RESEARCH ARTICLE Modeling of polymer electrolyte membrane fuel cell with circular and elliptical cross‐section gas channels: A novel procedure Nima Ahmadi 1,2 | Abdolrahman Dadvand 2 | Iraj Mirzaei 2 | Sajad Rezazadeh 2 1 Department of Mechanical Engineering, Faculty of Shaheed Beheshti, Technical and Vocational University (TVU), Urmia, Iran 2 Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran Correspondence Nima Ahmadi, Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran. Email: nima.ahmadi.eng@gmail.com Summary The main objective of this paper is to develop an analytical solution based on the perturbation method to solve the continuity and momentum equations governing the flow in gas channels of a PEMFC having circular and elliptical cross sections. The equations are solved in both the anode and cathode gas channels with appropriately defined perturbation parameters to obtain the velocity profile in these channels. It was observed that by changing the circular cross section to an elliptical one (ie, increasing the value of perturbation parameter), the axial velocity increases. As a result, the penetration of species into the reaction areas decreases. Then, the effect of species penetration speed on the performance of PEMFC is discussed. Increasing the penetration speed (ie, radial velocity) of the reactant gases causes the maximum value of the gas velocity in the channel to decrease. This would imply that the diffusion rate of the reactant species to the reaction areas, and thereby the cell performance would be optimized. Apart from the analytical solution, 3‐D numerical solution of the governing equations using collocated finite volume method along with the SIMPLE algorithm is also performed. The results are validated against the available published data. The numerical results confirm that by converting the circular cross section to the elliptical one, while other conditions are fixed, the PEMFC produces less current density. KEYWORDS analytical solution, numerical procedure, PEMFC, performance, perturbation method 1 | INTRODUCTION Among the energy conversion devices, the fuel cell is a promising future energy resource. Among the various types of fuel cells, the polymer electrolyte membrane fuel cell (PEMFC) is of great importance due to its high power density. In this system, the electrochemical energy is converted to the electrical energy. 1-4 A typical PEMFC Nomenclature: Re, Reynolds number; U, Average velocity of fluid flow [dimensionless]; F, Faraday constant [C/mol]; I, Local current density [A/m 2 ]; C, Mass fraction; ω, Porosity [dimensionless]; D eff , Mass diffusion coefficient [m 2 /s]; S, Source term; T, Temperature [K]; κ eff , Electrode electronic conductivity (S/m); Φ, Phase potential [V]; V cell , Cell voltage [volt]; r, Radius [Dimensionless]; θ, Angle [dimensionless]; ε, Perturbation parameter [dimensionless]; P, Pressure [Pa]; u ! , Velocity vector [m/s]; PEMFC, Protonic electrolyte membrane fuel cell; μ, Viscosity [kg/m·s]; ρ, Density (kg/ m 3 ); γ eff , Effective electrode thermal conductivity (W/m/K) Subscripts: eff, Effective; In, Inlet; m, Mass; mom, Momentum; sol, Solid phase; mem, Membrane phase Received: 4 January 2018 Revised: 17 February 2018 Accepted: 3 March 2018 DOI: 10.1002/er.4069 Int J Energy Res. 2018;1–18. Copyright © 2018 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/er 1