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Research ArticleTheoretical Energy and Exergy Analyses ofProton Exchange Membrane Fuel Cell by Computer Simulation

I D Gimba1 A S Abdulkareem12 A Jimoh1 and A S Afolabi3

1Department of Chemical Engineering School of Engineering and Engineering Technology Federal University of TechnologyPMB 65 Gidan Kwano Minna Niger State Nigeria2Energy Research Group Centre for Genetic Engineering and Biotechnology Federal University of Technology PMB 65 BossoMinna Niger State Nigeria3Department of Chemical Metallurgical and Materials Engineering Botswana International University ofScience and Technology (BIUST) Plot 10071 Boseja Palapye Botswana

Correspondence should be addressed to A S Afolabi afolabiabiustacbw

Received 25 April 2016 Revised 21 July 2016 Accepted 7 August 2016

Academic Editor Junsheng Yu

Copyright copy 2016 I D Gimba et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A mathematical model of a proton exchange membrane fuel cell (PEMFC) was developed to investigate the effects of operatingparameters such as temperature anode and cathode pressures reactants flow rates membrane thickness and humidity on theperformance of the modelled fuel cell The developed model consisted of electrochemical heat energy and exergy componentswhich were later simulated using a computer programme The simulated model for the voltage output of the cell showed goodconformity to the experimental results sourced from the literature and revealed that the operating pressure temperature andflow rate of the reactants positively affect the performance and efficiencies (energy and exergy) of the cell The results alsoindicated that high membrane thickness above 150120583m is unfavourable to both the fuel cell performance and the cell energy andexergy efficiencies The simulated results obtained on the influence of membrane humidity on the cell performance indicated thatmembrane humidity positively favours both the performance and energy and exergy efficiencies of the cell It can therefore beinferred that the performance of the PEMFC and energy and exergy efficiencies of the cell are greatly influenced by the operatingpressure temperature membrane thickness membrane humidity and the flow rates of fuel and oxidant

1 Introduction

Over the years the world has been greatly dependent onvirtually only one energy source known as fossil fuel whichis nonbiodegradable and quite limited for its domestic andindustrial utilization This condition led to disparity inworldrsquos fossil fuel production and demand which resulted inenergy crisis due to scarcity in supply and price fluctuation[1 2] The price instability and environmental pollution offossil fuel are some of the major problems derived from overdependence on this source of energy It is widely documentedthat the combustion of fossil fuel is harmful to human healthas well as the environment and this resulted in increase incampaign for cleaner energy source in order to safeguard theenvironment and protect man from the inhalation of toxicsubstances [3] For instance it is a known fact that the exhaust

from the combustion of fossil fuel emits harmful gases suchas CO2 CO and SO2 into the atmosphere [1 4] Thesegases constitute severe health and environmental hazard andhence create a serious global environmental problem [5]Theconcern for the price instability due to excessive reliance onfossil fuel and increasing awareness on the environmentalimpact of burning fossil fuel has led to increased callsfor alternative energy sources that can compete well withthe existing sources of energy [6 7] Fuel cells which aredescribed as electrochemical devices that convert the energyof a chemical reaction directly into electricity with water asits by-product are now considered promising economicaland sustainable alternative energy source [8ndash10]

Fuel cells produce little or no pollutants depending onthe type of fuel used [11] They also have an advantage thatmakes them better than some industrial combustion which

Hindawi Publishing CorporationJournal of Applied ChemistryVolume 2016 Article ID 2684919 15 pageshttpdxdoiorg10115520162684919

2 Journal of Applied Chemistry

is their ability to capture excess heat generated and use itin a cogeneration-like manner or for spacewater heating[12 13] Other major advantages that fuel cells hold overinternal combustion engines include the high efficiency ofoperation and lack of harmful pollutant emission Despiteresearchers and government accorded recognition to fuelcells particularly the proton exchange membrane fuel cell(PEMFC) as the environmentally friendly alternative energysource that can competewell with the existing energy sourcesthe high cost of its allied parts and monopoly of the technol-ogy have hindered the commercial availability of fuel cells asalternative energy sources [14ndash16] In the past few years goodprogress has been made to achieve the commercialization ofthis alternative energy source by reducing the cost of the cellcomponents which are made of the electrode flow field plateand membrane [17] However lack of understanding of theinfluence of various parameters on the rate of production ofenergy by the fuel cell system remains a serious issue whichis the focus of this present study On this note the first andsecond laws of thermodynamics have been recognised asmajor tools for measuring the energy and exergy of the fuelcell technologies [18]

The first law of thermodynamics (energy analysis) dealswith the quantity of energy and states that energy can neitherbe created nor destroyedThe lawmerely serves as a necessarytool for accounting for the energy during a process and offersno challenges to engineers The second law (exergy analysis)however deals with the quality of energy degradation ofthis energy during a process entropy generation and lostopportunities to do work and offers plenty of room forimprovement The second law of thermodynamics has beenproven to be a powerful tool in the optimization of complexthermodynamic systems [19ndash21] In recent times exergyanalysis has become a key aspect in providing a betterunderstanding for the analysis of power system processes thequantification of sources of inefficiencies and distinguishingquality of energy (or heat) used [22ndash24]

The aim of this study is therefore to develop a predictivemathematical model to determine the quantity of energythat can be produced by fuel cells as a function of operatingparameters Simulation of the developedmodel is expected toprovide information on the interaction of various parametersthat affect the performance of proton exchange membranefuel cell

2 Conceptualization ofthe Modelling Technique

This study is focused on the theoretical mathematical modelthat can be used to quantify the performance of a fuel cellas a function of operating parameters The mathematicalmodel will consist of electrochemical heat energy and exergyanalysis components The following assumptions were madein developing the predictive model

(i) There is incomplete utilization of the fuel and oxidantgases during the reaction process

(ii) The voltage losses encountered are activation polar-ization ohmic polarization and concentration polar-ization

(iii) The enthalpy calculations are based on standardtemperature

(iv) The heat losses in the system are by natural convec-tion forced convection and radiation

Equations (1)ndash(3) represent the reactions taking place ina typical PEMFC system [13]

anode 2H2 997888rarr 4H+ + 4eminus (1)

cathode O2 + 4H+ + 4eminus 997888rarr 2H2O (2)

overall 2H2 +O2 997888rarr 2H2O (3)

The actual (or net) output voltage of the PEMFC 119881cell as afunction of current temperature partial pressure of reactantand membrane humidity can be expressed as follows

119881cell = 119864Nernst minus 120578act minus 120578ohmic minus 120578conc (4)

where 119864Nernst is the thermodynamic equilibrium potential oropen circuit voltage and 120578act 120578ohmic and 120578conc are activationohmic and concentration overvoltages respectively Othernames for overvoltages are polarization or losses and theyrepresent voltage drop

The reversible cell voltage or thermodynamic potential isthe maximum voltage attained from a fuel cell at thermody-namic equilibrium which can be obtained by applying theNernst equation as shown as follows

119864Nernst = 119881∘ + 119877119879119899119865 ln[[1199011015840H2 (1199011015840O2)051199011015840H2O ]

] (5)

where 119881∘ is the standard state reference potential (29815 Kand 1 atm) at unit activity 1199011015840H2 1199011015840O2 and 1199011015840H2O are par-tial pressures of hydrogen oxygen and water respectively119877 is the universal gas constant (8314 Jmole K) 119879 is thecell operating temperature (K) 119865 is the Faraday constant(96485 Cmole) and 119899 represents the number of moles ofelectrons transferred having a value of 2

Equation (4) shows that part of the voltage is lost indriving the chemical reaction at the electrodes This lostvoltage is known as activation overvoltage (120578act) which occursat both the anode and cathode Activation overvoltage ishowever more predominant at cathode since the hydrogenoxidation is faster than oxygen reduction A parametricequation for representing activation overvoltage as proposedby Uma [25] is shown in the following equation

120578act = minus [1205851 + 1205852119879 + 1205853119879 [ln (119888lowastO2)] + 1205854119879 [ln (119894)]] (6)

Journal of Applied Chemistry 3

The values of the parametric coefficients 1205851 1205852 1205853 and 1205854 aredetermined using linear regression analysis [26]These valuesare

1205851 = minus09481205852 = 000286 + 00002 ln (119860) + 43 times 10minus5 ln (119888lowastH2)1205853 = 76 times 10minus51205854 = minus193 times 10minus4

(7)

where 119888lowastH2 and 119888lowastO2 are concentrations of hydrogen andoxygen respectively at the reaction sites while119860 is the activecell area

The concentrations of hydrogen and oxygen at theelectrode-membrane interface can be determined fromHenryrsquos law equation [27] of the forms expressed in thefollowing two equations

119888lowastH2 = 1199011015840H29174 times 10minus7 exp(minus77119879 ) (8)

119888lowastO2 = 1199011015840O2197 times 10minus7 exp(498119879 ) (9)

Substituting the values of the parametric coefficients into (6)we obtain the expression in the following equation

120578act = minus [minus0948+ 000286 + 00002 ln (119860) + 43 times 10minus5 ln (119888lowastH2)sdot 119879 + 76 times 10minus5119879 [ln (119888lowastO2)] minus 193times 10minus4119879 [ln (119894)]]

(10)

The voltage loss as a result of resistance to the flowof electronsthrough the electrodes and various interconnections andresistance to the flow of ions through the electrolyte is knownas ohmic overvoltage (120578ohmic) which can be expressed asfollows

120578ohmic = 119894119877 = 119894 (119877electronic + 119877ionic) (11)

It has been reported that the resistance to flow of ions (119877ionic)is predominant hence its contribution to ohmic overvoltageis more significant than the resistance to the flow of electrons(119877electronic) [26] The ionic resistance is a function of themembrane water content which in turn is a function oftemperature and current Hence the ionic resistance can beexpressed as follows [28]

119877ionic = 119903119872119897mem119860 (12)

where 119903119872 is the membrane resistivity 119897mem is the membranethickness and 119860 is the active cell area The membraneresistivity in (12) was correlated by Rezazadeh et al [26] asshown in the following equation

119903119872= 1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25]

[120582 minus 0634 minus 3 (119894119860)] exp [418 ((119879 minus 303) 119879)] (13)

Substituting the expression in (13) into (12) we obtain thefollowing

119877ionic = (1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25] [120582 minus 0634 minus 3 (119894119860)] exp [418 ((119879 minus 303) 119879)]) 119897mem119860 (14)

Substituting (14) into (11) we also obtain 120578ohmic expression asfollows

120578ohmic = 119894(1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25] [120582 minus 0634 minus 3 (119894119860)] exp [418 ((119879 minus 303) 119879)]) 119897mem119860 (15)

The concentration overvoltage (120578conc) is another factor thatcan also affect the performance of the fuel cell As reactant isconsumed at the electrode by electrochemical reaction thereis a loss of potential due to the inability of the surroundingmaterial to maintain the initial concentration of the bulkfluid (formation of concentration gradient) [28] Severalprocesses that may contribute to concentration polarization

include slow diffusion in the gas phase in the electrodepores solutiondissolution of reactantsproducts intoout ofthe electrolyte or diffusion of reactantsproducts throughthe electrolyte tofrom the electrochemical reaction site[28] Concentration overvoltage (or polarization) is alsocalled mass transportation losses However at practical cur-rent densities slow transport of reactantsproducts tofrom


the electrochemical reaction site is a major contributor toconcentration polarization Concentration overpotential canbe expressed as follows

120578conc = minus119861 ln(1 minus 119869119869max) (16)

where 119861 is a parametric coefficient and 119869 represents the actualcurrent density of the cell (Acm2) Substituting (5) (10)(15) and (16) into (4) gives a generalized equation for voltageoutput of the cell 119881cell as follows

119881cell = 119881∘ + 119877119879119899119865 ln[

[1199011015840H2 (1199011015840O2)051199011015840H2O ]

]

minus 0948 + 000286 + 00002 ln (119860) + 43 times 10minus5 ln (119888lowastH2) 119879+ 76 times 10minus5119879 [ln (119888lowastO2)] minus 193 times 10minus4119879 [ln (119894)]minus 119894 (1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25] [120582 minus 0634 minus 3 (119894119860)] exp [418 ((119879 minus 303) 119879)]) 119897mem119860 + 119861 ln(1 minus 119869119869max

)

(17)

Equation (17) is the predictive model expression for thevoltage output from PEMFC as a function of the operatingparameters for a single fuel cell

The actual efficiency of the fuel cell can be obtained fromthe expression shown as follows

cell efficiency = 119881cell119881119888 times 100 (18)

where 119881119888 is the actual voltage having a value of about 123Vand 119881cell is determined from (17)

In practice not all the reactants going into the systemreact completely as some fractions of the fuel pass through thecell without taking part in energy production process hencefuel utilization term is introduced in calculating the protonexchange membrane fuel cell efficiency [29]

The fuel utilization coefficient is given as follows

120575119891 = mass of fuel (H2) reacted in the cellmass of fuel (H2) input into the cell

(19)

If (19) is substituted into (18) it gives the following expression


21 Mass Balance for the PEMFC As a requisite to carryingout energy balance for the PEM fuel cell material balancebecomes necessary The mass balance was performed basedon the inflow and outflow of the reactants (H2 and O2) intoand out of the fuel cell system as shown in Figure 1

Considering the fact that not all reactants that entered thefuel cell were utilized the component material balance forhydrogen and oxygen can be written as follows

119898H2 in = 119898H2 react + 119898H2 out (21)

119898O2 in = 119898O2 react + 119898O2 out (22)

where 119898H2 in and 119898O2 in are the mass flow rates of hydrogenand oxygen entering the PEM fuel cell respectively In addi-tion 119898H2 out and 119898O2 out are the mass flow rates of hydrogenand oxygen from PEM fuel cell respectively They representhydrogen purged out of the fuel cell and the unreactedoxygen respectively The mass balance of the reactants (O2and H2) requires the essential electrochemistry principlesto calculate the hydrogen and oxygen consumption rates119898H2 react and 119898O2 react and the water production 119898H2Oout asfunctions of current density 119894 (Acm2) and Faradayrsquos constant[30]

Hydrogen reacts on the anode side thus the consumptionrate of hydrogen is given as

119898H2 react = 120577119860119872H2119869119860cell2119865 times 10minus3 (23)

where 120577119860 stands for the anode stoichiometry 119872H2 is themolecular weight of hydrogen 119869 is the current density 119860cellis the effective area of the cell and 119865 is Faradayrsquos constantSimilarly the consumption rate of oxygen can be calculatedfrom the following equation [30]

119898O2 react = 120577119862119872O2119869119860cell2119865 times 10minus3 (24)

where 120577119862 represents the cathode stoichiometry and119872O2 is themolecular weight of oxygen

Assuming water produced from the fuel cell to be liquidwater production rate can be expressed as follows

119898H2Oout = 119872H2O119869119860cell2119865 times 10minus3 (25)

where119872H2O represents the molecular weight of waterHydrogen and oxygen which leave the system unutilized119898H2 out and119898O2 out respectively will be determined from (21)

and (22) as follows

119898H2 out = 119898H2 in minus 119898H2 react (26)


PEMFC

Fuel cell system

H2in H2out

H2O

O2inO2out

Figure 1 Schematic mass balances for the PEMFC

Substituting for119898H2 react gives

119898H2 out = 119898H2 in minus 120577119860119872H2119869119860cell2119865 times 10minus3 (27)

Similarly

119898O2 out = 119898O2 in minus 119898O2 react (28)

119898O2 out = 119898O2 in minus 120577119862119872O2119869119860cell2119865 times 10minus3 (29)

Larminie and Dicks [31] give alternate equations for calculat-ing the inletmass flow rates of hydrogen and oxygen as shownin the following equations

119898O2 in = oxygenin = 357 times 10minus7 (120582119904 times 119882net119881cell) (30)

119898H2 in = hydrogenin = 105 times 10minus8 (119882net119881cell) (31)

Similarly mass flow rates of unused oxygen and productwater are given in expression in the following equations

119898O2 out = oxygenout

= 357 times 10minus7 (120582119904 times 119882net119881cell) minus 829

times 10minus8 (119882net119881cell)

(32)

119898H2Oout = waterout = 934 times 10minus8 (119882net119881cell) (33)

where 120582119904 is the stoichiometry of oxygen

22 Energy Analysis for the PEMFC The conservation law ofenergy which is the first law of thermodynamics is used toanalyze the energy model of the proton exchange membranefuel cell The energy balance around a fuel cell is based onthe energy absorbingreleasing processes (power producedreactions and heat loss) that occur in the cell As a result theenergy balance varies for the different types of cells becauseof the differences in reactions that occur according to the celltypes

The cell energy balance states that the enthalpy flowof reactants entering the cell will be equal to the enthalpy

PEMFuel cell system Electric energy generated

QH2O

cathode and anode electrochemicalreaction

QO2 in

Qloss

QH2 in

QO2 out

QH2 out

Qrxtn heat or reaction from

QE (VIt)

Figure 2 Schematic energy (enthalpy) balances for the PEMFC

flow of the products leaving the cell plus the sum of threeterms namely (i) the net heat generated by physical andchemical processes within the cell (ii) the dc power outputfrom the cell and (iii) the rate of heat loss from the cell toits surroundings The energy balance according to the heatflow into and out of the cell as shown in Figure 2 can berepresented mathematically as follows

119876input minus 119876output minus 119876acc = 0 (34)

where 119876input and 119876output are the total heat input and outputrespectively and 119876acc is the heat accumulation which is thenet heat generated by physical and chemical processes withinthe cell

By replacing 119876acc in (34) with 119876net and rearranging weobtain the following expression

119876net = 119876input minus 119876output (35)

From the schematic shown in Figure 2 the total heat inputinto the system is

119876input = 119876H2 in + 119876O2 in (36)

where 119876H2 in and 119876O2 in are the heats from the reactant feedsSimilarly the total heat output from the system is as shown asfollows

119876output = 119876H2 out + 119876O2 out + 119876H2O + 119876rxtn + 119876119864+ 119876loss (37)

From (37) 119876H2 out and 119876O2 out are the heats from the unre-acted hydrogen and oxygen respectively 119876H2O is the heatfrom water produced 119876rxtn is the heat of reaction fromcathode and anode electrochemical reaction119876loss is the heatloss to the surroundings and 119876119864 is the electrical energy(119881cell times 119868119905) generated

The heat generated by the fuel cell system is transferredthrough the stack by conduction which then dissipatesinto the surroundings using natural convection forced con-vection and radiation [30] Hence the three heat transfermechanisms play important roles to transfer the heat from thefuel cell stack to the ambient In addition some heat is carriedaway from the fuel cell stack by the product gases and waterHeat lost termed119876loss from the fuel cell can be represented asfollows

119876loss = 119876nc + 119876fcn + 119876rad (38)


where 119876nc 119876fcn and 119876rad are heat losses via natural con-vection forced convection and radiation respectively Theexpressions for 119876cond 119876nc 119876fcn and 119876rad can be obtained byconsidering a fuel cell slab of solid material of area 119860 locatedbetween two large parallel plates at distance 119884 apart the rateof heat flow by conduction per unit area is given by Fourierexpression as follows [32]

119876cond119860 = QΔ119879119884 (39)

That is the rate of heat flow per unit area is proportional tothe temperature decrease over the distance119884The constant ofproportionality Q is the thermal conductivity of the slabΔ119879 isgiven as (1198791 minus1198790) where 1198790 and 1198791 are the initial temperatureand the temperature at a steady-state condition of heat flowacross the slab119876nc and119876fcn are calculated separately from (40) and (41)respectively

119876nc = ℎnc119860FC (119879FC minus 1198790) (40)

119876fcn = 119898coolant119862119901air (119879coolantout minus 1198790) (41)

Air is used as coolant in fuel cells ℎnc is the natural convectiveheat transfer coefficient 119860FC is the total heat transfer areaof the fuel cell it can be estimated from the dimensions ofthe fuel cell system 1198790 is the ambient temperature which isassumed to be the dead state temperature of 298K

For nonblack surfaces at temperature 119879 the emittedenergy flux is given by Stefan-Boltzmann law [33] as

119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)

where 119879 is the absolute temperature and 119860FC is the total heatsurface area of the fuel cell system The Stefan-Boltzmannconstant 120590 has been found to have the value of 567 times10minus8Wm2 K4 and 120576 is the emissivity having standard valuesfor various materials

Substituting (36) to (38) and (40) to (42) into (35) willyield

119876net = 119876H2 in + 119876O2 in minus 119876H2 out minus 119876O2 out minus 119876H2O

minus 119876rxtn minus 119876119864 minus ℎnc119860FC (119879FC minus 1198790)minus 119898coolant119862119901air (119879coolantout minus 1198790)minus 120576120590119860FC (1198794FC minus 11987940 )

(43)

Equation (43) can be rewritten in terms of enthalpies to yieldthe following equation

119876net = Δ119867H2in + Δ119867O2in minus Δ119867H2out minus Δ119867O2out

minus Δ119867H2O minus Δ119867rxtn minus 119876119864minus ℎnc119860FC (119879FC minus 1198790)minus 119898coolant119862119901air (119879coolantout minus 1198790)minus 120576120590119860FC (1198794FC minus 11987940 )

(44)

whereΔ119867O2 Δ119867H2 andΔ119867H2O are the enthalpies of oxygenhydrogen and water respectively and Δ119867rxtn is the enthalpyof reaction

The electrical energy dissipated 119876119864 is related to the netoutput voltage 119881cell by

119876119864 = 119881cell times 119868119905 (45)

where 119868 is the current and 119905 is the duration of operationEquation (44) can be rearranged to obtain

119876net = Δ119867H2 in + Δ119867O2in minus Δ119867H2 out minus Δ119867O2out

minus Δ119867H2O minus Δ119867rxtn minus 119881cell119868119905minus ℎnc119860FC (119879FC minus 1198790)minus 119898coolant119862119901air (119879coolantout minus 1198790)minus 120576120590119860FC (1198794FC minus 11987940 )

(46)

The enthalpy of reaction term Δ119867rxtn in the energy balanceequation is computed as follows [34]

Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)

Upon integration of (47) Δ119867rxn becomes

Δ119867rxtn = Δ119867∘rxtn + Δ119862119901 (119879 minus 298) (48)

where Δ119867∘rxtn = (119899119894Δ119867∘119891119894)prdcts minus (119899119894Δ119867∘119891119894)rxtntsFor the PEMFC where 2H2 +O2 rarr 2H2O 2 moles of H2

and 1 mole of O2 give 2 moles of H2O

Δ119867∘rxtn = (2 times Δ119867∘119891H2O)prdctsminus [(2 times Δ119867∘119891H2) + (1 times Δ119867∘119891O2)]rxtnts

(49)

And also from the reaction stoichiometry

Δ119862119901 = (2 times Δ119862119901H2O)prdctsminus [(2 times Δ119862119901H2) + (1 times Δ119862119901O2)]rxtnts

(50)

Therefore the energy efficiency of the PEMFC system is

120578energysystem = netHHVH2 times 119898H2 in

(51)

Higher heating value of a fuel (HHV) is the negative valueof the standard heat of combustion when water in thecombustion products is in form of a liquid [35] Here HHVH2is the higher heating value of hydrogen 119882net(119881cell times 119868) is thenet power production of the fuel cell system and119898H2 in is themass flow rate of hydrogen to the PEMFC


23 Exergy Analysis The flow exergy of a substance refersto the theoretically obtainable work when that substance isbrought to total equilibrium with the local environment Itcan be divided into thermomechanical and chemical flowexergies [36] Hence the total exergy rate can be written as

= tm + CH (52)

The thermomechanical exergy is also known as physicalexergy and it represents the deviation in temperature andpressure between the flowing matter and the ambient Italso includes the kinetic and potential exergies However thechemical exergy represents the deviation in chemical compo-sition between the flowing matter and the local environmentTherefore (52) becomes

= ke + pe + tm + CH (53)

Amir et al [37] also give the specific total exergy (Jkg) as thesum of kinetic exergy potential exergy thermomechanicalexergy and chemical exergy as

119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)

where 119890 = 119898 is the total exergy rate (Jhr) and 119898represents themass flow rate (kghr)Therefore (54) becomes

= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)

The specific kinetic exergy term 119890ke is expressed as

119890ke = 12V2 (56)

where V is the velocity relative to the earth surface (ms) andthe specific potential exergy term 119890pe is given by

119890pe = 119892119885 (57)

where119892 is the earth gravity (ms2) and119885 is the stream altitudeabove the sea level (m)

The thermomechanical exergy shown in (54) can besimplified as a function of fuel cell operating temperature andpressure [38] as

119890tm = (ℎ minus ℎ0) minus 1198790 (119904 minus 1199040) (58)

where ℎ0 and 1199040 represent the specific enthalpy (Jkg) andentropy (JkgsdotK) at standard conditions respectively (ℎminusℎ0)and (119904 minus 1199040) are changes in enthalpy and entropy respectively

Meanwhile Masanori and Abdelaziz [38] expressed thespecific molar chemical exergy of component 119894 present in theenvironment at partial pressure 11987500119894 as

119890CH = 1198771198790 ln( 119875011987500119894) (59)

where 1198750 is the environmental pressure (usually taken as1 atm) and 11987500119894 is the partial pressure of the reference com-ponent and 119877 is the ideal gas constant

Hence substituting (56) to (59) into (54) yields an expres-sion for the specific total exergy thus

119890 = 12V2 + 119892119885 + (ℎ minus ℎ0) minus 1198790 (119904 minus 1199040)+ 1198771198790 ln( 119875011987500119894)

(60)

The specific thermomechanical exergy term (ℎ minus ℎ0) minus 1198790(119904 minus1199040) of (58) can be evaluated further as a function of fuel celloperating condition

(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)

Based on ideal gas assumption 119875120597119881 = 119877120597119879 so that120597119881120597119879 = 119877119875 (63)

where 119877 is the universal gas constant substituting (63) into(62) gives

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)

Integrating (63) yields

(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)

Specific heats at constant pressure 119862119901 and at constantvolume 119862V are related to 119877 as [32]

119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)

Substituting for 119877 in (65)

(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus (119862119901 minus 119862V) ln( 1198751198750) (67)

Rearrange (67) to obtain

(119904 minus 1199040) = 119862119901 [ln( 1198791198790) minus (1 minus 119862V119862119901) ln( 1198751198750)] (68)

119862V119862119901 can be expressed in terms of the specific heat ratio 119896thus

119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes

(119904 minus 1199040) = 119862119901 [ln( 1198791198790) minus (119896 minus 1119896 ) ln( 1198751198750)] (70)

Substituting (61) and (70) into (58) gives an expression for thespecific thermomechanical (physical) exergy as

119890tm = 119862119901 (119879 minus 1198790)minus 1198790119862119901 [ln( 1198791198790) minus (119896 minus 1119896 ) ln( 1198751198750)] (71)

Simplifying (71) further yields

119890tm = 1198621199011198790 [ 1198791198790 minus 1 minus ln( 1198791198790) + ln( 1198751198750)((119896minus1)119896)] (72)

By substituting (72) into (60) we obtain the total specificexergy

119890 = 12V2 + 119892119885+ 1198621199011198790 [ 1198791198790 minus 1 minus ln( 1198791198790) + ln( 1198751198750)

((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)

Hence substituting (73) into (55) gives the overall total exergyrate equation that can be used for calculating the exergy ofeach component in the model equation

= 12119898V2 + 119898119892119885

+ 1198981198621199011198790 [ 1198791198790 minus 1 minus ln( 1198791198790) + ln( 1198751198750)((119896minus1)119896)]

+ 1198981198771198790 ln( 119875011987500119894)

(74)

From a thermodynamics point of view the exergetic effi-ciency which is known as second law efficiency gives thetrue value of the performance of an energy system [39]Exergy is defined as themaximumamount ofwork obtainablefrom a system or a flow of matter when it is brought toequilibrium with the reference environment [37] The exergyconsumption during a process is proportional to the entropyproduction due to irreversibilities It is a useful tool forfurthering the goal of more efficient energy use as it enablesthe determination of the location type and true magnitudeof energy wastes and losses in a system

For a PEM fuel cell system the exergetic efficiency isdefined as

120576 = electrical output(exergy)Rxtnt minus (exergy)Prdct (75)

120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)

Current density (Acm2)

Model simulationActual

Figure 3 Comparative polarization curve of the simulated andliterature results for PEMFC

where O2 119877 H2 119877 O2119875 and H2O119875 are the total exergies ofthe reactants oxygen and fuel (hydrogen) and the productsoxygen and water respectively The net electrical poweroutput produced by the cell is given as [40]

net = 119881cell sdot 119868 (77)

where 119881cell is the fuel cell output voltage and 119868 is the currentThe computer simulation of the model developed for

theoretical energy and exergy analyses of the proton exchangemembrane fuel cell is achieved using computer codes todemonstrate the performance and behaviour of the system byvarying the operating parameters

3 Results and Discussion

Fuel cell which can be described as a self-contained energygeneration device is a reliable alternative energy for residen-tial and industrial applications However despite the wideacceptance of this device as an alternative energy source thatcan compete favourably with the existing energy sourcesthe technology is yet to be commercially available Onemajor reason for nonavailability of fuel cells at commercialscale can be attributed to lack of understanding of theinteraction between the various parameters that influence theperformance of these cells A better understanding of fuel celltechnology can be achieved through predictive mathematicalmodel which is the focus of this study The simulated resultsobtained on the influence of various parameters on thevoltage output and energy and exergy of proton exchangemembrane fuel cell are presented in Figures 3ndash15 Figure 3represents the simulated performance of PEMFC at operatingconditions of 1 atmosphere for the cathode and anodeoperating temperature of 343K and membrane thickness of178 120583m

The results presented in Figure 3 indicate that operat-ing single stack of proton exchange membrane fuel cell at


0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K

Figure 4 Effect of cell temperature on the voltage-current densitycharacteristics

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)

Volt 1 atmVolt 2 atmVolt 3 atmVolt 4 atmVolt 5 atm

Power 1 atmPower 2 atmPower 3 atmPower 4 atmPower 5 atm

Figure 5 Effect of anode pressure on PEMFC performance

operating conditions of 1 atmosphere 343K and membranethickness of 178 120583m will produce a maximum voltage (opencircuit voltage) of 1019V At a current density of 005Acm2there is a sudden reduction in voltage to 0896V after whichthe cell output voltage decreased gradually with increase incurrent density The sudden drop in voltage as the currentdensity increases from 0 to 005Acm2 can be attributed toactivation losses known as overpotentials in the cell [41] Theliterature result is used to validate the results obtained fromnumerical simulations The computed polarization curve iscompared with the literature results of previous study by

14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)



Figure 6 Effect of cathode pressure on PEMFC performance

0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate

Figure 7 Hydrogen flow rate variations of PEMFC

Abdulkareem [13] and the value of the correlation coefficientfor both sets of data was calculated as 098033 which showsthat the calculated results are in good agreement with theexperimental data The variation between the simulationand experimental results could be attributed to the factthat the simulation result is an instantaneous value whichmeasures the possible cell voltage at a given time while theexperimental results will take some time to stabilize beforeproducing voltage The variation can also be attributed tosome assumptions made during the conceptualization of themodel For instance the reaction in the fuel cell is incompleteand the extent of electrochemical reaction that produced


0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate

Figure 8 Oxygen flow rate variations of PEMFC

8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)

Membrane thickness (120583m)

Figure 9 Effect of membrane thickness on voltage output

the voltage is varied for the simulated and experimentalresults It can be observed that despite the little variationbetween the simulated and experimental results their polar-ization curves are still very similarThemodel developed wasfurther simulated to investigate the influence of operatingparameters on the performance of the proton exchangemembrane fuel cell fueled with hydrogen

Aside from the inherent qualities of proton exchangemembrane fuel cell which depend on materials and manu-facturing conditions the operating conditions also affect itsperformance to a large extent because they can alter the shapeand position of the polarization curve [28] After validationof the simulated results with the literature values the PEMFCmodel is subjected to different values of input variables inorder to study their effect on the V-I characteristics theoutput voltage of the PEMFC and polarization losses Thebase-case operating conditions of the system temperatureanode and cathode pressures and membrane thickness are343K 1 atm and 178 120583m respectively Figure 4 presents thetemperature dependent V-I characteristics of the PEMFC atoperating anode and cathode pressure of 1 atm It has beenproven that temperature has a more significant influenceon the performance of the PEMFC than other operationvariables [28]

80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()

Figure 10 Effect of predicted membrane humidity on PEMFCperformance

0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()


Figure 11 Efficiency of the PEMFC at 1 atm anode and cathodepressures and 343K operating temperature

From the simulated results presented in Figure 4 showingseries of polarization curves at different operating tempera-tures it can be seen that with the increase in temperaturefrom 333 to 400K the PEMFC performance also increasesand so does the power density For instance at current densityof 02 Acm2 the cell voltage output is 0788V at 333 K whichincreases to 0884V at 400K It thus implies that for highertemperature values the overpotentials (activation ohmicand concentration losses) in the PEMFC are reduced andhence the cell can operate with a higher performance [42]The shift of the PEMFC polarization curves also indicates theimprovement of electrical efficiency as temperature increasesThis is due to the improvement in some parameters suchas the exchange current density of the oxygen reductionreaction membrane conductivity reversible thermodynamicpotential119864Nernst and binary diffusivities [40] Also the rise ofthe temperature increases proton mobility in the membraneand improves catalyst activity and gas diffusion [43] Withlimitations to marginal improvement of the voltage at highertemperatures which result from membrane dryness and


30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()

Energy efficiencyExergy efficiency


Figure 12 Variations of energy and exergy efficiencies of thePEMFC at 343K and 1 atm

increased internal resistance a much higher temperature istherefore beneficial for the PEMFC to improve electrical per-formance [40] However in reality increasing the operatingtemperature beyond a certain limit will negatively affect theperformance of fuel cell depending on the nature of themembrane For instance it has been reported that thermalstability ofNafion (120ndash150∘C) is amajor drawback for protonexchange membrane fuel cell development Emphasis is nowplaced on the development of alternative membrane withhigh thermal stability for the purpose of improving the fuelcell performance which is indicated by the simulated model

Also investigated through the simulation of the developedmodel is the influence of anode and cathode pressure on theproton exchangemembrane fuel cell performance at constantoperating temperature of 343K The operating pressures ofanode and cathode sites also play important role in theperformance of fuel cells Figures 5 and 6 show the simulatedresults obtained on the influence of anode and cathodepressure respectively at 343K cell operating temperature

From Figures 5 and 6 it can be observed that increasein pressure of anode and cathode resulted in an increase inthe output voltage of the fuel cell The results also indicatethat at current density of 02 Acm2 the voltage output of thecell is 0803V at cathode pressure of 1 atm whereas at thesame current density but with the cathode operating pressureat 50 atm the voltage output is 0934V A closer observationof Figures 5 and 6 reveals that though the cell performanceincreased monotonously in both cases the cathode pressureismore sensitive than anode pressure For instance at currentdensity of 04 Acm2 and operating pressure of 50 atm the celloutput at the cathode is 0885V with the equivalent value of087V at the anodeThe variation in the output voltage of thecell at the same operating pressure of the anode and cathodecan be attributed to the fact that the electrochemical reactionthat generates power in the cell takes place at the cathode [42]Though the simulated results reveal that increase in pressurefavours the performance of fuel cells care must be taken notto exceed the limiting operating pressure of the stack

537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)


Figure 13 Effect of membrane thickness on energy efficiency of thePEMFC

48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)


Figure 14 Effect of membrane thickness on exergy efficiency of thePEMFC

Figures 7 and 8 present the simulated results on the influ-ence of hydrogen and oxygen flow rates on the performanceof proton exchange membrane fuel cell As can be seen inthese figures more hydrogen and oxygen are consumed bythe fuel cell system with increase in current density Theconsumption of more fuel reduces the concentrations ofhydrogen and oxygen at various points in the PEM fuelcell gas channels and increases the concentrations of thesereactants at the input of the stack The results also show thatvoltage output of the cell behaved contrary to the behaviourof hydrogen and oxygen flow rates with current densitySince less pressure produced less voltage it can thus beinferred from this relationship between voltage and flow ratesthat more hydrogen and oxygen consumptions by fuel cellsystem lead to lower pressure [30] resulting in decreasedoutput voltage The reduction in output voltage at high flowrate can be attributed to concentration loss which is due tothe change in concentration of reactants at the surface ofthe electrodes as the fuel is used causing reduction in thepartial pressure of reactants resulting in reduction in voltage[41]

Another factor that can affect the performance of fuelcell is the membrane thickness proton exchange membranefunctions as an ionic conductor between the anode and


47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()


Figure 15 Effect of humidity on energy and exergy efficiencies

cathode a barrier for passage of electron and gas crossleakage between electrodes [41] The simulated results onthe influence of membrane thickness on performance of theproton exchange membrane fuel are presented in Figure 9The result presented is simulated at operating temperatureof 343K operating pressure of 1 atm and current density of02 Acm2 It can be observed from the results in Figure 9that membrane thickness affects the performance of thePEMFC It can also be seen from the results that with themembrane thickness in the range of 50 to 150 120583m the outputvoltage followed a continuous reduction pattern This showsthat for larger values of membrane thickness the voltagedecreases with increasing membrane thickness and hencereductions in PEMFC performance This is because ohmicloss increases with increase in membrane thickness Thisloss occurs due to the electrical resistance of the electrodesand the resistance to the flow of ions in the electrolyteBecause it represents the resistance to the transfer of protonsthrough the membrane [41] greater membrane thicknesseswill favour ohmic loss which results in decrease in outputvoltage

Also affecting the performance of proton exchangemem-brane fuel cell is the membrane humidity For effectiveperformance of the proton exchange membrane fuel cellthere is a need to properly control the membrane humiditybecause lack of proper management of membrane humiditycould lead to voltage degradation and reduction in the fuelcell durability [16] Figure 10 shows the simulated effect ofmembrane humidity on the cell performance

Though there is no term for direct representation ofmembrane humidity in the developed model of PEMFC inthis study the term 120582 is considered as an adjustable parameterwhich depends on membrane humidity and stoichiometricratio of anode feed gas having value between 10 and 23Thus its value was varied between 10 and 23 (10 12 14

16 18 20 22 and 23) in order to study its effect on cellvoltage It can be seen that the output voltage increasedwith increase in 120582 This predicts that membrane humidityhas influences on the performance of the PEMFC It hasbeen reported that water uptake affects the ionic conductivityof membrane in fact it was reported that when the wateruptake by the membrane is too low the ionic conductivityof the membrane will be low and this will enhance themethanol permeability [1 10] However high water uptakethough improves the ionic conductivity of the membranebut with high possibility of loss of dimensional stability ofthe membrane It is also worth mentioning that fuel cells asa device for energy conversion convert chemical energy toelectrical energy with heat and water as the only by-productHence in addition to humidification of the membrane thedevice also generates water and hence the need to regulatethe process of humidification of the membrane Attemptswere also made in this study to extend the humidity beyond23 the output obtained was negative indicating that athigher humidity the ionic conductivity of the membrane isnegatively affected

31 Analyses of Energy and Exergy Efficiencies The processesthat involve heat are highly inefficient from the point of viewof the second law analysis This is because the exergy value ofheat is often much lower than its energy value particularlyat temperatures close to ambient temperature The exergyanalysis provides information onhow effective a process takesplace towards conserving natural resources [23] This makesit possible to identify areas in which technical and otherimprovements could be undertaken It also indicates thepriorities that could be assigned to conservation proceduresCognizance of exergy utilization of energy sources wouldhelp advance technological development towards resource-saving and efficient technology can be achieved by improvingdesign of processes with high exergetic efficiency Furtherapplication of exergy analysis in design and developmentof sustainable processes provides information for long-termplanning of resource management

The efficiency of a system can be defined in variousways Conventionally it is based upon the maximum energyobtainable from a fuel by burning it called the heating orcalorific value For a fuel cell the energy available is calledthe Gibbs energy and represents the maximum amount ofelectricity that can be gained from the cell The Gibbs energyis smaller than the calorific value Fuel cell efficiencies relatedto Gibbs energies are nearly always 100 Thus efficiency isnormally defined as the electrical energy extracted dividedby the calorific value of the fuel This enables fuel cells to becompared directly to combustion-based processes but placesan upper limit on fuel cell efficiencies due to the chemicalproperties of the fuel A hydrogen fuel cell operating at 25∘Cfor instance has a maximum theoretical efficiency of 83[29] even when the fuel cell is extracting all the electricalenergy possible This compares to a maximum theoreticalefficiency in a combustion engine at 500∘C of 58 Figure 11shows the efficiency variation of the PEMFC with currentdensity


Figure 11 indicates that the fuel cell efficiency increasedwith increase in current density until a maximum of 75 wasattained The maximum fuel cell efficiencies typically rangefrom60 to 80After themaximumefficiency of 75 a grad-ual decrease is noticeable which can be attributed to the factthat at initial condition the system consumes more powerthan its production This affects the efficiency and causes theincrease until the first loading at 005Acm2 After the powerdemand of resistive load starts the efficiency decreases dueto voltage losses and parasitic power consumption [30]

32 Energy and Exergy Efficiencies The energy and exergyanalyses of the fuel cell system are carried out to evaluate thefuel cell efficiency Figure 12 shows the variations of energyand exergy efficiencies with current density In this studythe energy efficiency obtained is between 505 and 682for 0ndash040Acm2 current density while exergy efficienciesvary from 453 to 612 Both energy and exergy efficienciesdecreased with increase in current density because of thereactantsrsquo flow rates and hydrogen pressure [30] It is alsoobserved from the results on this Figure that the energy andexergy efficiency curves behave similar to the polarizationcurves the influences of voltage losses are obviousThereforeimproved performance through higher energy and exergyefficiencies can be achieved if the voltage losses are greatlyminimized This can be done by operating the PEMFC atmoderate temperatures and pressures

The comparative plots of the variations of energy andexergy efficiencies with current density as shown in Figure 12also establish the second law of thermodynamics whichexplains exergy as ldquouseful workrdquo Not all energy from thefuel cell system is useful hence exergy efficiency is less thanenergy efficiency Also investigated through simulation of themodel is the effect of membrane thickness on energy andexergy efficiencies of proton exchangemembrane fuel cell andresults obtained are presented in Figures 13 and 14

It can be observed from these Figures (Figures 13 and 14)that energy and exergy efficiencies decreased with increase inmembrane thickness between 50 and 150 120583mThis is becauselarge membrane thicknesses will favour ohmic voltage lossesresulting in lower output voltage and hence poor perfor-mance Again this implies that large membrane thicknessesare disadvantageous to the fuel cell performance

The effect of membrane humidity of PEMFC on energyand exergy efficiencies is also simulated and the resultsobtained are illustrated in Figure 15 As seen in this figuremembrane humidity has an influence on the performanceof the PEMFC The energy and exergy efficiencies increasedwith increase in membrane humidity This is because as thehumidity increases the cell output voltage also increasesleading to higher efficienciesThe excesswater removal causesmembrane drying resulting in increased ionic resistance andthus decreasing the electrical efficiency which in turn resultsin further drying of the membrane (hot spots) [25] On theother hand the excess water stored in the membrane resultedin cell flooding In order to avoid degradation of voltage andto extend fuel cell stack life membrane humidity must becontrolled properly [25]

4 Conclusions

A mathematical model representing a proton exchangemembrane fuel cell unit was developed and validated bycomparing the polarization curves obtained with the one inopen literature A parametric study was also conducted toexamine the effect of various operating conditions on theperformance and energy and exergy efficiencies of the cellThe analyses of the results obtained indicated that operatingtemperature pressure membrane thickness and reactantsrsquoflow rates influenced the performance of the PEMFC asrevealed by the developed model The results obtained fromthe numerical simulation of the developed model are foundto be in good agreement with the experimental data availablein the literature thus the model developed can accuratelyrepresent the performance specifications of the system overthe entire range of system operation The energy and exergyefficiencies of the PEMFC can be improved by having ahigher operating pressure However a high pressure differ-ence between the cathode and the anode is recommendedin order to enhance the electroosmotic drag phenomenabetween the two electrodes The efficiency of the fuel cellcan also be enhanced by increasing the fuel cell operatingtemperature despite the small and low temperature rangeof a PEMFC as opposed to other types of fuel cells thatoperate at high temperatures Higher exergetic efficiencycould be attained if the fuel cell operates at relatively highercell voltages that would require less mass flow rates forthe reactants and the products to achieve a high electricaloutput Generally high performance can be achieved fromthe extended model results by significant improvement ofthe fuel cell through adopting any or a combination of thedifferent optimum operating conditions Any increase in thesystem performance will greatly affect the overall efficiencyand will contribute to the growth of the fuel cell systems invarious markets

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

University Board of Research (UBR) and STEP-B project ofthe Federal University of Technology Minna Nigeria arehighly appreciated for their supports

References

[1] A S Abdulkareem A S Afolabi C A Idibie H C Pienaarand S E Iyuke ldquoA predictive model for the energy analysis of aproton exchange membrane fuel cell by computer simulationrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 35 no 1 pp 32ndash41 2013

[2] A S Abdulkareem A Jimoh A S Afolabi E Muzenda andA C Okeke ldquoPredictive mathematical modeling and computersimulation of direct ethanol fuel cellrdquo Energy Sources Part ARecovery Utilization and Environmental Effects vol 38 no 5pp 635ndash643 2016


[3] X Li Principles of Fuel Cells Taylor and Francis Group NewYork NY USA 1st edition 2006

[4] J O Odigure A S Abdulkareem and O D Adeniyi ldquoCom-puter simulation of soil temperature due to heat radiation fromgas flaringrdquo Association for the Advancement of Modelling andSimulation in Enterprises vol 72 no 6 pp 1ndash10 2003

[5] M Ahmad S Samuel M Zafar et al ldquoPhysicochemicalcharacterization of Eco-friendly rice Bran oil biodieselrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 33 no 14 pp 1386ndash1397 2011

[6] J S Yi and T Van Nguyen ldquoMulticomponent transport inporous electrodes of proton exchangemembrane fuel cells usingthe interdigitated gas distributorsrdquo Journal of the Electrochemi-cal Society vol 146 no 1 pp 38ndash45 1999

[7] J H Lee T R Lack and A J Appleby ldquoModeling electrochem-ical performance in large scale proton exchange membrane fuelcell stacksrdquo Journal of Power Sources vol 70 no 2 pp 258ndash2681998

[8] D Cheddie and N Munroe ldquoReview and comparison ofapproaches to proton exchange membrane fuel cell modelingrdquoJournal of Power Sources vol 147 no 1-2 pp 72ndash84 2005

[9] M Shibasaki T Yachi and T Tani ldquoA new direct methanol fuelcell with a zigzag-foldedmembrane electrode assemblyrdquo Journalof Power Sources vol 145 no 2 pp 477ndash484 2005

[10] S E Iyuke A B Mohamad A A H Kadhum W R W Daudand C Rachid ldquoImproved membrane and electrode assembliesfor proton exchange membrane fuel cellsrdquo Journal of PowerSources vol 114 no 2 pp 195ndash202 2003

[11] M Bischoff ldquoLarge stationary fuel cell systems status anddynamic requirementsrdquo Journal of Power Sources vol 154 no2 pp 461ndash466 2005

[12] B Smitha S Sridhar and A A Khan ldquoSynthesis and character-ization of proton conducting polymermembranes for fuel cellsrdquoJournal of Membrane Science vol 225 no 1-2 pp 63ndash76 2003

[13] A S Abdulkareem Design and development of proton exchangemembrane from PSBR and carbon nanoballs for PEM fuel cellapplication [PhD thesis] University of the WitwatersrandJohannesburg South Africa 2009

[14] H Bashir A Linaries and J L Acosta ldquoHeterogeneous sulfona-tion of blend systems based on hydrogenated poly(butadiene-styrene) block copolymer Electrical and structural characteri-zationrdquo Solid State Ionics vol 139 no 3-4 pp 189ndash196 2001

[15] M K Song Y T Kim and J M Fentom ldquoChemically-modifiedNafionPoly (vinylidene fluoride) blend ionomers for protonexchange membrane fuel cellsrdquo Journal of Polymer Science vol117 pp 114ndash121 2003

[16] E Chen W Chen G Sun et al ldquoTest on the degradation ofdirect methanol fuel cellrdquo Electrochimica Acta vol 51 no 12pp 2391ndash2399 2006

[17] K Sopian and W R Wan Daud ldquoChallenges and future devel-opments in proton exchange membrane fuel cellsrdquo RenewableEnergy vol 31 no 5 pp 719ndash727 2006

[18] I B Hussein M Z B Yusoff and M H Boosroh ldquoExergyanalysis of a 120MW thermal power plantrdquo in Proceedingsof the 1st BSME-ASME International Conference on ThermalEngineering p 177 Dhaka Bangladesh 2001

[19] G Crawley ldquoProton exchange membrane (PEM) fuel cellsopening doors to fuel cell commercializationrdquo Fuel Cell Todaypp 1ndash12 2006

[20] Z Houcheng S Shanhe L Guoxing and C Jincan ldquoEfficiencycalculation and configuration design of a PEM electrolyzer

system for hydrogen productionrdquo International Journal of Elec-trochemical Science vol 7 pp 4143ndash4157 2012

[21] C Mborah and E K Gbadam ldquoOn the energy and exergyanalysis of a 500 kW steam power plant at Benso Oil PalmPlantation (BOPP)rdquo Research Journal of Environmental andEarth Sciences vol 2 no 4 pp 239ndash244 2010

[22] W-M Yan C-Y Chen S-C Mei C-Y Soong and F ChenldquoEffects of operating conditions on cell performance of PEMfuel cells with conventional or interdigitated flow fieldrdquo Journalof Power Sources vol 162 no 2 pp 1157ndash1164 2006

[23] Z S Ahmet Importance of exergy analysis in industrial processes[PhD thesis] King FahdUniversity of Petroleum andMineralsDhahran Saudi Arabia 2004

[24] C BrianAn Introduction to Fuel Cells andHydrogenTechnologyHeliocentris Vancouver Canada 2001

[25] T Uma Nonlinear state estimation in polymer electrolyte mem-brane fuel cells [MS dissertation] Cleveland State UniversityCleveland Ohio USA 2008

[26] A Rezazadeh M Sedighizadeh and M Karimi ldquoProtonexchange membrane fuel cell control using a predictive controlbased on neural networkrdquo International Journal of Computerand Electrical Engineering vol 2 article 1 2010

[27] R OrsquoHayre S W Cha W Colella and F B Prinz Fuel CellFundamentals John Wiley amp Sons New York NY USA 2005

[28] R Chris and S Scott Introduction to Fuel Cell TechnologyDepartment of Aerospace and Mechanical Engineering Uni-versity of Notre Dame Notre Dame Ind USA 2003

[29] R Baker andZ Jiujun ldquoProton exchangemembrane or PolymerElectrolyte Membrane (Pem) fuel cellsrdquo Electrochem Encyclope-dia vol 1 pp 11ndash22 2011

[30] A Yilanci I Dincer and H K Ozturka ldquoPerformance analysisof a PEM fuel cell unit in a solar-hydrogen systemrdquo InternationalJournal of Hydrogen Energy vol 33 no 24 pp 7538ndash7552 2008

[31] J Larminie and A Dicks Fuel Cell Systems Explained JohnWiley amp Sons New York NY USA 2nd edition 2003

[32] A C Yunus and A B MichaelThermodynamics An Engineer-ing Approach 5th edition 2007

[33] R B Bird W E Stewart and E N Lightfoot TransportPhenomena John Wiley amp Sons New York NY USA 2ndedition 2002

[34] E Himmelblau and A Lesdon Optimization of Chemical Engi-neering Processes McGraw-Hill Chemical Engineering SeriesMcGraw-Hill 2nd edition 2001

[35] M Bogani Analysis of proton exchange membrane fuel cell bycomputer simulation [MS thesis] University of the Witwater-srand Johannesburg South Africa 2009

[36] S Ivar Sensitivity of the Chemical Exergy for AtmosphericGases and Gaseous Fuels to Variations in Ambient ConditionsDepartment of Energy and Process Engineering NorwegianUniversity of Science and Technology Trondheim Norway2006

[37] V Amir N Aminreza G Mohammad and V Sadegh ldquoExergyconcept and its characterizationrdquo International Journal of Mul-tidisciplinary Sciences amp Engineering vol 2 pp 47ndash51 2011

[38] S Masanori and H Abdelaziz ldquoIntroduction to the concept ofexergy-for a better understanding of low-temperature-heatingand high-temperature-cooling systemsrdquo Research Notes vol2158 p 45 2002

[39] A Kazim ldquoExergy analysis of a PEM fuel cell at variableoperating conditionsrdquo Energy Conversion amp Management vol45 no 11-12 pp 1949ndash1961 2004


[40] M Miansari K Sedighi M Amidpour E Alizadeh and MO Miansari ldquoExperimental and thermodynamic approach onproton exchange membrane fuel cell performancerdquo Journal ofPower Sources vol 190 no 2 pp 356ndash361 2009

[41] R Seyezhai and B L Mathur ldquoMathematical modeling ofproton exchange membrane fuel cellrdquo International Journal ofComputer Applications vol 20 no 5 pp 1ndash6 2011

[42] M Tafaoli-Masoule M Shakeri and A Bahrami ldquoProcessparameters for maximum power of a proton exchange mem-brane fuel cellrdquo Journal of Petroleum and Gas Engineering vol3 no 2 pp 16ndash25 2012

[43] PMargalefOn the poly-generation of electricity heat and hydro-gen with high temperature fuel cells [PhD thesis] University ofCalifornia Irvine Irvine Calif USA 2010

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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ElectrochemistryInternational Journal of



CatalystsJournal of


is their ability to capture excess heat generated and use itin a cogeneration-like manner or for spacewater heating[12 13] Other major advantages that fuel cells hold overinternal combustion engines include the high efficiency ofoperation and lack of harmful pollutant emission Despiteresearchers and government accorded recognition to fuelcells particularly the proton exchange membrane fuel cell(PEMFC) as the environmentally friendly alternative energysource that can competewell with the existing energy sourcesthe high cost of its allied parts and monopoly of the technol-ogy have hindered the commercial availability of fuel cells asalternative energy sources [14ndash16] In the past few years goodprogress has been made to achieve the commercialization ofthis alternative energy source by reducing the cost of the cellcomponents which are made of the electrode flow field plateand membrane [17] However lack of understanding of theinfluence of various parameters on the rate of production ofenergy by the fuel cell system remains a serious issue whichis the focus of this present study On this note the first andsecond laws of thermodynamics have been recognised asmajor tools for measuring the energy and exergy of the fuelcell technologies [18]

The first law of thermodynamics (energy analysis) dealswith the quantity of energy and states that energy can neitherbe created nor destroyedThe lawmerely serves as a necessarytool for accounting for the energy during a process and offersno challenges to engineers The second law (exergy analysis)however deals with the quality of energy degradation ofthis energy during a process entropy generation and lostopportunities to do work and offers plenty of room forimprovement The second law of thermodynamics has beenproven to be a powerful tool in the optimization of complexthermodynamic systems [19ndash21] In recent times exergyanalysis has become a key aspect in providing a betterunderstanding for the analysis of power system processes thequantification of sources of inefficiencies and distinguishingquality of energy (or heat) used [22ndash24]

The aim of this study is therefore to develop a predictivemathematical model to determine the quantity of energythat can be produced by fuel cells as a function of operatingparameters Simulation of the developedmodel is expected toprovide information on the interaction of various parametersthat affect the performance of proton exchange membranefuel cell

2 Conceptualization ofthe Modelling Technique

This study is focused on the theoretical mathematical modelthat can be used to quantify the performance of a fuel cellas a function of operating parameters The mathematicalmodel will consist of electrochemical heat energy and exergyanalysis components The following assumptions were madein developing the predictive model

(i) There is incomplete utilization of the fuel and oxidantgases during the reaction process

(ii) The voltage losses encountered are activation polar-ization ohmic polarization and concentration polar-ization

(iii) The enthalpy calculations are based on standardtemperature

(iv) The heat losses in the system are by natural convec-tion forced convection and radiation

Equations (1)ndash(3) represent the reactions taking place ina typical PEMFC system [13]

anode 2H2 997888rarr 4H+ + 4eminus (1)

cathode O2 + 4H+ + 4eminus 997888rarr 2H2O (2)

overall 2H2 +O2 997888rarr 2H2O (3)

The actual (or net) output voltage of the PEMFC 119881cell as afunction of current temperature partial pressure of reactantand membrane humidity can be expressed as follows

119881cell = 119864Nernst minus 120578act minus 120578ohmic minus 120578conc (4)

where 119864Nernst is the thermodynamic equilibrium potential oropen circuit voltage and 120578act 120578ohmic and 120578conc are activationohmic and concentration overvoltages respectively Othernames for overvoltages are polarization or losses and theyrepresent voltage drop

The reversible cell voltage or thermodynamic potential isthe maximum voltage attained from a fuel cell at thermody-namic equilibrium which can be obtained by applying theNernst equation as shown as follows

119864Nernst = 119881∘ + 119877119879119899119865 ln[[1199011015840H2 (1199011015840O2)051199011015840H2O ]

] (5)

where 119881∘ is the standard state reference potential (29815 Kand 1 atm) at unit activity 1199011015840H2 1199011015840O2 and 1199011015840H2O are par-tial pressures of hydrogen oxygen and water respectively119877 is the universal gas constant (8314 Jmole K) 119879 is thecell operating temperature (K) 119865 is the Faraday constant(96485 Cmole) and 119899 represents the number of moles ofelectrons transferred having a value of 2

Equation (4) shows that part of the voltage is lost indriving the chemical reaction at the electrodes This lostvoltage is known as activation overvoltage (120578act) which occursat both the anode and cathode Activation overvoltage ishowever more predominant at cathode since the hydrogenoxidation is faster than oxygen reduction A parametricequation for representing activation overvoltage as proposedby Uma [25] is shown in the following equation

120578act = minus [1205851 + 1205852119879 + 1205853119879 [ln (119888lowastO2)] + 1205854119879 [ln (119894)]] (6)




(7)







(10)




119877ionic = 119903119872119897mem119860 (12)


119903119872= 1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25]












119881cell = 119881∘ + 119877119879119899119865 ln[

[1199011015840H2 (1199011015840O2)051199011015840H2O ]

]


)

(17)








(19)





119898H2 in = 119898H2 react + 119898H2 out (21)

119898O2 in = 119898O2 react + 119898O2 out (22)










and (22) as follows



PEMFC

Fuel cell system

H2in H2out

H2O

O2inO2out




Similarly










(32)






QH2O


QO2 in

Qloss

QH2 in

QO2 out

QH2 out


QE (VIt)








119876input = 119876H2 in + 119876O2 in (36)





119876loss = 119876nc + 119876fcn + 119876rad (38)



119876cond119860 = QΔ119879119884 (39)


119876nc = ℎnc119860FC (119879FC minus 1198790) (40)




119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)





(43)




(44)



119876119864 = 119881cell times 119868119905 (45)




(46)


Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)






(49)



(50)



(51)




= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




(7)







(10)




119877ionic = 119903119872119897mem119860 (12)


119903119872= 1816 [1 + 003 (119894119860) + 0062 (119879303)2 (119894119860)25]












119881cell = 119881∘ + 119877119879119899119865 ln[

[1199011015840H2 (1199011015840O2)051199011015840H2O ]

]


)

(17)








(19)





119898H2 in = 119898H2 react + 119898H2 out (21)

119898O2 in = 119898O2 react + 119898O2 out (22)










and (22) as follows



PEMFC

Fuel cell system

H2in H2out

H2O

O2inO2out




Similarly










(32)






QH2O


QO2 in

Qloss

QH2 in

QO2 out

QH2 out


QE (VIt)








119876input = 119876H2 in + 119876O2 in (36)





119876loss = 119876nc + 119876fcn + 119876rad (38)



119876cond119860 = QΔ119879119884 (39)


119876nc = ℎnc119860FC (119879FC minus 1198790) (40)




119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)





(43)




(44)



119876119864 = 119881cell times 119868119905 (45)




(46)


Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)






(49)



(50)



(51)




= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





119881cell = 119881∘ + 119877119879119899119865 ln[

[1199011015840H2 (1199011015840O2)051199011015840H2O ]

]


)

(17)








(19)





119898H2 in = 119898H2 react + 119898H2 out (21)

119898O2 in = 119898O2 react + 119898O2 out (22)










and (22) as follows



PEMFC

Fuel cell system

H2in H2out

H2O

O2inO2out




Similarly










(32)






QH2O


QO2 in

Qloss

QH2 in

QO2 out

QH2 out


QE (VIt)








119876input = 119876H2 in + 119876O2 in (36)





119876loss = 119876nc + 119876fcn + 119876rad (38)



119876cond119860 = QΔ119879119884 (39)


119876nc = ℎnc119860FC (119879FC minus 1198790) (40)




119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)





(43)




(44)



119876119864 = 119881cell times 119868119905 (45)




(46)


Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)






(49)



(50)



(51)




= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


PEMFC

Fuel cell system

H2in H2out

H2O

O2inO2out




Similarly










(32)






QH2O


QO2 in

Qloss

QH2 in

QO2 out

QH2 out


QE (VIt)








119876input = 119876H2 in + 119876O2 in (36)





119876loss = 119876nc + 119876fcn + 119876rad (38)



119876cond119860 = QΔ119879119884 (39)


119876nc = ℎnc119860FC (119879FC minus 1198790) (40)




119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)





(43)




(44)



119876119864 = 119881cell times 119868119905 (45)




(46)


Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)






(49)



(50)



(51)




= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119876cond119860 = QΔ119879119884 (39)


119876nc = ℎnc119860FC (119879FC minus 1198790) (40)




119876rad = 120576120590119860FC (1198794FC minus 11987940 ) (42)





(43)




(44)



119876119864 = 119881cell times 119868119905 (45)




(46)


Δ119867rxtn = Δ119867∘rxtn + int119879298

(Δ119862119901) 119889119879 (47)






(49)



(50)



(51)




= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



= tm + CH (52)


= ke + pe + tm + CH (53)


119890 = 119890ke + 119890pe + 119890tm + 119890CH (54)


= 119898119890ke + 119898119890pe + 119898119890tm + 119898119890CH (55)


119890ke = 12V2 (56)


119890pe = 119892119885 (57)






119890CH = 1198771198790 ln( 119875011987500119894) (59)




(60)


(ℎ minus ℎ0) = int1198791198790

119862119901 (119879) 119889119879 = 119862119901 (119879 minus 1198790) (61)

(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(120597119881120597119879)119889119875 (62)



(119904 minus 1199040) = int1198791198790

119862119901119879 119889119879 minus int1198751198750

(119877119875)119889119875 (64)


(119904 minus 1199040) = 119862119901 ln( 1198791198790) minus 119877 ln( 1198751198750) (65)


119862119901 = 119862V + 119877 or

119877 = 119862119901 minus 119862V (66)






119896 = 119862119901119862Vor

1119896 = 119862V119862119901 (69)


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Hence (68) becomes








((119896minus1)119896)]+ 1198771198790 ln( 119875011987500119894)

(73)


= 12119898V2 + 119898119892119885


+ 1198981198771198790 ln( 119875011987500119894)

(74)




120576 = net(O2119877 + H2 119877) minus (O2119875 + H2O119875) (76)

0

02

04

06

08

1

12

0 005 01 015 02 025 03 035 04 045

Cell

vol

tage

(V)





net = 119881cell sdot 119868 (77)







0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

01

02

03

04

05

06

07

08

09

1

05

06

07

08

09

1

11

12

0 02 04 06 08 1 12

Cel

l vol

tage

(V)


Pow

er d

ensit

y (W

cm

2)

333K

343K

353K373K 400K


0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)





14

0

01

02

03

04

05

06

07

08

09

1

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Volta

ge (V

)


Pow

er d

ensit

y (W

cm

2)




0

02

04

06

08

1

12

0

01

02

03

04

05

06

07

0 02 04 06 08 1 12

Volta

ge (V

)

Hyd

roge

n flo

w ra

te (m

gs)

Output voltage


H2 flow rate




0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

02

04

06

08

1

12

0

10

20

30

40

50

60

70

0 02 04 06 08 1 12

Volta

ge (V

)

Oxy

gen

flow

rate

(mg

s)

Output voltage


O2 flow rate


8025

80252

80254

80256

80258

8026

80262

50 70 90 110 130 150 170

Volta

ge (m

V)





80215

8022

80225

8023

80235

8024

80245

8025

10 12 14 16 18 20 22 24

Cell

vol

tage

(mV

)

Humidity ()


0

10

20

30

40

50

60

70

80

90

0 005 01 015 02 025 03 035 04 045

Fuel

cell

effici

ency

()





30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


30

35

40

45

50

55

60

65

0 005 01 015 02 025 03 035 04 045

Ener

gy an

d ex

ergy

effici

ency

()







537545375553756537575375853759

537653761537625376353764

50 60 70 80 90 100 110 120 130 140 150

Ener

gy effi

cien

cy (

)



48196

48197

48198

48199

482

48201

48202

48203

48204

50 60 70 80 90 100 110 120 130 140 150

Exer

gy effi

cien

cy (

)






47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


47

48

49

50

51

52

53

54

55

10 12 14 16 18 20 22

Ener

gy an

d ex

ergy

effici

ency

()

Humidity ()















4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of







4 Conclusions


Competing Interests


Acknowledgments


References
























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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