Free Lumped Model for Proton Exchange Membrane Fuel Cell Essay Sample

This article describes the development of a lumped model for proton exchange membrane fuel cells (PEMFC). During the development of the lumped model, a series of complex procedures were tested and proved. The created model was validated with genuine experimental outcomes. A lumped model created relies on linear algebra equations. According to the article, the model is used to analyze the influence of design and operating constraints on the performance of the fuel cell. The performance of a fuel cell is affected by a number of parameters ranging from input temperature, stoichiometric ratio, thickness of the membrane and diffusion layer size.

Introduction and problem description

A fuel cell is a mechanism that can be transformed swiftly from chemical energy to electrical energy and thermal energy. There are several types of types of fuel cells. Within this family, there is a proton exchange membrane fuel cell (PEMFC). The article has selected a proton exchange membrane. According to the article, a proton exchange membrane fuel cell can function at low temperatures. Temperatures can be as low as 80 degrees Kelvin but still high power will be produced with limited negative effects to the surrounding. The article further suggests that proton exchange membrane posse high start up system as well as shadow system performance.

The article points out the above listed advantages as have been extensively investigated in laboratories for the past ten years. The same experiments have been performed in mobile, stationery power generators and electric vehicles. The article sites low cost and high performance as the two main factors that have been controlled in the proliferation of fuel cell technology. Fuel cell technology, according to the authors of the article has been controlled by various elements such as material properties, operating conditions and cell properties. The article cautions that it is imperative to appreciate the effect of parameters on fuel cell performance. Firstly, the article sites physical and mathematical solutions as chief devices in fuel cell technology.

In this case, the article sites the mathematical model as a crucial contrivance in simulation and modeling.  The creation of physical models enables reliable simulation process beneath realistic conditions parameters, in which it is necessary for fuel cell development and optimization. The article presents a lumped model for proton exchange member fuel cell.  There is a correlation between proton exchange membrane fuel cell (PEMFC) with electrochemistry, thermodynamics, hydrodynamics and mass transfer theory. The authors suggest that this correlation makes it complicated to for scientists to come up with a complete mathematical model. The article thus gives credit to the lumped model, according to the authors of this article, the lumped model gives researchers a spring board to study the fuel cell model through the know input and output of fuel cell. Under this method, linear algebraic expressions have been applied. Parametric studies on fuel cell have been carried out and reviewed.

The proton exchange membrane fuel cell (PEMFC) is regarded by many researchers as the future source of clean energy. Researchers hail this technology as a solution to the current environmental crisis. Nevertheless, a number of setbacks and potential risks threaten this technology. There are serious questions regarding the durability, survivability, operation and instant start-up of fuel cell automobiles in low temperatures. The article only dealt with the positives of the proton exchange membrane fuel cell (PEMFC) but failed to highlight the negativities of the system. In as much as the proton exchange fuel cell membrane (PEMFC) is versatile, more studies need to be carried out to establish its reliability as a sole source of clean energy.

The authors of this article only focused on the operation of the fuel cell membrane at low temperatures. An in-depth analysis is needed to establish how the fuel cell system will function at subzero temperatures.  As at is now, the proton exchange fuel membrane can not be regarded as the future source of clean energy. The main problem of the proton exchange membrane is cannot function in subzero temperatures. The water entering the cell must leave the cell as either liquid or vapor. This is not possible under low temperatures below zero. Water is likely to condense inside the cathodes making it impossible for the fuel cell to transmit energy.  There is the issue of energy balance within the fuel cell is also a problem. The total input enthalpy is not guaranteed of a comparable quantity of power in the output enthalpy meaning that total input enthalpy may vary critically. That algebraic expressions as portrayed ion the model may tilt depending on the surrounding factors.

Novelty Claimed By Authors

The authors analyzed the ionic conductivity of and water spontaneous diffusion coefficient t of the membrane. They further explored the effects of the surrounding factors to the fuel cell. Among them was temperature dependence of the transport characteristics. The article also looked at the conductance of the Nafion in respect to the functions of temperature through impendence of spectroscopy. According to the article, a lumped model is a non dimensional model developed with assumptions like steady transport procedure that revolves the coupled transport within the membrane. Novel systematic reactions assume that all gases conform to the gas law, flows channels are laminar and slim catalysts. The water change flow was not given much prominence. The significance claimed by authors can be summarized in five main stages.

Computational  Domain

A whole cell would need a computational model with massive computing memory and extremely long simulation time. The article suggests that a whole computational domain include anode, cathode, gas diffusion layer paths and membrane electrode. All this would lead to a complete computational sphere of proton exchange membrane fuel cell model.

Model Equations

To model developed under by authors is centered on a set of chain equations. The equations control energy balance equations, mass conversion equations, energy balance equations, cell potential and energy cell equations.

mass conversation equation

The article suggests that mass balance of the cell need to be calculated first. This is based on the fact that mass calculations are crucial in determining the required fuel rate of the cell. Mass conversion calculations are dependant on current flow.

Energy balance equation

Energy balance of the cell is the total sum of energy input to the cell. It is equivalent to the total amount of energy generated by the cell.

cell power

It is the energy generated when the fuel is reacted with hydrogen. In this case, hydrogen is converted in two forms. That is, electricity and heat. The fuel produces cells by power as energy.

cell potential

It is the estimated voltage of an electrochemical cell. It is derived fro the thermodynamic doctrines. The moderate electrode potential is the real cell potential varied under typical conditions.


A lumped model for proton exchange membrane fuel cell consists of a series of linear equations as follows:

The rate of mass flow at the cathode can be expressed as follows;


In this case:

mH2 is the flow of hydrogen from anode.

SH2 is regarded as the stoichiometric rate of flow of hydrogen.

I  is taken as the current flow

MH2 represents the molecular mass

F is a faraday’s constant (96487 coulomb/ mole).

The rate of mass flow from the cathode is calculated as flows:


Using the conservation mass low, the rate of water generation can be calculated through the following formula.

Mh2, gen=I*MH2/2*F+I*Mo2/4*F.                                                                                        

In this case, the water that enters the cell leaves as vapor. The authors argued that vapor water was coming from vapor water that entered through the air at the cathode. This means that the total volume of water that runs out of the cell as follows:

(mH2O) l + (mh2O) v = (Mh2O) out                                                                                           

Under the circumstance, (MH2O)l is regarded as the mass flow of liquid water (mH2O) is regarded as the mass flow of water in vapor form.

The article suggested that the rate of vapor water could be estimated as follows

Mh2O=MH2O [PH2O (V)/P cathode (mo2) out/Mo2+ (mN2) sys/MN2]                                 

MH2O, MO2, MN2 is the molecular mass of water, nitrogen and oxygen.

PH2O (v) is the relative pressure of water.

Pcathode is the cathode pressure.

The linear equations continue up to the last level where the final cell volt is determined. The linear equations where solved by use of a MATLAB software. Values of molecular mass, currency density and stoichiometric are used as regarded as input parameters. Mass conversion rate was calculated. Similarly, mass flow rate of input and output was calculated. Through compensation on the amount of the heat equation, the out gas temperature can be calculated.

Losses at the cell can be calculated through standard electrode potentials. The figures of geometric details of the cell can be calculated and displayed in tabular format.

The lumped model as put forward by authors was created because of experiments done under current densities in the mass transport limited environments. There is an expected variance at each process. However, this is not unique to this lumped mode alone, it is a common feature in many single-phase models.


The authors of this article studied that a lumped model is an appropriate model for proton exchange membrane fuel cell. This model was developed in the face of serious assumptions. This hypothesis centered on the effects of the surrounding conditions. The study presumed that the transportation process would be always constant around the transport membrane. The other assumption was that gas processes would obey the gas laws. The study dissected the model into five phases namely; heat transport, mass transport, water management and electric characterization. If the proton exchange membrane fuel cell (PEMFC) is to be accepted as a future source of clean energy, then a number of issues need to be put into perspective in relation to its reliability. At the same time, the durability of the model needs to be examined seriously. The study did not do experiments on the how the model would function in low temperature or subzero temperatures. 

Furthermore, there are no clear objectives for the model.  The authors need to have studied and discovered in-depth strategies for robust start-up of proton exchange membrane fuel cell in extreme temperatures. Looking at the model, it is apparent that the study needed to have analyzed the issues surrounding the question of subzero temperatures. The authors need to have carried out through investigations and explore possible solutions in regard to the challenge of low temperatures.

A single-phase model like the one detailed in the article should have carried out a detailed literature review to determine the magnitude of free problems and possible solutions to the problem.

The authors observed that the lumped model is ideal for proton exchange membrane fuel cell. They further stated that the model was pegged on linear algebraic equations. This might not be appropriate for experiments of this nature. The authors need to have carried out a component level energy analysis to have in-depth facts concerning energy requirements for start-up from subzero temperature. If a model of this kind is to be adopted globally, then issues surrounding start up issues need to have been ironed out at infant stages.

The article further points out that the proton exchange membrane contains high start up capability and shadow system output. According to the authors, this is the main advantage of the lumped model.

The authors failed to carry out infant steps with the aim of evaluating the myriad freeze-start remedies and potential technologies to address the issues. Why did the study failed to conduct analytical analysis concerning the fuel cell cooling time. The article mentions little about the effects of potential fuel cell use. Currently, the world is in need of technology of this nature to combat challenges carbon emissions. It is not enough for authors to assume that large regions of populated areas hardly low temperatures beyond the recommended. World temperatures are changing at an alarming rate. A serious research need to appreciate this phenomenon from the outset.

In order to bolster the effectiveness of the proton exchange membrane fuel cell, hostic approaches need to be adopted. A number of combined freeze management supporting techniques should be adopted to contain issues arising from subzero temperatures. Furthermore, various technologies should be adopted to help ease the challenge of proton exchange membrane fuel cell Freeze and swift start. The only problem with the application of multiple approaches is the high cost. Application of numerous technologies would require more funding and more time than the lumped model. A clear transition channel within the fuel cell need to be investigated adequately if this model is to be adopted in the future use. As it is now, it is not known whether the transmission within the cell is reliable or not.