 to the higher values, the diffusion of the reactant toward the gas channel to the GDL is improved too, leading to the enhancement of the performance of the PEMFC. The axial velocity profile tends to the bottom of the flow channel. This fact helps the reactant to transfer into the reaction area quickly. For perturbation parameter 0.5, in the species equation, the distribution of species in the reaction areas is more regular and uniform. For the lower magnitudes of the Peclet number, the species gradient is enhanced, and as a result, the concentration loss takes place at the exit region of the channel. Also, increasing the perturbation parameter causes an increase in the temperature gradient along the flow channel. For higher perturbation parameters, there is a higher temperature gradient from the bottom to the top of the track in the flow direction. The temperature profile in the y direction has a nonlinear profile at the inlet region of the channel, which is converted to the linear profile at the exit region. To verify the extracted analytical results, the three-dimensional computational fluid dynamic model based on the finite volume method is developed. All of the achieved analytical results are compared to the numerical ones in the same condition with perfect accordance.