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PROTON EXCHANGE MEMBRANE FUEL CELL (PEMFC)
                                                                                   MODELING and SIMULATION
                                                                                   using COMSOL MULTIPHYSICS
                                                                                                                                           Ercüment SÖNMEZ – Coşkun TOPRAK
                                                                                                                                       Supervisor : Prof. Dr. Mustafa DEMİRCİOĞLU
                                                                                                             Ege University, Engineering Faculty, Department of Chemical Engineering, 35100 Bornova, İZMİR


                                                                                                             ABSTRACT                                                                                                                                                                                        ÖZET
   ABSTRACT/ÖZET




                       Energy generation and consumption plays an important role worldwide in both the advancement of modern technology and the                                                                                            Enerjinin üretimi ve tüketimi; teknolojinin gelişimi ve global ekonomiye etkiyen eğilimler üzerinde büyük rol oynamaktadır. Fosil
                       trends on global economy. Fossil fuel sources have been drastically used during last century which has caused a series of                                                                                           yakıt kaynakları son yüzyıl içerisinde büyük ölçeklerde kullanılmış olup, etkileri ciddi çevresel sorunlara neden olmaktadır. Sonuç
                       environmental problems. As a concequence, alternative energy sources have been sought to diminish these problems. Research                                                                                          olarak, bu sorunları azaltmak için alternatif enerji kaynakları üzerinde çalışmalar devam ediyor. Yakıt hücreleri üzerindeki
                       on fuel cell technology has been boomed recently to supply a response both economically and environmentally solutions to the                                                                                        araştırmalar; artan enerji talebine, hem ekonomik hemde çevresel etki yönünden bir cevap olabilmesi için, son zamanlarda artış
                       increasing energy demand. In this project, the effects of various design parameters and operating conditions on PEM fuell cell                                                                                      göstermiştir. Bu projede, PEM yakıt hücresinin performansını etkileyen çeşitli çalışma koşulları ve tasarım değişkenleri üzerinde
                       performance have been studied by using a pionering software “COMSOL Multiphysics” which requires integrated engineering                                                                                             çalışılmış olup; diğer mühendislik dalları ile etkileşimli ve ileri derecede mühendislik bilgisi gerektiren ve bu konuda öncü bir yazılım
                       disciplineand sound knowledge.                                                                                                                                                                                      olan “COMSOL Multiphysics”kullanılmıştır.


                                               AC/DC MODULE                                                                                                    ACOUSTICS MODULE                                                                  CHEMICAL ENGINEERING MODULE                                                           EARTH SCIENCE MODULE

                                                                                                                                                                   Contains built‐in application modes and                                                                                                                                  Models single and coupled processes 
                                               Simulates electrical components and                                                                                                                                                                           Analyzes CFD,mass and energy balances 
                                                                                                                                                                   boundary settings for the modeling of                                                                                                                                    for geologic and environmental 
                                               devices that depend on electrostatics,                                                                                                                                                                        coupled to chemical reaction kinetics. 
                                                                                                                                                                   acoustic wave propagation in solids and                                                                                                                                  phenomena particularly based around 
                                               magnetostatics and electromagnetic                                                                                                                                                                            Incorporates a plethora of application 
                                                                                                                                                                   stationary fluids.                                                                                                                                                       sub‐surface flow. 
                                               quasi‐statics applications, particulary                                                                                                                                                                       modes for the field of the transport 
                                               coupled to other physics.                                                                                                                                                                                     phenomena including ionic transport 
                        Generator                                                                                                      Flow Duct                                                                                      Centrifugal Pump                                                             Discrete Fracture
                                                                                                                                                                                                                                                             and multicomponent diffusion.
COMSOL




                                       HEAT TRANSFER MODULE                                                                                                                                                     COMSOL MULTIPHYSICS                                                                                                          MEMS MODULE

                                                                                                                                    A finite‐element based program for simulating unlimited multiphysics and single‐physic applications. It incorporates                                                                                   Represents coupled processes in micro‐
                                             Consists of advanced application modes 
                                                                                                                                    easy‐to‐use application interfaces, complete control over meshing and powerful solvers. COMSOL Multiphysics                                                                                            electro‐mechanical and microfluidic 
                                             for the analysis of heat transfer by 
                                                                                                                                    also offers an extensive and well‐managed interface to MATLAB and its toolboxes for a large variety of                                                                                                 devices. Incorporates specific 
                                             conduction, convection, and radiation.
                                                                                                                                    programming, preprocessing and post‐processing possibilities.                                                                                                                                          multiphysics couplings for applications 
                                             Specific for industrial applications such 
                                                                                                                                    Similar interfaces are offered with COMSOL Multiphysics which are COMSOL Script,                                                                                                                       such as electroosmotic flow, film 
                                             as electronics cooling and process 
                                                                                                                                    COMSOL Reaction Engineering Lab.
                    Brake Disc of  a Car                                                                                                                                                                                                                                                                             Comb Drive            damping, and fluid‐structure interaction.
                                             engineering. 

                                                    RF MODULE                                                                                                                                                                                             CAD IMPORT MODULE
                                                                                                                                                  STRUCTUAL MECHANICS MODULE                                                                                                                                                              MATERIAL LIBRARY

                                              Characterizes electromagnetic fields,                                                                                                                                                                                                                                 Internal material property database with more than 
                                                                                                                                                                   Performs classical stress‐strain analyses                                                 Facilities the reading of most 
                                              currents, and waves for RF, microwave,                                                                                                                                                                                                                                2500 materials and 20000 properties. The database 
                                                                                                                                                                   with full multiphysics capabilities.                                                      industry‐standard CAD formats. 
                                              optical and other high frequency                                                                                                                                                                                                                                      contains temperature dependence of electrical, thermal, 
                                                                                                                                                                   Comprises nonlinear material models,                                                      Includes add‐on packages that 
                                              devices.                                                                                                                                                                                                                                                              and structural properties of solid materials.
                                                                                                                                                                   large deformation and contact abilities;                                                  support the file formats for specific 
                                                                                                                                                                   all able to be freely coupled to other                                                    CAD programs geometry kernels.
                                                                                                                                                                                                                                      Communication 
                                                                                                                                                                   physics.
                     Microwave Oven                                                                                               Car Wheel Rim
                                                                                                                                                                                                                                         Mast


                   FUEL CELL                                                                                                                                                                                                                                                                                                                                            PEM FUEL CELL
                   A fuel cell is an energy generation device that converts hydrogen and                                                                                                                                                                                           PEM fuel cell use a solid polymer membrane (a thin plastic film) as the
                   oxygen into usable electric power by way of simple chemical reactions. As a                                                                                                                                                                                     electrolyte. This polymer is permeable to protons when it is saturated
                   simple electrochemical device, a fuel cell does not actually burn fuel,                                                                                                                                                                                         with water, but it does not conduct electrons.
                                                                                                                                                                                                                             ‐        ‐
                                                                                                                                                                                                                                      ‐
                                                                                                                                                                                                                             ‐
                   allowing it to operate pollution‐free. The only emissions produced by a fuel
                   cell are pure water and heat. This also makes a fuel cell quiet, dependable,                                                                                                                                                                                    The fuel for the PEMFC is hydrogen and the charge carrier is the hydrogen
                   and very fuel‐efficient.                                                                                                                                                                                                                                        ion (proton). At the anode, the hydrogen molecule is split into hydrogen
                                                                                                                                                                                    Fuel Hydrogen                                                         Oxygen (O2) 
                                                                                                                                                                                                                            ‐
                                                                                                                                                                                                                                                                                   ions (protons) and electrons. The hydrogen ions permeate across the
                                                                                                                                                                                                                            ‐
                                                                                                                                                                                              (H2)                                                        İn the air
                   A fuel cell has two electrodes, one positive and one negative, called the                                                                                                                                                                                       electrolyte to the cathode while the electrons flow through an external
                                                                                                                                                                                                                                 ++
PEMFC




                   cathode and the anode. The reactions that produce electricity take place at                                                                                                                                                                                     circuit and produce electric power. Oxygen, usually in the air, is supplied
                                                                                                                                                                                                                             ‐
                   the electrodes. Every fuel cell also has an electrolyte, which carries                                                                                                                                                                                          to the cathode and combines with the electrons and the hydrogen ions to
                                                                                                                                                                                                                             ‐
                   electrically charged particles from one electrode to the other, and a                                                                                                                                                                                           produce water. The reactions at the electrodes are as follows:
                   catalyst, which accelerates the reactions at the electrodes.                                                                                                                                                                                                                                                               2H2      4H+ + 4e‐
                                                                                                                                                                                                                                                                                                                    Anode Reactions:
                                                                                                                                                                                                                                 ++



                                                                                                                                                                                                                                                                                                                                 Cathode Reactions: O2 + 4H+ + 4e‐
                   Some types of fuel cell:                                                                                                                                                                                                                                                                                                                                                 2H2O
                                                                                                                                                                                           Used Fuel 
                                                                                                                                                                                                                                                          Air + Water Vapor
                                                                                                                                                                                         Recirculates
                      Alkaline Fuel Cells (AFCs)                                                                                                                                                                                                                                                                          Overall Cell Reactions:                       2H2 + O2     2H2O
                      Phosphoric Acid Fuel Cells (PAFCs)
                                                                                                                                                                                                                                                                                                                                                                PEMFC General Properties
                      Molten‐Carbonate Fuel Cells (MCFCs)                                                                                                                          Flow Field Plate                                                        Flow Field Plate
                                                                                                                                                                                                                                                                                      Operating 
                                                                                                                                                                                                                                                                                                    SystemOutput   Efficiency        Applications          Advantages            Disadvantages
                      Solid Oxide Fuel Cells (SOFCs)                                                                                                                                                                                                                                 Temperature
                                                                                                                                                                                                    Anode                                                  Cathode
                      Polymer Electrolyte Membrane Fuel Cells (PEMFCs)                                                                                                                                                                                                                                                                                   •Solid electrolyte 
                                                                                                                                                                                               Catalyst                                                    Catalyst                                                                                                                 • Requires 
                                                                                                                                                                                                                                                                                                                                   • Back‐up power 
                                                                                                                                                                                                                                                                                                                                                       reduces corrosion & 
                      Direct Methanol Fuel Cells (DMFCs)                                                                                                                                                                                                                                                                                                                       expensive catalysts 
                                                                                                                                                                                                                                                                                                                                   • Portable power 
                                                                                                                                                                                            (Platinum)                                                     (Platinum)                                                                                        electrolyte 
                                                                                                                                                                                                                                                                                                                                                                               • High sensitivity to 
                                                                                                                                                                                                                                                                                                                                        • Small 
                                                                                                                                                                                                                     Proton Exchange Membrane                                                                                                              management 
                                                                                                                                                                                                                                                                                                                    40‐60%
                                                                                                                                                                                                                                                                                      50 ‐ 100°C    1kW – 250kW
                      Zinc Air Fuel Cells (ZAFCs)                                                                                                                                                                                                                                                                                                                                 fuel impurities 
                                                                                                                                                                                                                                                                                                                                      distributed 
                                                                                                                                                                                                                                                                                                                                                              problems 
                                                                                                                                                                                                                                                                                                                    electric 
                                                                                                                                                                                                                                                                                                                                                                               • Low temperature 
                                                                                                                                                                                                                                                                                                                                      generation 
                                                                                                                                                                                                                                                                                                                                                        • Low temperature 
                      Biological Fuel Cells (BFCs)                                                                                                                                                          Proton Exchange Membrane Fuel Cell (PEMFC)                                                                                                                              waste heat 
                                                                                                                                                                                                                                                                                                                                   • Transportation 
                                                                                                                                                                                                                                                                                                                                                          • Quick start‐up 




                                                                                                                                                                                                                                                          DRAW and MESH MODE
                                                                                                  MODELING PROCESS                                                                                                                                                                                                                        SUBDOMAIN MODE
                           The model uses current balances, mass balances (Maxwell‐Stefan diffusion for reactant, water and nitrogen
                                                                                                                                                                                                                                                     2D design is selected using
                           gas), and momentum balances (gas flow) to simulate a 2D PEM fuel cell’s behavior.
                                                                                                                                                                                                                                                     rectangular coordinates. After
                                           Application Modes                                Module                Dependent Variables                              Governing Equations
                                                                                                                                                                                                                                                     specifying geometry (1) mesh
                                                                                                                                                                                                                                                                                                                                           As created in draw mode, three 
                                     COMSOL                                         Conductive Media DC                Solid Phase 
                                                          Electromagnetics
                                                                                                                                                                                                                                                     mode (2) is applied to control
                                    Multiphysics                                        (Electrodes)                    Potential
                                                                                                                                                                                                                                                                                                                                           subdomains (1, 2, 3) are defined as 
                                                                                                                                                                                                                                                     the distribution of elements
                                                                                                                                                                                                                                                                                                                                           anode, membrane, and cathode. In each
                                     COMSOL                                         Conductive Media DC                    Electrolyte 
PEM MODELING




                                                          Electromagnetics
                                                                                                                                                                                                                                                     easily. A mesh is a partition of
                                    Multiphysics                                       (Membrane)                           Potential
                                                                                                                                                                                                                                                                                                                                           Subdomain, material properties and 
                                                                                                                                                                                                                                                     the geometry model into small
                                     Chemical                Momentum 
                                                                                                                                                                                                                                                                                                                                           boundaries are determined freely.
                                                                                          Darcy’s Law                       Pressure
                                Engineering Module            balance
                                                                                                                                                                                                                                                     units of simple shapes. Dividing
                                                                                Maxwell‐Stafen Diffusion 
                                     Chemical                                                                       Mass Fraction of
                                                                                                                                                                                                                                                     current geometry into meshes
                                                            Mass balance            and Convection
                                Engineering Module                                                                   H2 and H2O
                                                                                  (Anode side) [Msa]
                                                                                                                                                                                                                                                     (small shapes) provides full
                                                                                Maxwell‐Stafen Diffusion 
                                                                                                                                                                                                                                          ( 1)                                                      ( 2)
                                     Chemical                                                                       Mass Fraction of 
                                                                                                                                                                                                                                                     control of boundaries and easy‐
                                                            Mass balance            and Convection
                                Engineering Module                                                                  O2, H2O and N2
                                                                                 (Cathode side) [MSc]
                                                                                                                                                                                                                                                     solve problem.

                                                                                                                                                                                                                                                                                                                                   PARAMETRIC INVESTIGATION
                                                                                                     BOUNDARY MODE                                                                                                                                        SOLVE and POST MODE
                                                                                                                                                                          SOLVE MODE
                                                       Electrodes                      Membrane                                 Darcy                                MSa                              MSc

                                                                                                                                                                                                                                                                 COMSOL Multiphysics includes a set 
                                            Boundary               Type         Boundary             Type         Boundary                Type          Boundary            Type         Boundary             Type
                                                                                                                                                                                                                                                                 of solvers for PDE‐based problems 
                                             1‐7,9,14‐
                                                                    EI              11,12               EI                 1               P                  1              MF                13               F
                                                                                                                                                                                                                                                                 for linear and non‐linear equations. 
                                             16,18‐22

                                                                                                                                                                                                                                                                 In post mode, given a solver/mesh 
                                                   8                EP               10              ICF                   4               P                  4              CF                21              CF
                                                                                                                                                                                                                                                                 pair, a variety of tools are available 
                                                   10               ICF              13              ICF               10                 I/O                 10             F                 22              MF
                                                                                                                                                                                                                                                                 for data visualization. In PEM 
                                                   13               ICF                                                13                 I/O
                                                                                                                                                                                                                                                                 Modeling, power generation, 
                                                                                                                                                                                                                                                                                                                    Various parameters such as temperature , pressure, 
                                                                                                                                                                                                                                                                 efficiency, geometry and raw
                                                   17               EP                                                 21                  P
                                                                                                                                                                                                                                                                                                                    geometry/mesh, properties of used materials ( porosity, 
                                                                                                                                                                                                                                                                 material properties are analyzed .
                                                                                                                       22                  P
                                                                                                                                                                                                                                                                                                                    conductivity etc.) is investigated to analyze the effects on 
                                                       CF : Convective Flow                    EI : Electric Insulation                        EP : Electric Potential                   F : Flux
                                                                                                                                                                                                                                                                                                                    PEM fuel cell performance.
                                                       ICF : Inward Current Flow               I/O : Inflow/Outflow                            MF : Mass Fraction                        P : Pressure



                   DESIGNING & BUILDING FUEL CELLS, Colleen S. Spiegel , McGraw Hill Book Co. , 2007          ‐    INTRODUCTION TO CHEMICAL ENGINEERING COMPUTING, Bruce A. Finlayson, John Wiley Inc., 2006 ‐    CONTROL OF FUEL CELL POWER SYSTEMS (Priciples, Modeling, Analysis
   REFERENCES




                   and Feedback Design)”, Jay T. Pukrushpan, Anna G. Stefanopoulou, Huei Peng, Springer, 2005         ‐     PROCESS MODELıNG AND SıMULATıON WıTH FıNıTE ELEMENT METHODS, William B. J. Zimmerman, World Scientific Publishing Co., 2004 ‐  FUEL CELL HANDBOOK,
                   EG&G Technical Services, Inc., Seventh Edition, U.S. Department of Energy Office of Fossil Energy National Energy Technology Laboratory, November 2004 ‐ AN INTRODUCTION TO FUEL CELLS AND HYDROGEN TECHNOLOGY, Brian Cook, Heliocentris, December 2001

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Diploma Project - Poster

  • 1. PROTON EXCHANGE MEMBRANE FUEL CELL (PEMFC) MODELING and SIMULATION using COMSOL MULTIPHYSICS Ercüment SÖNMEZ – Coşkun TOPRAK Supervisor : Prof. Dr. Mustafa DEMİRCİOĞLU Ege University, Engineering Faculty, Department of Chemical Engineering, 35100 Bornova, İZMİR ABSTRACT ÖZET ABSTRACT/ÖZET Energy generation and consumption plays an important role worldwide in both the advancement of modern technology and the Enerjinin üretimi ve tüketimi; teknolojinin gelişimi ve global ekonomiye etkiyen eğilimler üzerinde büyük rol oynamaktadır. Fosil trends on global economy. Fossil fuel sources have been drastically used during last century which has caused a series of yakıt kaynakları son yüzyıl içerisinde büyük ölçeklerde kullanılmış olup, etkileri ciddi çevresel sorunlara neden olmaktadır. Sonuç environmental problems. As a concequence, alternative energy sources have been sought to diminish these problems. Research olarak, bu sorunları azaltmak için alternatif enerji kaynakları üzerinde çalışmalar devam ediyor. Yakıt hücreleri üzerindeki on fuel cell technology has been boomed recently to supply a response both economically and environmentally solutions to the araştırmalar; artan enerji talebine, hem ekonomik hemde çevresel etki yönünden bir cevap olabilmesi için, son zamanlarda artış increasing energy demand. In this project, the effects of various design parameters and operating conditions on PEM fuell cell göstermiştir. Bu projede, PEM yakıt hücresinin performansını etkileyen çeşitli çalışma koşulları ve tasarım değişkenleri üzerinde performance have been studied by using a pionering software “COMSOL Multiphysics” which requires integrated engineering çalışılmış olup; diğer mühendislik dalları ile etkileşimli ve ileri derecede mühendislik bilgisi gerektiren ve bu konuda öncü bir yazılım disciplineand sound knowledge. olan “COMSOL Multiphysics”kullanılmıştır. AC/DC MODULE ACOUSTICS MODULE CHEMICAL ENGINEERING MODULE EARTH SCIENCE MODULE Contains built‐in application modes and  Models single and coupled processes  Simulates electrical components and  Analyzes CFD,mass and energy balances  boundary settings for the modeling of  for geologic and environmental  devices that depend on electrostatics,  coupled to chemical reaction kinetics.  acoustic wave propagation in solids and  phenomena particularly based around  magnetostatics and electromagnetic  Incorporates a plethora of application  stationary fluids.  sub‐surface flow.  quasi‐statics applications, particulary  modes for the field of the transport  coupled to other physics. phenomena including ionic transport  Generator Flow Duct Centrifugal Pump  Discrete Fracture and multicomponent diffusion. COMSOL HEAT TRANSFER MODULE COMSOL MULTIPHYSICS MEMS MODULE A finite‐element based program for simulating unlimited multiphysics and single‐physic applications. It incorporates Represents coupled processes in micro‐ Consists of advanced application modes  easy‐to‐use application interfaces, complete control over meshing and powerful solvers. COMSOL Multiphysics electro‐mechanical and microfluidic  for the analysis of heat transfer by  also offers an extensive and well‐managed interface to MATLAB and its toolboxes for a large variety of devices. Incorporates specific  conduction, convection, and radiation. programming, preprocessing and post‐processing possibilities. multiphysics couplings for applications  Specific for industrial applications such  Similar interfaces are offered with COMSOL Multiphysics which are COMSOL Script, such as electroosmotic flow, film  as electronics cooling and process  COMSOL Reaction Engineering Lab. Brake Disc of  a Car Comb Drive damping, and fluid‐structure interaction. engineering.  RF MODULE CAD IMPORT MODULE STRUCTUAL MECHANICS MODULE MATERIAL LIBRARY Characterizes electromagnetic fields,  Internal material property database with more than  Performs classical stress‐strain analyses  Facilities the reading of most  currents, and waves for RF, microwave,  2500 materials and 20000 properties. The database  with full multiphysics capabilities.  industry‐standard CAD formats.  optical and other high frequency  contains temperature dependence of electrical, thermal,  Comprises nonlinear material models,  Includes add‐on packages that  devices. and structural properties of solid materials. large deformation and contact abilities;  support the file formats for specific  all able to be freely coupled to other  CAD programs geometry kernels. Communication  physics. Microwave Oven Car Wheel Rim Mast FUEL CELL PEM FUEL CELL A fuel cell is an energy generation device that converts hydrogen and PEM fuel cell use a solid polymer membrane (a thin plastic film) as the oxygen into usable electric power by way of simple chemical reactions. As a electrolyte. This polymer is permeable to protons when it is saturated simple electrochemical device, a fuel cell does not actually burn fuel, with water, but it does not conduct electrons. ‐ ‐ ‐ ‐ allowing it to operate pollution‐free. The only emissions produced by a fuel cell are pure water and heat. This also makes a fuel cell quiet, dependable, The fuel for the PEMFC is hydrogen and the charge carrier is the hydrogen and very fuel‐efficient. ion (proton). At the anode, the hydrogen molecule is split into hydrogen Fuel Hydrogen  Oxygen (O2)  ‐ ions (protons) and electrons. The hydrogen ions permeate across the ‐ (H2) İn the air A fuel cell has two electrodes, one positive and one negative, called the electrolyte to the cathode while the electrons flow through an external ++ PEMFC cathode and the anode. The reactions that produce electricity take place at circuit and produce electric power. Oxygen, usually in the air, is supplied ‐ the electrodes. Every fuel cell also has an electrolyte, which carries to the cathode and combines with the electrons and the hydrogen ions to ‐ electrically charged particles from one electrode to the other, and a produce water. The reactions at the electrodes are as follows: catalyst, which accelerates the reactions at the electrodes. 2H2      4H+ + 4e‐ Anode Reactions: ++ Cathode Reactions: O2 + 4H+ + 4e‐ Some types of fuel cell: 2H2O Used Fuel  Air + Water Vapor Recirculates Alkaline Fuel Cells (AFCs) Overall Cell Reactions: 2H2 + O2     2H2O Phosphoric Acid Fuel Cells (PAFCs) PEMFC General Properties Molten‐Carbonate Fuel Cells (MCFCs) Flow Field Plate Flow Field Plate Operating  SystemOutput Efficiency  Applications  Advantages Disadvantages Solid Oxide Fuel Cells (SOFCs) Temperature Anode Cathode Polymer Electrolyte Membrane Fuel Cells (PEMFCs) •Solid electrolyte  Catalyst Catalyst • Requires  • Back‐up power  reduces corrosion &  Direct Methanol Fuel Cells (DMFCs) expensive catalysts  • Portable power  (Platinum) (Platinum) electrolyte  • High sensitivity to  • Small  Proton Exchange Membrane management  40‐60% 50 ‐ 100°C  1kW – 250kW Zinc Air Fuel Cells (ZAFCs) fuel impurities  distributed  problems  electric  • Low temperature  generation  • Low temperature  Biological Fuel Cells (BFCs) Proton Exchange Membrane Fuel Cell (PEMFC) waste heat  • Transportation  • Quick start‐up  DRAW and MESH MODE MODELING PROCESS SUBDOMAIN MODE The model uses current balances, mass balances (Maxwell‐Stefan diffusion for reactant, water and nitrogen 2D design is selected using gas), and momentum balances (gas flow) to simulate a 2D PEM fuel cell’s behavior. rectangular coordinates. After Application Modes Module Dependent Variables Governing Equations specifying geometry (1) mesh As created in draw mode, three  COMSOL  Conductive Media DC  Solid Phase  Electromagnetics mode (2) is applied to control Multiphysics (Electrodes) Potential subdomains (1, 2, 3) are defined as  the distribution of elements anode, membrane, and cathode. In each COMSOL  Conductive Media DC Electrolyte  PEM MODELING Electromagnetics easily. A mesh is a partition of Multiphysics (Membrane) Potential Subdomain, material properties and  the geometry model into small Chemical Momentum  boundaries are determined freely. Darcy’s Law Pressure Engineering Module balance units of simple shapes. Dividing Maxwell‐Stafen Diffusion  Chemical  Mass Fraction of current geometry into meshes Mass balance and Convection Engineering Module H2 and H2O (Anode side) [Msa] (small shapes) provides full Maxwell‐Stafen Diffusion  ( 1) ( 2) Chemical  Mass Fraction of  control of boundaries and easy‐ Mass balance and Convection Engineering Module O2, H2O and N2 (Cathode side) [MSc] solve problem. PARAMETRIC INVESTIGATION BOUNDARY MODE SOLVE and POST MODE SOLVE MODE Electrodes Membrane Darcy MSa MSc COMSOL Multiphysics includes a set  Boundary Type Boundary Type Boundary Type Boundary Type Boundary Type of solvers for PDE‐based problems  1‐7,9,14‐ EI 11,12 EI 1 P 1 MF 13 F for linear and non‐linear equations.  16,18‐22 In post mode, given a solver/mesh  8 EP 10 ICF 4 P 4 CF 21 CF pair, a variety of tools are available  10 ICF 13  ICF 10 I/O 10 F 22 MF for data visualization. In PEM  13 ICF 13 I/O Modeling, power generation,  Various parameters such as temperature , pressure,  efficiency, geometry and raw 17 EP 21 P geometry/mesh, properties of used materials ( porosity,  material properties are analyzed . 22 P conductivity etc.) is investigated to analyze the effects on  CF : Convective Flow  EI : Electric Insulation  EP : Electric Potential  F : Flux PEM fuel cell performance. ICF : Inward Current Flow  I/O : Inflow/Outflow  MF : Mass Fraction P : Pressure DESIGNING & BUILDING FUEL CELLS, Colleen S. Spiegel , McGraw Hill Book Co. , 2007 ‐ INTRODUCTION TO CHEMICAL ENGINEERING COMPUTING, Bruce A. Finlayson, John Wiley Inc., 2006 ‐ CONTROL OF FUEL CELL POWER SYSTEMS (Priciples, Modeling, Analysis REFERENCES and Feedback Design)”, Jay T. Pukrushpan, Anna G. Stefanopoulou, Huei Peng, Springer, 2005 ‐ PROCESS MODELıNG AND SıMULATıON WıTH FıNıTE ELEMENT METHODS, William B. J. Zimmerman, World Scientific Publishing Co., 2004 ‐ FUEL CELL HANDBOOK, EG&G Technical Services, Inc., Seventh Edition, U.S. Department of Energy Office of Fossil Energy National Energy Technology Laboratory, November 2004 ‐ AN INTRODUCTION TO FUEL CELLS AND HYDROGEN TECHNOLOGY, Brian Cook, Heliocentris, December 2001