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The Ohio State University

Department of Chemical & Bimolecular Engineering

Lab E-13

Fuel Cell

Group no. 39

Zach Reyes, Group Leader MB# 610

Steven Nystrom, Operations Engineer

Austin Hounshell, Design Engineer

Mark Ferris, Development Engineer

Date Due/Submitted: May 29, 2013

Abstract

Hydrogen fuel cells are of interest to research because of their ability to generate power

with water as a byproduct instead of harmful greenhouse gasses. While the hydrogen supply for

fuel cells can be produced from fossil fuels, it can also be produced from cleaner bio-fuels as

well as the electrolysis of water. The purpose of this experiment was to determine the desirable

operating conditions to generate maximal power at a high efficiency. Two fuel cells were used,

one made of plastic and one made of metal. The fuel cells were tested individually with a ‘dead-

end’ configuration and also tested together in series with an ‘open-ended’ configuration with

their circuits wired in both series and parallel. The effect of inlet hydrogen flowrate and

humidity content were also tested for each configuration. The results were applied to a design

extension where the cost of replacing standard electricity with hydrogen fuel cells was

calculated. The results of the experiment showed that the dead-end flow setup is more efficient.

Increasing the hydrogen flowrate proved to decrease the efficiency for all set-ups. The plastic

fuel cell produced more power in general, despite having less total surface area on the cells. The

parallel circuit showed better current and power production than the series circuit. The design

extension showed that it is not cost effective to replace standard electricity with hydrogen fuel

cells with the current technology.

Table of Contents

Table of ContentsPurpose........................................................................................................................................................1

Introduction.................................................................................................................................................2

Experimental Description............................................................................................................................5

Results and Discussion.................................................................................................................................7

Error Analysis.............................................................................................................................................23

Conclusions................................................................................................................................................25

Recommendations.....................................................................................................................................26

Design Extension.......................................................................................................................................27

Notation....................................................................................................................................................36

Works Cited...............................................................................................................................................37

Appendix A..................................................................................................................................A1

Appendix B..................................................................................................................................B1

Appendix C..................................................................................................................................C1

Appendix D..................................................................................................................................D1

Appendix E..................................................................................................................................E1

Appendix F...................................................................................................................................F1

List of FiguresFigure 1: Plastic Fuel Cell Voltage Plot.......................................................................................................10Figure 2: Plastic Fuel Cell Power and Current Plot.....................................................................................10Figure 3: Open Ended Fuel Cell Trials........................................................................................................12Figure 4: Metal Fuel Cell Voltage Plot........................................................................................................13Figure 5: Metal Fuel Cell Current Plot........................................................................................................13Figure 6: Metal Fuel Cell Power Plot..........................................................................................................14Figure 7: Dead End Fuel Cell Efficiency......................................................................................................15Figure 8: Dead End Voltage Plot................................................................................................................16Figure 9: Dead End Current and Power Plot..............................................................................................17Figure 10: Parallel Circuit Voltage Plot......................................................................................................18Figure 11: Parallel Circuit Current Plot......................................................................................................19Figure 12: Parallel Circuit Power Plot........................................................................................................20Figure 13: Series Circuit Voltage Plot.........................................................................................................21Figure 14: Series Circuits Plot....................................................................................................................22Figure 15: Series Circuit Power Plot...........................................................................................................22Figure 16: Plastic Fuel Cell, Volume of Room Plot.....................................................................................29Figure 17: Metal Fuel Cell, Volume of Room Plot......................................................................................29Figure 18: Plastic Cost Analysis..................................................................................................................30Figure 19: Metal Cost Analysis...................................................................................................................30Figure 20: Cost Analysis Varying Humidity.................................................................................................31Figure 21: Plastic Fuell Cell Total Cost Analysis..........................................................................................32Figure 22: Metal Fuel Cell Total Cost Analysis...........................................................................................32Figure 23: 6 Year Project Cost Analysis......................................................................................................33Figure 24: 100 Year Forecast Cost Analysis................................................................................................34

List of TablesTable 1: Plastic Open-Ended Fuel Cell Efficiency..........................................................................................7Table 2: Metal Open-Ended Fuel Cell Efficiency........................................................................................11Table 3:Dead-End Flow, Varying Pressure Each Trial.................................................................................15Table 4: Series Flow, Parallel Circuit, Varying 3 Flowrates & 3 Humidities................................................17Table 5: Series Flow, Series Circuit, Varying Flowrate & Humidity............................................................20Table 6: Error Analsysis Quantitative Results............................................................................................23Table 7: Number of Stack Required for Plastic Fuel Cells..........................................................................28Table 8: Number of Stack Required for Metal Fuel Cell.............................................................................28Table 9: Overall Efficiency..........................................................................................................................35

Purpose

There are a few purposes of running the fuel cell lab. First, they procedure is not given

thus there is a lot of autonomy in choosing how to test the parameters given. Next, the effect that

humidity has on the performance and power out of the fuel cell. By varying the hydrogen

flowrates at various humidities, one can extrapolate how to best optimize a fuel cell system.

Furthermore, the dead end or open ended flow will be compared as well as two different kinds of

fuel cells. Lastly, the cells will be connected in series and parallel to compare the different

effects the order of fuel cells can play on its efficiency. It is also to compare and learn the theory

and theoretical equations as to gain knowledge on future potential paths of this technology.

1

Introduction

Hydrogen fuel cells are an area of interest due to the ability to generate energy without

using highly polluting fossil fuels. This is done by converting chemical energy into electricity as

opposed to energy produced in other processes such as combustion engines.

A particularly common type of fuel cell to be examined is the proton exchange membrane

(PEM). Similar to a battery hydrogen fuel cells have both anode and cathode layers.

Components of the cell include these layers, the membrane, and gas diffusion layers. As the

name suggests hydrogen gas is the fuel fed into the anode layer of the cell as fuel which can be

split using platinum. The reaction follows per the subsequent equation.

H2→2H++2e (1)

Oxygen is a typical oxidant but can be difficult to split even with platinum and other gasses can

be used such as nitrogen or carbon. Iron-based catalysts are becoming more viable than before

but still do not meet the Department of Energy’s benchmark for energy production. The Oxygen

fed into the cathode can be either in pure gaseous form or in air and proceeds according to the

following equation.

12O+2H++2e→H 2O

(2)

Upon oxidation of hydrogen protons and electrons each are passed through the PEM and the

cathode, respectively. These reactions are governed by the equation below used to calculate

theoretical potential of a cell.

ETheo0 = ΔG

0

nF (3)

2

In the experiment cell type, cell configuration, hydrogen flow rate, and humidity are

tested to observe their effects on the efficiency of a hydrogen fuel cell system. Configurations

consist of dead-ended and continuous flow. The two fuel cell types used in this experiment are a

plastic and metal fuel cell with five and four cells in them, respectively. The plastic fuel cell is

comprised of five cells each with an active fuel area of 10 cm2 while the metal cell contains four

cells each with an active area of 25 cm2. These active cell areas result in the metal cell having a

greater active area than the plastic one. In a fuel cell power can be related directly to area of the

fuel cell used and number of actual cells used in the system. Running the cells in open-ended

configuration means that the exhaust valves of the system are open while performing the

experiment. The dead-ended configuration, on the other hand, is performed with the exhaust

valves closed forcing the hydrogen to pass through the membrane. Dead-ended fuel cells are

usually found to have a high overall efficiency if the theoretical Faraday efficiency is assumed to

be one. This assumption is typically made because the configuration forces hydrogen through

the membrane discounting the fact that only a stoichiometric amount of hydrogen can be

oxidized in a certain amount of time. The cells are also put in series and parallel configurations

to test the efficiency of each. This change is mainly through the circuit and not through the flow

as changing flow direction can be difficult.

Fuel cells must constantly have a certain amount of water inside them as too much will

cause the membrane to flood and too little will cause the membrane to become too dry. This

results in a need for water management to be important which is problematic due to the fact that

polarization causes water to be attracted to the cathode. Preventing undesired water flow can be

done by utilizing an electroosmotic pump. Independent of water management, a platinum

catalyst can be easily “poisoned” by carbon monoxide gas which must be kept to levels as low as

one part per million (ppm). Experiments are being run in hopes to find a catalyst that is less

sensitive to such impurities as currently hydrogen is not produced via hydrolysis due to it not

being cost effective so it is produced by steam reforming light hydrocarbons which produces

carbon monoxide. The integrity of the catalyst can also be damaged when coming into metal

ions produced by corrosion in the system.

3

The PEM fuel cell is best used when low to medium outputs of energy are required and a

high sensitivity to load changes are needed (Cite Efficiency and Economics). The fuel cell is

limited by the inherent electrical deficiency which leaves the cell only able to operate at about 30

percent of maximum power when using the Higher Heating Value (HHV) of hydrogen.

Efficiency and power output are inversely related confirming the best use to be for lower energy

requirement situations. Overall efficiency can be calculated per the following equation.

ηoverall=ηf∗V eff∗ηmax (4)

Additionally different models of the PEM can be considered. The first model to consider

is the stack flow model. In this model fuel cells are combined in series to generate power. In

stack cells, non-uniform flow can occur which is known to cause worse performance and can be

prevented by sufficiently increasing the diameter. Controlling the temperature inside the fuel

cells is another way to affect performance.

The major issue right now with the PEM fuel cell is its sensitivity to gasses such as

carbon monoxide inside the system reaction and the fact that using platinum as a catalyst is

exorbitantly expensive and must be reduced to roughly one fourth the amount in order to begin

competing with combustion engines in terms of cost.

4

Experimental Description

To begin the experiment, the system had to be purged and calibrated. The nitrogen gas

was turned on for approximately 15 minutes in order to dry out the cell of any moisture and any

other species that may be in the cell. While the system is being purged a calibration on the

electrical and computer system must be done. This is accomplished by taking a base line with

nothing connected to the board and then the current, volts and power are zeroed. Then the circuit

is shorted and the same baseline is established. To test the system and do trials the nitrogen was

turned off and the hydrogen was turned on; the humidity flow meter read 80 mL/min while the

total read 100 mL/min. There is an inlet feed that gets split into 2 streams, one gets put through a

humidifier that is assumed to get air fully saturated with water vapor and the other is sent to the

last flow meter where it is coupled with the humidified air. This 80% humidified hydrogen gas

was run for 5 minutes to rehydrate the cell in an attempt to get better results. All the trials tested

air flowrates of 20-145 mL/min and humidity from 10 to 90 percent.

The metal fuel cell (FC) was hooked up and trials could begin to run. For the open ended

tests, the following flowrates and humidity are used 20, 45, 70, 95, 120, and 145 mL/min and

10%, 50% and 90%. The flowrate was set by simultaneously changing the total and humidified

air flow rates to achieve the proper humidity and flowrate. For the first 3 trials the flowrate is

kept constant and the humidity changes, then the next flowrate is chosen and the humidity varies.

After every 5 trials the system was purged for 5 minutes with the nitrogen in order to get more

consistent results. The computer that was used to analyze the data measured voltage (mV),

current (mA) and power (mW), and made 4 plots. The max value was recorded and that was the

data point that was used per trial. The max is taken due to the way the instrument measures

energy and how the fuel cell makes energy. The voltage is max around the first few seconds of

testing since the resistance was varied in the program from infinity to 0. The max current comes

in about half way through the testing when the resistance and optimum electron flow from the

FC was obtained. After the 18 trials were completed, the plastic fuel cell was hooked up and the

same 18 trials were run purging with nitrogen every 5 trials.

5

To test a dead end configuration, the outlet stream was closed and a pressure was built

up. Before the valve was closed an inlet humidity and total flow was 90 and 100 mL/min and

started at 1 psig. First, the metal FC was run at the 1 psig pressure, and then the valves were

changed so that the plastic FC could run at those conditions. The valves were opened and the

pressure was changed to 1.5 and 2 psig and ran both the metal and plastic FC.

For the last set of trials, the flow was set in series with the outlet of the metal FC set to go

directly into the inlet of the plastic one. The circuit was set in parallel in which the black leads

from both FCs' went into the black hole and the red leads in the red hole. 9 trials were conducted

for this configuration; they were 20, 80 and 140 mL/min and 10%, 50% and 90% humidity.

After the results were collected the circuit was switched to series where the metal FC black lead

went into the black hole on the circuit board, the red lead went into the plastic FC’s black lead,

and the plastic FC’s red lead was put into the red hole. The same 9 trials were conducted. Lastly

the system was purged for 6 minutes with nitrogen to make sure there were any damaging

species in the fuels cell that would just sit in there until the next lab were pushed out.

6

Results and Discussion

The fuel cell experiment information is first collected for an open-ended cell with varying

flow rates and humidity while maintaining a system pressure of 1.5 psig. The data for the plastic

fuel cell is seen below in Table 1.

Table 1: Plastic Open-Ended Fuel Cell Efficiency

Flow Rate (mol/min)1.50E-

05

3.38E-

05

5.26E-

05

7.14E-

05

9.02E-

05

1.09E-

04

Theoretical Current

(mA)2901.07 6527.41

10153.7

5

13780.1

0

17406.4

4

21032.7

8

Overall Efficiency Plastic Open-Ended (10% Humidity)

Faraday Efficiency 0.33 0.14 0.09 0.07 0.05 0.04

Veff 0.75 0.79 0.79 0.78 0.79 0.78

Overall Efficiency 0.21 0.09 0.06 0.04 0.04 0.03



Veff 0.78 0.79 0.79 0.78 0.79 0.79




Veff 0.79 0.78 0.79 0.79 0.79 0.79


It appears that as molar flow rate is increased Faraday efficiency and overall efficiency

decrease while effective voltage is stable. Humidity is also seen to have little to no effect on the

efficiency for the plastic fuel cell membrane. Overall efficiency is seen to decrease every time

flow rate is increased.

7

The decrease in efficiency despite greater amount of H2 gas being pumped into the

system is because this is considering all of the H2 gas being fed into the fuel cell is utilized. The

membrane hits a certain limit when it does not matter how much more H2 is fed into the system

no additional power can be produced. All extra H2 entering the system at this point will not be

reacted and will only decrease the efficiency, as seen by the results.

The plastic cell shows lower than typical performance which is about 30 percent for an

average fuel cell. Most fuel cells in good working condition see overall efficiencies ranging

from 40 to 60 percent. The cells that were tested have been used for many years and their

effective area is likely lower than when new due to membrane deformation and very minor

fouling that can be attributed to small contaminants in the surrounding air and inlets. An issue

inherent with the meter readings in the system also causes an issue with efficiency calculations in

that meters often ranged between values as opposed to staying close to the value desired. This

issue is discussed in more depth in the error analysis section of this report. Values for molar

flow rate are calculated with the Ideal Gas Law in Equation 5 below.

η=PVRT (5)

If the assumption that the Ideal Gas Law is incorrect, it would throw off the calculated

molar flow rate, the results calculated for the overall efficiency for each trial could be off. The

system is considered to be running at 25 degrees Celsius or about 298 Kelvin which would result

in a larger than actual molar flow rate if running at a lower temperature. However it must be

noted that compressed air is very cold and there is a good chance the temperature in the inlet

flow is not 25 ºC and not all consistent.

After calculating the molar flow rate the theoretical current can be found by the following

Equation 6

ITheoretical=2∗η∗F (6)

Theoretical current can only vary with molar flow rate which means any error associated

will be due to any errors in calculating the flow rate. Once the theoretical voltage is found the

8

Faraday efficiency can be found by dividing experimental current by theoretical current as seen

below in Equation 7.

η f=I ExperimentalITheoretical (7)

Any error from normal values in the Faraday efficiency is the result of theoretical current

calculations and equipment error in recording the experimental current. The next value to be

calculated is the effective voltage as follows.

V eff=

V Experimental¿cellsV Theoretical (8)

Any fluctuations or abnormalities in effective voltage are again mainly resulting from any

error in recording the experimental voltage. The maximum efficiency calculated is done so

assuming the values used to be exact so no error can be analyzed. The last calculation made is of

the overall efficiency which is according to Equation 9 underneath.

ηOverall=ηmax∗V eff∗ηf (9)

As each of the values used in determining the overall efficiency have already been

calculated any error propagation in the value is due to error previously described.

Figure 1 below shows the voltage vs. flowrates with each line representing the constant

humidity throughout the trial. It appears that each humidity has a dampened sin wave on its

output voltage showing the voltage may be function of a few parameters that are going through

maxima and minima as the flowrate increases. As also seen in Figure 4 the 10% humidity shows

a large increase with the transition from the first to second flowrate. This may be due to the fact

that there is a critical minimum flowrate that is sensitive. These lines of the graph though stay

relatively straight showing the Veff remains approximately constant.

9

0 20 40 60 80 100 120 140 1604500

4550

4600

4650

4700

4750

4800

4850

4900

Plastic FC Voltage vs Flowrate

10%50%90%

Flowrate (mL/s)

Figure 1: Plastic Fuel Cell Voltage Plot

Figure 2 below is the power and current of the plastic FC vs. its flowrate. The nonlinear

growth of the power is contributed to its equation 10, since the current I and its voltage V change

at much different rates the line takes on a skewed appearance. The current (bottom 3 lines) also

takes on a sinusoidal theme with its output relative to the flowrate.

P=IV (10)

0 20 40 60 80 100 120 140 160800900

100011001200130014001500160017001800

Plastic FC Power&Current vs Flowrate

Current 10%Current 50%Current 90%Power 10%Power 50%Power 90%

Flowrate (mL/s)

mA

& m

W

Figure 2: Plastic Fuel Cell Power and Current Plot

10

The metal fuel cell provided also shows lower than typical efficiency. As seen in Table 2

below.

Table 2: Metal Open-Ended Fuel Cell Efficiency

Flow Rate (mol/min)x10-5 1.50 3.38 5.26 7.14 9.02 10.9

Overall Efficiency Metal Open-Ended (10% Humidity)


Veff 0.65 0.67 0.67 0.67 0.67 0.67




Veff 0.67 0.67 0.67 0.67 0.67 0.67




Veff 0.67 0.67 0.67 0.67 0.67 0.67


Here, similar to the plastic fuel cell, the overall efficiency and Faraday efficiency appear

to be decreasing with increased flow rate while effective voltage stays roughly constant. The

overall efficiency decreases after the 10 percent humidity trials but this is likely more of a

correlation than causation.

The decreased overall efficiency can again be accounted for in multiple ways, one of

which is decreased effective membrane area due to age. Once again assuming the Ideal Gas Law

holds true, the calculated molar flow rate of H2 could be incorrect. In using the Ideal Gas Law

the temperature could be different from the 298 Kelvin it is assumed to be. The fact that the

metal fuel cell has only four stacks of cells while the plastic fuel cell has five could account for a

difference in overall efficiency. However, the metal cell appears to work just as well if not a

small amount more efficiently when compared to the plastic cell as the same conditions.

11

0 20 40 60 80 100 120 140 1600.00

0.05

0.10

0.15

0.20

0.25

0.30

Open Ended Fuel Cell Efficiency

Plastic 10% HumidityPlastic 50% HumidityPlastic 90% HumidityMetal 10% HumidityMetal 50% HumidityMetal 90% Humidity

Flow Rate of Hydrogen (mL/min)

Over

all E

fficie

ncy

Figure 3: Open Ended Fuel Cell Trials

Figure 3 above shows the metal fuel cell operation at 20 (mL/min) and 10 percent

humidity yielded the greatest efficiency while also operating at the least efficiency at 145

(mL/min) at all humidity variations. The metal cell is the logical choice as the better performing

cell due to its increased total membrane size. Though the metal cell has only four stacks of cells

each cell has an active area of 25 cm2 and the plastic cell holds five cells, each of the plastic cells

have an active area of only 10 cm2. As seen above humidity does not appear to have any

significant effect on the efficiency of the cells.

Figure 4 below is the metal FC voltage plot. A decreased flattened sampling sin wave

can be observed here as well as in the plastic FC, with this showing a higher dampening to

almost a plateau. This voltage overall though is around 1500 mV less than its plastic equivalent.

It appears this FC has a peak performance around the 50 mL/s flowrate setting for all humidities.

12

0 20 40 60 80 100 120 140 16031203140316031803200322032403260328033003320

Metal FC Voltage vs Flowrate

10%50%90%

Flowrate (mL/s)

Figure 4: Metal Fuel Cell Voltage Plot

The current and power plots for the metal FC are in Figure 5 and 6. In these trials

the trends for power and current are almost the same as the lines from both graphs line up on top

of each other so nicely it is hard to depict any one line from the plot. They both decrease with

output as the flowrate increases reinforcing the Faraday efficiency to go down as the flowrate

increased.

0 20 40 60 80 100 120 140 1600

200

400

600

800

1000

1200

1400

1600

Metal FC Current vs Flowrate

Current 10%Current 50%Current 90%

Flowrate (mL/s)

Curr

ent (

mA)

Figure 5: Metal Fuel Cell Current Plot

13

0 20 40 60 80 100 120 140 1600

200

400

600

800

1000

1200

Metal FC Power vs Flowrate

Power 10%Power 50%Power 90%

Flowrate (mL/s)

Pow

er (m

W)

Figure 6: Metal Fuel Cell Power Plot

After the open-ended configuration values are obtained the fuel cells were switched to a

dead end configuration where the exhaust valves are closed as system pressure is allowed to vary

as opposed to humidity and H2 gas flow rate. The values obtained for the metal fuel cell are

shown in Table 7 below.

In these trials the humidity is kept constant at 90 percent and the flow rate of H2 is kept

constant at 100 (mL/min). The theoretical current is calculated as above and increases with

molar flow rate. Faraday efficiency is assumed to be equal to 1.00 which means that

experimental current achieved is equal to theoretical. This is due to the fact that theoretical

current is calculated assuming that all of the H2 gas fed into the cell is reacted and pushed across

the membrane when in fact this is not true. In the dead-end configuration the exhaust valve is

closed leaving no room for the H2 gas to go anywhere but through the membrane therefore

experimentally obtained data is assumed equal to theoretical.

14

Table 3:Dead-End Flow, Varying Pressure Each Trial

Pressure (psig) 1 1.5 2

Metal

89/100 90/102 90/100Actual Meters

(humidity/total)

3264 3268 3264 Voltage (mV)

710 778 674 Current (mA)

593 661 583 Power (mW)

Plastic

90/99 90/99 89/100Actual Meters

(humidity/total)

4810 4568 4776 Voltage (mV)

996 778 974 Current (mA)

1687 661 1645 Power (mW)

Above in Table 3 are the experimental values for the dead-ended configuration of the

plastic fuel cell. The humidity is again maintained at 90 percent and the flow rate of H2 gas is

held at 100 (mL/min). The Faraday efficiency is again taken to be 1.00 again as it is for the

metal fuel cell. Overall efficiency for the plastic cell is greater than the metal cell in the dead-

ended configuration which is the opposite of what is expected due to active membrane area.

0.8 1 1.2 1.4 1.6 1.8 2 2.20.000.100.200.300.400.500.600.700.800.901.00

Dead-End Fuel Cell Efficiency

Metal 90% Humidity Plastic 90% Humidity

System Pressure (psig)

Ove

rall

Effien

cy

Figure 7: Dead End Fuel Cell Efficiency

15

Above in Figure 7 is the relationship of system pressure to overall efficiency with

constant humidity and H2 flow rate. For the metal cell efficiency is lower than the plastic cell

and roughly constant. The plastic cell shows a lower overall efficiency at the 1.5 psig system

pressure but this is likely reading or measurement error. Metal cell efficiency should be higher

due to increased active membrane but could be lower due to having a more damaged or aged

relative to the plastic cell. An increased system pressure results in an increased molar flow rate

of H2 gas when calculating flow rate using the Ideal Gas Law.

0.8 1 1.2 1.4 1.6 1.8 2 2.22500

3000

3500

4000

4500

5000

Dead End Voltage vs Flowrate

Metal FCPlastic FC

Pressure (psig)

Volta

ge (m

V)

Figure 8: Dead End Voltage Plot

Figure 8 above depicts the voltage output of both fuel cells when run at 90% humidity

under dead end configuration. The voltage remains unchanged by the pressure for the most part

with the metal cell staying linear with the proper significant figures and the plastic fuel cell

dipping a little below which can almost be linearized with rounding and experimental error.

Verifying voltage is independent of flowrate which in this case is being tested in the form of

pressure gradients.

Figure 9 below shoes the current and power plots of the dead end trials. The plastic FC

has a parabolic shape to its current and power with the power having a much greater sensitivity

to the pressure. This could either be from the FC being very dependent upon pressure and that

this 1.5 psig is just a local minimum or the membrane degradation coupled with these few

16

parameters makes this a bad operating pressure. Also, although the graph shows a 1.5 psig the

gauge fluctuated ±0.2 psig making the results vary.

0.8 1 1.2 1.4 1.6 1.8 2 2.2400

600

800

1000

1200

1400

1600

1800

Dead End Current&Power vs Pressure

Metal CurrentPlastic CurrentMetal PowerPlastic Power

Pressure (psig)

mW

& m

W

Figure 9: Dead End Current and Power Plot

Table 4: Series Flow, Parallel Circuit, Varying 3 Flowrates & 3 Humidities

Series Flow: Parallel Circuit

Flowrate (mL/s) 20 80 140

10%

4/23 8/81 16/142 Actual Meters (humidity/total)

4140 4270 4286 Voltage (mV)

1454 1488 1518 Current (mA)

2106 2410 2272 Power (mW)

50%


4252 4172 4296 Voltage (mV)

1500 1488 1548 Current (mA)

2236 2252 2474 Power (mW)

90%


4278 4270 4288 Voltage (mV)

1492 1526 1550 Current (mA)

2361 2328 2538 Power (mW)

17

Table 4 shows series flow with a parallel circuit at various H2 gas flow rates and humidity

settings and humidity is seen to have a direct correlation with power. Power is calculated

according to Equation 10.

As long as the product of current and voltage increases the amount of power generated in

the fuel cell will increase. The data above shows that current increases with H2 gas flow rate

along with voltage. Current should increase as the flow rate of H2 gas is increased because the

amount of electrons produced is increased which results in a more electrons flow. Theoretically

H2 gas could be fed fast enough to utilize all of the platinum catalyst reaction sites which would

slow down the reaction rate but since power is seen to increase for all trials it is likely that this

maximum H2 flow rate is not reached in the experimental parameters.

The parallel circuit series flow voltage is on Figure 10. The average voltages for the

metal and plastic FC are 3279 and 4821 mV and this average, although having a dynamic change

is 4250 mV. This is more than the average of the two showing that the recycling of unused

hydrogen increases the possible voltage.

0 20 40 60 80 100 120 140 1604050

4100

4150

4200

4250

4300

4350

Parallel Circut Voltage

10%50%90%

Flowrate (mL/s)

Volta

ge (m

V)

Figure 10: Parallel Circuit Voltage Plot

18

Figure 11 is the current plot in the parallel circuit and shows a nearly linear trend that is

directly proportional to the flowrate. The following Figure 12 is the power plot. With the

exception of the 10% humidity, which has a local minima around 80 mL/s, the trend is a

nonlinear, increasing exponential like function. This shows that there is a relatively stable power

output until a critical point of about 80 mL/s in which the power increases drastically. The

average FC’s current and power is 715 mA and 1183 mW. This configuration leads to an

average current and power of 1507 mA and 2330 mW. These results, by putting the circuit in

parallel and by effectively recycling part of the unused hydrogen that wasn’t consumed by the

metal FC the current and power was doubled. This makes the efficiency of the device from a

power standpoint double by putting them in parallel. This is influenced from the increase in

current with higher flowrates since voltage is less affected by flowrates.

0 20 40 60 80 100 120 140 1601400

1420

1440

1460

1480

1500

1520

1540

1560

Parallel Circut Current

10%50%90%

Flowrate (mL/s)

Curr

ent (

mA)

Figure 11: Parallel Circuit Current Plot

19

0 20 40 60 80 100 120 140 1602000

2100

2200

2300

2400

2500

2600

Parallel Circut Power

10%50%90%

Flowrate (mL/s)

Pow

er (m

W)

Figure 12: Parallel Circuit Power Plot

Table 5: Series Flow, Series Circuit, Varying Flowrate & Humidity

Series Flow: Series Circuit

Flowrate (mL/s) 20 80 140

10%


8290 8134 8166 Voltage (mV)

914 1000 1022 Current (mA)

2027 2185 2165 Power (mW)

50%


8234 8272 8158 Voltage (mV)

1006 992 1046 Current (mA)

2113 2269 2189 Power (mW)

90%


8314 8168 8166 Voltage (mV)

1008 1014 1004 Current (mA)

2092 2216 2152 Power (mW)

20

In Table 5 for series flow and a series circuit above shows a decrease of voltage with H2

flow rate but a marginal increase with humidity. Current increases similarly but power decreases

for every trial when increasing H2 flow rate from 80 (mL/min) to 140 (mL/min). The increase of

current is likely due to the reduced space as electrons flow less quickly than if in parallel.

Parallel circuits will have greater electron flow and therefore greater current due to the number

of outlets for electrons to flow being doubled. (Is this true?).

The series circuit voltage in Figure 13 shows, with the exception of 50%, a decrease and

levels out with increasing flowrates. This again is due to the critical limit of how fast the

electron and protons can be stripped in each cell. The average voltage is 8211 which is about

double the average voltages of the fuel cells in open ended flow. Which makes sense since the

number of reactions taking place to produce the voltage has been nearly double by putting them

in series flow.

0 20 40 60 80 100 120 140 1608000

8050

8100

8150

8200

8250

8300

8350

Series Circut Voltage

10%50%90%

Flowrate (mL/s)

Volta

ge (m

V)

Figure 13: Series Circuit Voltage Plot

The series flow with the series circuit’s currents and power are Figures 14 and 15. The

average current and power presented are 1000 mA and 2156 mW making the current about 30%

higher and the power almost 50% more again. The current results vary too much to come up

with a defiant pattern but for the most part the higher humidity propagated a higher current. The

powers followed a similar pattern; they arise and fall around the same flowrates with the 50%

21

outputting the most power followed by the 90% then the 10% which partially follows theory that

increased humidity to a certain point enhances the efficiency but the polarization of the water on

the membrane in high quantities degrade performance.

0 20 40 60 80 100 120 140 160800

850

900

950

1000

1050

1100

Series Circut Current

10%50%90%

Flowrate (mL/s)

Curr

ent (

mA)

Figure 14: Series Circuits Plot

0 20 40 60 80 100 120 140 1601900

1950

2000

2050

2100

2150

2200

2250

2300

Series Circut Power

10%50%90%

Flowrate (mL/s)

Pow

er (m

W)

Figure 15: Series Circuit Power Plot

22

Error Analysis

There were several sources of error when determining the molar flowrate of hydrogen

into the fuel cells. Four devices were available to measure the volumetric flowrate of gas; a

rotameter and a mass flow meter to determine the flowrate of humidified gas, a rotameter to

determine the flowrate of dry gas, and a mass flow meter to determine the overall gas flowrate.

Only the mass flow meters were used because they gave a digital reading and there was no error

in interpreting their readings. However, there was a discrepancy between the reading on the

mass flow meter and rotameter for the humidified gas, (10 mL/min?!?!?), so the reading on the

mass flow meters may not have been entirely accurate. The readings from the mass flow meters

were converted to molar flowrates using the ideal gas law, assuming standard temperature and a

pressure of 1.5 psig. However, the actual temperature of the gas was not measured and could

have been different. The pressure also varied from 1.2-1.8 psig during the actual experiment

which will cause some error in calculation, though this is probably minimal compared to the

temperature error and mass flow meter error. All of these errors will affect the calculated molar

flowrates which will affect the theoretical current and consequentially the faraday efficiency.

There were two possible sources of error when adjusting the humidity setting between

trials. The desired humidity was obtained by directing a portion of the flow through a humidifier

and then joining it with un-humidified hydrogen in the desired proportion. Because of this, any

error from the flowrate readings will affect the actual percent humidity. It was also assumed that

the humidifier added 100% humidity to the hydrogen stream, but the actual humidity of the

stream was not tested. If the humidifier added less than 100% humidity, the actual humidity

content was lower than what was recorded.

If a fuel cell membrane is too dry, the resistance across it will increase, reducing the

voltage in the cell (Nagle). However, excess water in the fuel cell can decrease its performance

(Wu,239). Water buildup on the fuel cell membrane can cause polarization and prevent

electrons from flowing through the circuit. The water that builds up can come from the

humidified hydrogen stream as well as from the product of the fuel cell reaction. Purging the

23

system with nitrogen every trial ensures the water build up does not become too great, but the

moisture content in the cell will still slowly increase for the five trials in between purges. This

does not cause error in the calculation steps, but it is another variable that is affecting the

recorded data that will interfere with analysis when trying to determine the effect of manipulated

variables on fuel cell operation.

Table 6: Error Analysis Quantitative Results

Percent ErrorFlowrate (mL/s) 20 45 70 95 120 14510% Humidity 41% 50% 22% 28% 15% 14%50% Humidity 27% 9% 6% 5% 4% 3%90% Humidity 13% 6% 4% 3% 2% 2%

Table 6 above shows the percent error of the humidity and flowrate of the open ended

plastic fuel cell trials. It can be assumed that the percent error in the humidity and total flowrates

will maintain the same error with only negligible changes. Also, since these values are used to

calculate the Veff and overall efficiency and since these numbers are kept linear throughout the

whole calculation process the same percent error at each of the specified conditions will have the

same percent error in any data used in all the other results section. This also holds true for the

dead end or series flow configuration with a linear interpolation between the flowrates and

percent’s.

24

Conclusions

The hydrogen fuel cell experiment tested the effects of hydrogen flowrate,

humidity and flow configurations on the output power and overall efficiency. For part 1 an open

ended configuration was ran with the following flowrates and percent humidities 20, 45, 70, 95,

120, and 145 mL/min and 10%, 50% and 90%; these tested the first two parameters. The effect

of pressures 1, 1.5 and 2 psig were tested on the membrane in a dead end system. The effect of

series flow was tested in two ways; first the circuit was set in parallel and run at 20, 80 and 140

mL/min and 10%, 50% and 90% humidity then the circuit was set in series.

The voltage and effective voltage in the open ended trials in both fuel cells are unaffected

by flowrates. However the overall efficiency is indirectly proportional to flowrate; going against

theory, the trends show that the efficiency and voltage is independent of humidity level in the

open ended trials. The plastic fuel cell has the capability of outputting more power than its

counterpart, but it also has double the membrane area but only about 40% greater. The metal

cell is the most efficient cell for the open ended configuration.

For the dead end configuration not many definitive results lied in the data. The plastic

was more efficient in these trials. The voltage was relatively unaffected by the pressure change

but the plastic fluctuated more perhaps due to its weaker plastic base support opposed to a sturdy

metal structure.

The series flow was tested in parallel and series circuit configuration. The power output

for the parallel circuit remained constant till about 80 then increases where the series rose greatly

and lowered slightly indicating a critical flowrate maximum for them both at different rates. The

power increase is attributed to the greater current in the parallel circuit; overall the average

power in parallel was greater. The increase in power out follows typical circuit laws in terms of

adding in series or parallel but also comes from using more of the unused hydrogen that the

metal cell couldn’t use and the plastic one did.

25

Recommendations

Although expensive the use of a different kind of fuel cell such as an ethanol or methanol

FC could be used to talk better discuss theories that are behind one FC over another and how

they differ fundamentally. It would also aid in getting more diverse data that can be analyzed

plus better see the future technology that fuel cells may or may not go and why. The flowmeters

and rotameters differed greatly sometimes and although the flowmeters was taken to be more

accuracy it would be nice to have meters that all measured the same value to increase certainty in

the results. Fitting the system with more advance or precise rotameters can increase the accuracy

and assurance of all the propagated data. The dials and valves were very far back in the fume

hood; the people with shorter arms had to basically put their head under the glass to turn the

dials. This poses a possible asphyxiation and other problems; it is recommended the somehow

the dials become more accessible. The current configuration for series flow only allows for the

metal FC to go to the plastic one. The plastic to metal series flow could be made by putting in

another simple bypass valve and once again can lead to even more data and comparison that can

be made. Lastly, different operating temperatures may affect the performance and efficiency.

Although hydrogen is flammable, the proper heat coil could safely manipulate the inlet air so that

new testing parameters could be established.

26

Design Extension

Think Smart Inc. wants to provide 4,500,000 kWh per year of power to their office

building using a Proton Exchange Membrane (PEM) fuel cell stack. PEM fuel cell stacks take

hydrogen from an inlet stream and separate the protons and electrons. The electrons are used to

create electricity and then the remaining components combine with oxygen to create water as a

byproduct. To determine the most cost effective way to do this the flow rates and humidity of the

inlet hydrogen stream was analyzed in an open-ended configuration. The initial startup costs will

also be taken into account, which can be determined by the amount of hydrogen fuel cell stacks

needed.

The formation of water by reacting oxygen and hydrogen is catalyzed by platinum in

PEM hydrogen fuel cells. The fuel cell is dependent on several factors including molar flow

rate, efficiency, and the number of cells that make up the fuel cell. With grow molar flow rate

there will be a greater amount of hydrogen flowing into the fuel cell and assuming that all of it

can be reacted the cell should be more efficient and produce more power. This is usually not the

case as all fuel cells have a limit as to how much hydrogen can be processed in a given time.

The amount of cells inside the fuel cell can be increased but what matters more than the number

of cells is the active membrane area the cells provide. As long as active membrane area is

increased efficiency should increase. Increased humidity will increase the efficiency and power

output of fuel cells due to influence of the resistivity of the membrane.

Assuming 365 days a year and 24 hours in a day the amount of power that Think Smart

Inc. would need to achieve is 513.699 kW. From our experiment one stack of fuel cells put out

power on the magnitude of 10-3 kW. So the number of stacks needed would be the power needed

divided by the power produced by one stack. The results from this calculation are shown below

in Tables 7 and 8. Table 7 shows the amount of stacks needed for the plastic fuel cell, while

Table 8 shows the results for the metal fuel cell.

27

Table 7: Number of Stack Required for Plastic Fuel Cells

Table 8: Number of Stack Required for Metal Fuel Cell

20 mL/min 45 mL/min 70 mL/min 95 mL/min 120 mL/min 145 mL/min10%

humidity484621.6981 496327.5362 632634.2365 708550.3448 784273.2824 810250.7886

50% humidity

554750.54 551179.1845 643733.0827 751021.9298 729686.0795 816691.5739

90% humidity

517320.2417 590458.6207 597324.4186 746655.5233 784273.2824 842129.5082

20 mL/min 45 mL/min 70 mL/min 95 mL/min 120 mL/min 145 mL/min10%

humidity404487.4016 346625.5061 315152.7607 317294.0086 313613.5531 327823.2291

50% humidity

380236.1214 309084.8375 302175.8824 335531.6786 312089.3074 313422.2087

90% humidity

353057.732 318474.2715 310392.145 318869.6462 315152.7607 311144.1551

The metal and plastic fuel cells show quite different results. As flow rate increases the number of

stacks needed increases for the metal fuel cell but decreases for the plastic fuel cell. The number of stacks

needed directly affect the initial startup cost of the fuel cells as well as the size of the room needed to

house them. Figure 16 below shows the size of the room required vs. flow rate for the plastic fuel cell and

Figure 17 shows the same thing for the metal fuel cell.

28

0 20 40 60 80 100 120 140 160110

120

130

140

150

160

170

Volume of Room vs. Flow Rate

10% humidity

50% humidity

90% humidity

Flow Rate (mL/min)

Volu

me

of R

oom

(m^3

)

0 20 40 60 80 100 120 140 160160

180

200

220

240

260

280

300

320


10% humidity50% humidity90% humidity

Flow Rate (mL/min)

Volu

me

of R

oom

(m^3

)

Figure 17: Metal Fuel Cell, Volume of Room Plot

From the data it clearly shows for the metal fuel cell as the flow rate of hydrogen

increases the size of the room needed will also increase. However, for the plastic fuel cell the

optimum room size comes at a flow rate of 70 mL/min and 50% humidity. If room size is a

serious concern for ThinkSmart Inc. then these are calculations that need to be considered.

29

0 20 40 60 80 100 120 140 160110

120

130

140

150

160

170


10% humidity

50% humidity

90% humidity

Flow Rate (mL/min)

Volu

me

of R

oom

(m^3

)

Figure 16: Plastic Fuel Cell, Volume of Room Plot

Now that the size of the room and the initial amount of the stacks has been identified now

the optimum flow rate to minimize cost needs to be determined. Figures 18 and 19 below show

the amount spent on hydrogen fuel per year vs. flow rate for plastic and metal respectively.

0 20 40 60 80 100 120 140 16002468

101214161820

Cost vs. Flow Rate


Flow Rate (mL/min)

Cost

in M

illio

ns o

f Dol

lars

Figure 18: Plastic Cost Analysis

0 20 40 60 80 100 120 140 1600

10

20

30

40

50

60

Cost vs. Flow Rate


Flow Rate (mL/min)

Cost

in M

illio

ns o

f Dol

lars

Figure 19: Metal Cost Analysis

The cost of hydrogen used to calculate these costs were $9 per Kg (Hydrogen Production

and Delivery) with the 85-cent discount the final cost was $8.15 per Kg. As one would expect

the cost of hydrogen per year increases greatly as the flowrate increases. This is due to the fact 30

that an increase in flow rate does not necessarily mean an increase in power output, in fact

sometimes in means just the opposite.

From this graph it is difficult to detect if humidity plays any sort of significant role on the

efficiency of the fuel cell. Figure 20 shows the effect of humidity on cost from the 20 mL/min

trials.

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Cost vs Percent Humidity

MetalPlastic

Figure 20: Cost Analysis Varying Humidity

The metal fuel cell seems to have no real trend with 10% humidity having the least

amount of cost. The plastic fuel cell, however, has an inverse relationship between cost and

humidity with 90% humidity proving to be the most cost efficient.

So far cost of hydrogen and the initial startup costs have been discussed separately,

Figures 21 and 22 show the initial startup costs and the cost of 1 years’ worth of hydrogen, for

the plastic and metal fuel cells respectively. The initial startup costs were calculated by

multiplying the number of stacks needed by the cost of one stack. For the plastic fuel cell the

price was $349 per stack and for the metal the cost was $889 per stack.

31

0 20 40 60 80 100 120 140 160100105110115120125130135140145150

Total Cost vs Flow Rate 10% humidity

50% humidity

90% humidity

Flow Rate

Cost

in M

illio

ns o

f Dol

lars

Figure 21: Plastic Fuel Cell Total Cost Analysis

0 20 40 60 80 100 120 140 160400

450

500

550

600

650

700

750

800

850

Total Cost vs. Flow Rate


Flow Rate

Cost

in M

illion

s of D

ollar

s

Figure 22: Metal Fuel Cell Total Cost Analysis

For the metal fuel cell the data is straight forward showing that a flow rate of 20 mL/min

and a humidity of 10% optimizes the cost of the fuel cell. For the plastic fuel cell the one-year

projection has a flow rate of 45 mL/min and a humidity of 50% being the optimum conditions.

However if you consider the fact that running a fuel cell at lower flow rates decreases the amount

spent on hydrogen a year then 20 mL/min and 90% humidity could be the optimum conditions in

32

which to run the plastic fuel cell. Figure 23 shows the 6 year cost projection between the

competing flow rates of 20, 45, and 70 mL/min.

1 2 3 4 5 6 7110

120

130

140

150

160

170

Cost vs Time

20 mL/min45 mL/min70 mL/min

Time (Years)

Cost

in M

illion

s of D

ollar

s

Figure 23: 6 Year Project Cost Analysis

After five years of powering the company the 20 mL/min flow rate will have

surpassed the 50 mL/min flow rate as the most cost effective.

So the most cost effective parameters for the metal fuel cell are 20 mL/min flow

rate and 10 % humidity, which also gives a required room volume of 171 m3. For the plastic fuel

cell the optimum conditions were 20 mL/min and 90% humidity, which gave a required room

volume of 139m3. To determine whether or not it would be worthwhile for ThinkSmart Inc. to

change over to hydrogen fuel cell power, the cost of each optimized fuel cell was plotted against

the cost of electricity over a 100-year period; this can be found in Figure 22. The cost of

electricity used was 9.99 cents/kWh (U.S Energy Information Administration).

33

0 20 40 60 80 100 1200

100

200

300

400

500

600

700

800

900 Projected CostPlastic 90% Humid-ityMetal 10% HumidityElectricity

Years

Cost

in M

illion

s of D

ollar

s

Figure 24: 100 Year Forecast Cost Analysis

From the data it is determined that switching to hydrogen fuel cell technology would not

be worthwhile for ThinkSmart Inc. Electricity proves to be cheaper than fuel cell technology by

hundreds of millions of dollars. Electricity requires no initial startup costs and it also has the

lowest cost per year. Hydrogen fuel cells also require a significantly large room in order to house

them. Fuel cells may also require maintenance, which adds additional costs that aren’t included

in this model. Electricity is all around more cost effective and also requires no start up

maintenance. If ThinkSmart still wants to use hydrogen fuel cells for environmental reasons then

the plastic fuel cell with a flow rate of 20 mL/min and a humidity of 90% is the most cost

effective solution.

NASA also wants to use hydrogen fuel cells to power their futuristic Mars interplanetary

shuttle. The cell stack needs to have an estimated operational load of 7kW. For this kind of

mission efficiency is more important than cost. NASA will need a fuel cell that uses the smallest

amount of hydrogen possible while still giving the required power. It is also essential that the

fuel cells take up as little room as possible. For this kind of specification the best kind of

configuration is dead end configuration. Dead end configuration had an overall efficiency over

34

two times greater than open-ended configuration. The greatest efficiencies produced by each

type of cell for each configuration can be found in Table 9 below.

Table 9: Overall Efficiency

Overall efficiencyMetal Open-ended 0.248187549Plastic Open-ended 0.211522485Metal Dead-ended 0.551282051Plastic Dead-ended 0.649122807

From this data the plastic fuel cell dead-ended fuel cell has the greatest efficiency. The

pressure at which this fuel cell preformed the best was at 1 psig, though it was concluded that

pressure had no real significant correlation as proven by Figure 23 in the results and discussion

section of this report. The plastic dead-ended configuration also gives the smallest volume

needed to store the unit, which is 1.633 m3.

ThinkSmart Inc. and NASA’s problems require completely different solutions.

ThinkSmart Inc. needed to produce a vast amount of electricity as cheaply as possible so the

company could handle the financial strain. In the end standard electricity turned out to be the

least expensive option and required the smallest amount of maintenance. NASA on the other

hand could not use standard electricity because their shuttle would be going into space. NASA

also required much less power than ThinkSmart Inc. For NASA’s concerns cost was also not a

factor, the fuel cells had to be as efficient as possible so they would take up the least amount of

space on the shuttle. Another thing to consider when deciding which fuel cell to use in the space

shuttle would be to find out the weights of the metal and plastic fuel cell stacks. When launching

a shuttle into space everything needs to be as light and compact as possible. In the end the plastic

fuel cell stack seemed to be the best fit for both ThinkSmart Inc. and for NASA providing the

most efficient and least costly solutions.

35

Notation

η : Molar flowrate

I: Current [=] Ampere or mA

F: Faraday Constant

Ƞf: Faraday Efficiency

Veff: Cell Voltage Efficiency, Vex/number of cells/Vtheo

∆G: Change in gibbs free energy

ɳmax: Maximum Efficiency

∆H: Change in Enthalpy

36

Works Cited

Nystrom, Steven V. Matlab & Simulink Student Version R2013a. [Natick, Ma.]: MathWorks, 2007. Computer software.

C. Geankoplis, “Transport Processes and Separation Process Principles 4 (2003)

37

Appendix A

Prelaboratory Work

Appendix B

Experimental Summary Report

Appendix C

Sample Calculations

Appendix D

Calibration Data

0

20

40

60

80

100

120

140

Bub

ble

Flow

rate

0 20 40 60 80 100 120 140Mass Flowrate

Regression Plot

RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)

0.9982090.99791

2.12878276.775

8

Summary of Fit

ModelErrorC. Total

Source167

DF15151.105

27.19015178.295

Sum ofSquares

15151.14.5

Mean Square3343.351

F Ratio

<.0001*Prob > F

Analysis of Variance

Lack Of FitPure ErrorTotal Error

Source246

DF3.390274

23.80000027.190274

Sum ofSquares

1.695145.95000

Mean Square 0.2849F Ratio

0.7662Prob > F

0.9984Max RSq

Lack Of Fit

InterceptMass Flowrate

Term0.37260271.0186986

Estimate1.5206630.017618

Std Error0.25

57.82

t Ratio0.8146<.0001*

Prob>|t|

Parameter Estimates

Response Bubble Flowrate

D1

1

1.5

2

2.5

Spl

it(P

last

ic/M

etal

)

0 20 40 60 80 100 120 140Mass Flow Total

Transformed Fit to Reciprocal

Split (Plastic/Metal) = 1.0267929 + 22.786793*Recip(Mass Flow Total)

RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)

0.7290710.6839160.270387

1.526358

Summary of Fit

ModelErrorC. Total

Source167

DF1.18042140.43865421.6190756

Sum ofSquares

1.180420.07311

Mean Square16.1460F Ratio

0.0070*Prob > F

Analysis of Variance

InterceptRecip(Mass Flow Total)

Term1.026792922.786793

Estimate0.1568275.670876

Std Error6.554.02

t Ratio0.0006*0.0070*

Prob>|t|

Parameter Estimates

Transformed Fit to Reciprocal

Bivariate Fit of Split (Plastic/Metal) By Mass Flow Total

D2

Appendix E

Raw Data and Intermediate Calculations

Appendix F

Matlab

%Created by Steven Nystrom on 5/28/13%finds the % err varying humidty&flowrate %humidity flow meter +-2mL/shf=[8 24 36 41 63 72 19 41 64 90 107 133]; %total flowmeter +-2mL/stf=[18 46 72 93 123 145 23 47 75 97 119 114];er=zeros(length(hf),1,1);for i=1:length(hf) %finds the error with each value er(i)=sqrt((2./hf(i)).^2+(2./tf(i)).^2);end

F1

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