May 13, 2009 9:52 806 UHTE_A_397762
UHTE #397762, VOL 30, ISS 14
Spiral Methanol to Hydrogen
Micro-Reformer for Fuel Cell
Applications
Jeremy M. Gernand and Yildiz Bayazitoglu
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Spiral Methanol to Hydrogen Micro-Reformer for Fuel Cell Applications
Jeremy M. Gernand and Yildiz Bayazitoglu

May 13, 2009 9:52 806 UHTE_A_397762
Heat Transfer Engineering, 30(14):1–9, 2009
Copyright C© Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457630902975903
Spiral Methanol to Hydrogen
Micro-Reformer for Fuel Cell
Applications
JEREMY M. GERNAND and YILDIZ BAYAZITOGLU
Mechanical Engineering and Materials Science Department, Rice University, Houston, Texas, USA5
A spiral microchannel methanol reformer has been developed to provide power in conjunction with a micro fuel cell for
a portable, low-power device. The design is optimized for low pumping power and rapid operation as well as thermal
efficiency, overall size, and complete generation of the available hydrogen. An iterative, implicit, finite-element solution
code, which locates the boundaries between liquid, two-phase, and gaseous flow, provides a complete solution of the fluid
and heat transfer properties throughout the device. The solution employs experimentally verified available microchannel
fluid dynamics relations to develop accurate results. Based on this analysis, the proposed microreformer design will have an
overall maximum energy efficiency of 70%.
10
INTRODUCTION
Many battery chemistries in use today are mature technolo-
gies nearing their theoretical limit in terms of power density and15
they usually require a period of 1 up to 4 h to fully recharge,
which limits their utility and the distance that portable devices
can be taken away from the power grid. The energy density of
fuel cell systems is 3–10 times that of batteries [1]. Fuel cells
can be “recharged” instantly simply by adding more fuel. Ad-20
ditionally, there is no need for the device to ever be plugged
in to the power grid, which makes a fuel-cell-powered device
that much more portable. Fuel-cell exhaust products include
only water in some cases and perhaps also carbon dioxide de-
pending on the fuel, and these pose no harm to people or the25
environment. Although hydrogen is the best choice of fuel,
it is cumbersome to store, and presents unique hazards of its
own. A more energy-dense and more inert fuel would be prefer-
able, but many fuels used in fuel cells tend to be troubled by
contaminants. A better option would be to produce the hydro-30
gen on board the device from a safe, hydrogen-rich fuel like
methanol. Applications for portable electronic devices abound
all around us, including cell phones, satellite phones, global
positioning system (GPS) receivers, personal digital assistants
Address correspondence to Professor Yildiz Bayazitoglu, Mechanical En-
gineering and Materials Science Department, Rice University, Houston, TX
77005-1892, USA. E-mail: bayaz@rice.edu
(PDAs), notebook computers, sensing devices, and many oth- 35
ers. Customers continue to demand that even more applications
be freed from wires and become portable. Those devices that
are already portable show a continuing need for higher power
levels to support additional functionality and longer life be-
tween charges to increase their portability. Methanol reforming 40
is traditionally an energy-intensive, high-temperature operation
conducted at chemical process plants. Methanol reforming or
methanol–steam reforming converts a methanol–water mixture
to vapor and then heats it to a high temperature and pressure.
The mixture is passed through a catalytic reactor, where the out- 45
puts of the operation are carbon dioxide and hydrogen gas. Then
the carbon dioxide is separated from the hydrogen to result in a
pure product.
There is considerable challenge to conducting this operation
on board a small portable system. The lowest temperature, cur- 50
rently available catalyst is copper–zinc oxide (Cu/ZnO), which
operates at temperatures as low as 200◦C. Since the size of this
reformer must be minimized, the objective must be to provide
just the minimum dwell time required of the mixture in the
presence of the greatest possible amount of catalyst surface. 55
New manufacturing techniques have expanded the possibil-
ities for microchannel devices beyond silicon into glass, poly-
mers, and other materials [2]. Silicon was originally used, as the
manufacturing expertise already existed for that material, it was
acceptable for a wide range of applications, and the equipment 60
required was already in place throughout industry and university
laboratories. Silicon microchannel manufacturing has already
1

May 13, 2009 9:52 806 UHTE_A_397762
2 J. M. GERNAND AND Y. BAYAZITOGLU
demonstrated the thin-wall capability desired for this applica-
tion [3]. The spiral microreformer studied in this article can
provide an effective, miniaturized source for hydrogen gas to65
power a micro fuel cell, and a single microchannel is etched
onto a small piece of silicon and the spiral geometry permits a
very efficient use of space with which to provide the approxi-
mately 4 m of channel length required for this application.
A successful design for a methanol microreformer requires70
the application of several disciplines. Since traditional or classi-
cal fluid and heat transfer science may not be applicable for all
micro-scale applications, new studies are required to accurately
predict the behavior of various designs. The available research
is outlined here that is utilized for development analysis of this75
microreformer design. A review of polymer electrolyte fuel cells
by Prater [4] verifies the basic assumptions made about the oper-
ational requirements of proton exchange membrane (PEM) fuel
cells for this article, to ensure that the proposed microreformer
will successfully operate as part of a system. The fluid passing80
through this microreformer design will experience many flow
conditions, and a much wider variety will be experienced when
considering all of the geometric variations studied to arrive at
an optimized design.
Morini [5] and others have studied the laminar flow of liquid85
through microchannels. Among the significant findings is that
classical Navier–Stokes equations remain valid for microchan-
nels with hydraulic diameters as low as 30 µm. For flows of thin
gasses, the classical equations do not continue to have such a
strong hold on the phenomena of fluid flow in microchannels.90
Many investigators have studied the flow of gasses in microchan-
nels, and a review by Yener et al. [6] provides a good description
of the current state of research in this area. Relations identified
by this review as well as those developed by Turner et al. [7]
will be used to analyze the flow conditions in the superheat and95
catalytic reactor regions of the microreformer. Most research
on laminar gas flow in microchannels focuses on thin, single-
constituent gasses, or refrigerants [8]. In some cases steam is
investigated, but little in the way of anything approximating a
water–methanol mixture, so the study produced here will be em-100
ploying these experimentally derived relations on new ground,
although not outside of their prescribed flow conditions.
There is a need for verification of the flow effects of curved
channels at the micro scale. For macro scales, the effects on
flow separation, pressure drop, and other effects are known for105
pipe or channel bends and corners, but most microchannel stud-
ies involve only straight channels. The analysis presented here
utilize the macro relations for this effect [9].
Flow boiling is a complex phenomenon under any circum-
stances, and is made even more so, considering flow boiling in110
microchannels. However, considering the intrinsic benefits of
latent heat transfer, several researchers are studying the topic,
although the published results are not always in the best agree-
ment, and wide scatter between the variously proposed corre-
lated relations is a sign of the current state of research in this115
area. Kuznetsov et al. [10] conducted a review of various experi-
mental results in this field. Among the significant findings were
that accepted macrochannel relations would either drastically
overpredict or underpredict the flow conditions in microchannel
boiling. The relations given by Kandlikar [11] have been used. 120
Of interesting note are the flow regimes observed for microchan-
nel boiling, such as described by Bontemps et al. [12], and their
effects on the heat transfer coefficient. As with other boiling
applications, however, the best data will come as a result of
testing in the specific flow conditions expected for the microre- 125
former. Pattekar and Kothare [13] developed one application
similar to that presented in this article, creating a bead-packed
millimeter-wide channel reactor for the production of hydro-
gen sufficient for 10 W of electrical power. Their experimental
approach demonstrated the feasibility of the design of this com- 130
ponent as they successfully converted over 88% of the available
hydrogen with a copper–zinc oxide (Cu/ZnO) catalyst and an
operating temperature of 200◦C as proposed here. The width of
their rectangular channels was 1 mm and the overall device was
a square approximately 4 cm per side. Earlier research by this 135
team demonstrated the problem of catalyst fouling and the criti-
cality of sufficient surface area and fluid dwell time for complete
chemical conversion [14].
The catalyst for use in the chemical conversion region of
the microreformer is of critical importance in creating a fea- 140
sible device. Harold et al. [15], as well as others given in this
reference, have studied various catalysts available for methanol
reforming applications. From these studies, the most efficient
low-temperature catalyst for methanol reforming appears to be
copper–zinc oxide. Some unpublished research may prove that 145
some new noble metal catalysts (incorporating Pt or Pd) can
reduce the required reaction temperatures by as much as 80◦C.
Until those catalysts are available, however, feasibility analysis
of this microreformer must rest on what is currently available.
The design of the microreformer presented in this article 150
can provide an effective, miniaturized source for hydrogen gas
to power a micro fuel cell. As seen in the concept model in
Figure 1, a single microchannel is etched onto a small piece
of silicon. The spiral geometry permits a very efficient use of
space with which to provide the approximately 4 m of channel 155
length required for this application. The spiral geometry reduces
the amount of pressure required to drive the fluid through the
device. Insulation to protect the high-temperature component
from touch temperature hazards and eliminate excessive heat
loss forms the greater part of the component volume. The pri- 160
mary improvements of this design are reduced pressure drop as
compared to alternative nonspiral configurations and reduced
device size as compared to other channel configurations.
DESIGN REQUIREMENTS
Potential applications for this micro-reformer include cellu- 165
lar and satellite phones, navigation devices, and portable com-
puters. A gross power level of 1.5 W will be utilized as a design
requirement, with a net power supplied to the device of at least
heat transfer engineering vol. 30 no. 14 2009

May 13, 2009 9:52 806 UHTE_A_397762
J. M. GERNAND AND Y. BAYAZITOGLU 3
Figure 1 Design concept for microreformer assembly.
1 W. This should correspond to a wide variety of portable elec-
tronic devices, including multifunction cell phones and other170
personal electronic devices.
The chemical reaction of the methanol–water mixture into
hydrogen follows an endothermic reaction, and requires the
following heat of formation to sustain this reaction: qchem =
59.17 kJ/kmol. At these mass flow rates for this microreformer175
design, this results in a power rate required of 0.17 W. According
to [14], a 20-W PEM fuel cell operating at 80% efficiency re-
quires a hydrogen flow rate of 0.372 mol/h. The efficiency in this
case means that the fuel cell realizes 80% of the potential elec-
trical power from the supply of hydrogen provided. Therefore,180
a 1.5-W fuel cell operating at a similar efficiency will require
0.028 mol/h of H2. To continuously supply hydrogen sufficient
to provide 1.5 W of electricity, a water–methanol mixture feed
rate of 0.6074 cc/h is required, assuming a conversion efficiency
of 90%. This assumes that the fuel mixture is a liquid at room185
temperature (∼20◦C). In our case, the fuel supply is provided
by a pressurized cylinder sufficient to maintain the proper flow
rate. The pressure can be maintained at a nearly constant value
by the use of a suitable two-phase propellant where any increase
in volume of the propellant side of the cylinder will result in190
the vaporization of a portion of the remaining liquid-phase pro-
pellant until equilibrium is reached. A device using a total of
1.5 W would require a fuel cartridge approximately the size
of a single AA battery (∼6.2 cc) to power it for more than 10
h. This corresponds, for example, to the high-power mode or195
talk time of a cell phone. By comparison, most lithium ion bat-
teries currently in use for cell phones can support only about
3 h of active operational time. This is an increase of 3 to 5
times the power capacity on approximately one-half of the vol-
ume, when considering the impact of carrying additional power200
for extended periods away from the grid or other centralized
source. Active device time is equivalent to talk time for a cell
phone.
The metal oxide catalysts for the reforming reaction of the
water–methanol mixture generally operate at temperatures be- 205
tween 200◦C and 250◦C. Therefore, the temperatures of the
fluid and catalyst must be maintained at a temperature of at least
200◦C for a period of time. Previous research has demonstrated
that a dwell time of at least 750 ms is required to fully develop
all of the available hydrogen at 200◦C [16]. In order to maintain 210
the temperature of the microreformer at 200◦C, heat is applied
from the reverse side of the channels on the silicon chip. Sili-
con has a relatively good thermal conductivity, so with a small
package such as this microreformer the entire assembly is easily
maintained at the same temperature. This heater must be sized 215
so that its output balances the heat loss to the outside environ-
ment, the heat required to conduct the chemical reaction, and
the heat absorbed by the incoming water–methanol mixture.
The microreformer heater must have an on–off controller to
prevent energy consumption when the powered device is 220
turned off. In sizing the heater, a choice must be made be-
tween minimizing the transient response time and balancing
the heater output with the total heat loss from the microre-
former at the maximum temperature, which would mean that
no active thermostat-type control would be necessary. With 225
qchem = 0.17 W, qpreheat = 0.026 W , qphase−change = 0.22 W ,
and qsup erheat = 0.030 W the total power utilized to heat the fluid
and sustain the chemical reaction is 0.446 W. This is approxi-
mately one-third of the total energy available in the hydrogen
fuel stream generated by this microreformer and reserves ample 230
power for a device such as a cell phone (more than 1 W). The
overall efficiency of the reformer should be maintained as high
as possible, which includes minimizing the heat loss. Both the
size of the microreformer and the thickness of the insulation
material affect the heat loss. Increases in the flow rate will result 235
in more power output in the form of hydrogen gas, but will also
increase the power necessary for the heating and conversion of
the fuel.
heat transfer engineering vol. 30 no. 14 2009

May 13, 2009 9:52 806 UHTE_A_397762
4 J. M. GERNAND AND Y. BAYAZITOGLU
The microreformer heater should have an output of 0.446 W
plus any heat lost to the environment to balance the inputs and240
outputs. A number of devices already in existence are capa-
ble of providing the necessary heat within a small volume. If
commercial small-scale heating elements were not desired, a
simple printed wiring trace applied to the reverse side of the
microreformer could provide the necessary source through re-245
sistive heating. The concept modeled in this article includes a
disk-type heating element. The overall design configuration is
shown in Figure 1. Since the thermal mass of the microreformer
including the insulation is fairly small, the transient response of
the system to startup of the heater should be rapid. However,250
as the channel changes geometry the fluid velocity changes and
the transit time for the fluid varies significantly. The transient
heat-up time and the fluid transit time should each be no longer
than 2 s.
ANALYSIS AND OPTIMIZATION255
In order to design a microchannel device one must choose
an orientation of the channel to be constructed. While many
are possible, some are more beneficial to a microreforming ap-
plication than others. Among the most important criteria for
this design are ease of manufacture, available surface area cre-260
ated, ability to accept future surface enhancements, and ease of
packing the channel cross section into a compact device. While
various types of microchannels have been created in silicon,
such as triangular, trapezoidal, and rectangular, most previous
research and experience have focused on rectangular channels.265
The cross-sectional configuration of the channel affects the heat
transfer and fluid flow parameters of the device, with each con-
figuration being more useful depending on what phenomena the
designer is seeking to maximize or minimize. In consideration
of a range of variations, a rectangular channel with a width to270
height ratio of 2:1 was selected. As with the cross-sectional
configuration of the channel, the overall configuration of the
layout or packing of the microchannel into a device is impor-
tant. The packing configuration affects the pressure required to
drive fluid through the device, and it affects the overall size of275
the device. An efficient packing configuration is required to op-
timize the device. Once the channel dimensional ratio is chosen,
the layout of the channel within the device must be decided. Two
general options are considered, including Archimedes’ spiral,
and a square layout where the channel follows a rectangular280
path. The layout of the channel affects how much of the overall
device is functioning channel and how much is wall space or
other additional structure; this also determines how large the
overall device must be to contain the necessary channel length.
The layout of the channel through the sharpness and number of285
corners also affects how much pressure drop will be required to
force fluid through the device. These quantities are compared in
Table 1.
While many spiral configurations exist, the concentric spiral
or Archimedes’ spiral has been chosen to provide the layout290
Table 1 Comparison of channel packing orientations
Spiral Square
Outer dimension (mm) 31.6 28.5
Total area (mm2) 785.6 812.3
Area efficiency (ε) 44.6% 43.1%
Equivalent length due to
bends (Le/D)
1308 2280
Additional pressure drop
(mm H2O)
117.5 204.9
for this microreformer design. An Archimedes spiral increases
its radius by a constant amount with each full revolution. This
allows the microreformer to contain a constant channel width
and a constant wall thickness. If any variation were desired, such
as a constantly expanding channel, another Archimedean spiral 295
could be employed.
An additional factor to consider in the optimal layout of the
channel in the microreformer is the wall thickness required. This
wall thickness must resist the internal pressure applied to the
fluid to force it through the reformer. A thickness greater than is 300
necessary will increase the size of the device, making the system
less efficient. In order to determine the optimal thickness, a stress
analysis was conducted. The minimum feasible wall thickness
for current micro-electromechanical systems (MEMS) manu-
facturing techniques in silicon is 35 µm [3]. A finite-element 305
analysis conducted using a commercial finite-element method
(FEM) software package for the distributed loads caused by
fluid pressure against the silicon walls found that the internal
walls should have a thickness of 40 µm, while the exterior walls
require a thickness of 70 µm. These values maintain a factor of 310
safety of at least 5.
The microreformer accepts a liquid mixture of methanol and
water as an input, and through a catalyzed reaction outputs a
gaseous mixture of hydrogen, carbon dioxide, and water va-
por. To accomplish this fuel reforming operation, the fluids pass 315
through a heated microchannel and experience four distinct re-
gions: liquid preheating, phase change, vapor superheating, and
the catalyzed reactor. Each of these regions must be analyzed
by different relations. The solution parameters are depicted in
Figure 2. 320
Preheat Region
This zone consists of heating the incoming liquid mixture
from room temperature up to the boiling point of the mixture.
The entrance of the fluid mixture is assumed to be at a static pres-
sure of 1.06 MPa (10.46 atm) and a temperature of 20◦C. The 325
mixture is composed of water (H2O) and methanol (CH3OH) at
a 1:1 molar ratio. The respective volumetric and mass fractions
of methanol in the mixture are 69.2% and 64.0% and the molar
heat transfer engineering vol. 30 no. 14 2009

May 13, 2009 9:52 806 UHTE_A_397762
J. M. GERNAND AND Y. BAYAZITOGLU 5
Figure 2 Cell parameters for numerical solution.
flow rate of hydrogen required to supply 1.5 W of power is
0.028 mol/h. The fuel mixture supply rate necessary to provide330
this amount of hydrogen is 0.6074 cc/h. The microchannel wall
is maintained at a constant temperature of 200◦C by resistive
heaters.
The Nusselt number for fully developed liquid laminar flow
in a microchannel is identical to the classically derived value335
for hydraulic diameters as small as 30 µm [5], which is equal to
3.391.
In addition to the pressure drop required to force the fluid
through the rectangular channel, one must also consider the
pressure required to drive the fluid past the curved channel. The340
effects of curved channels or pipes or corners are given in terms
of the equivalent length, meaning that from a friction factor
perspective the bent channel is equal to its real length plus an
equivalent length to account for the bend. The equivalent length
data is determined by the ratio of the radius of the bend over the345
channel diameter. A curve fit to the data provided in [9] provides
the equivalent length for each cell in the solution routine. Table 2
includes each of the equations utilized for the solution of this
region.
Phase Change Region 350
This zone consists of converting the liquid mixture at the boil-
ing point to a saturated vapor mixture at the boiling point. The
1:1 molar mixture of water and methanol is directly heated by
the three sides of the silicon microchannel surface. The expected
flow regime is that of a vapor core surrounded by a liquid film 355
covering the channel surfaces until the film finally disappears as
the vapor quality reaches 100%. The convection coefficient for
this section is based on microchannel boiling correlation from
Lazarek and Black [17] in terms of the given boiling number Bo,
which is the ratio between the amount of heat that is available to 360
be absorbed by the liquid and the energy required to transform
the liquid into a vapor. The expression developed by Warrier
et al. [18] and also that developed by Kandlikar [11] are com-
pared against that of Lazarek and Black to evaluate the optimum
microreformer design. The complex relations for pressure drop 365
in two-phase flow in microchannels, developed by Lockhart and
Martinelli [19] and by Qu and Mudawar [20], are both used and
compared in the evaluation of the microreformer design. Table 2
includes each of the equations utilized for the solution of this
region. 370
Superheat Region
This zone consists of heating the saturated vapor mixture
at the boiling point to a superheated vapor mixture at 200◦C.
The value for the Reynolds number indicates that the flow is
laminar in this region, even considering the lower laminar to 375
turbulent transition value for microchannel flow. Microchannel
Table 2 Relations used for simulation model in each region
Region Relations utilized
Preheat Tn = Twall − Twall−Tn−1
exp( hnAsurfnm˙Cpn )
; ReDn =
ρnumeann Dh
µn
dPn = fn(Ln + ELnDh) ρnu
2
meann
2Dh ; fn =
62.2
Ren
Phase change Nu3 = 8.235(1 − 1.883β+ 3.767β
2
− 5.814β3 + 5.316β4 − 2.000β5)
Nu4 = 8.235(1 − 2.042β+ 3.085β2 − 2.477β3 + 1.058β4 − 0.186β5) [9]
Bon =
m˙Cp liqn (Twall−Tn)
Ghfg [17]
htp = Nu3Nu4 hsp max(E, S), hsp = 0.023(Reliq)
0.8(Prliq)0.4 kliqDh [23]
E = 0.6683Co−0.2 + 1058Bo0.7; Co = ( 1−VqVq )0.9(
ρgas
ρliq
)
S = 1.136Co−0.9 + 667.2Bo0.7
φ2liq = 1 +
C
Xvv +
1
X2vv
[24]
C = 21(1 − e(−0.319×103Dh))(0.00418G + 0.0613)
Superheat Nu = Re0.62 [6]; Nu = ¯hDhk ;Kn =
kB Tn
√
2πσ2PnDh
;
ReDn =
ρnumeann Dh
µn
; Tn = Twall −
Twall−Tn−1
exp( hnAsurf nm˙Cpn )
;
−
dp
dx =
96
Re ( 11+6Kn ) 12Dh ρV
2
m
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May 13, 2009 9:52 806 UHTE_A_397762
6 J. M. GERNAND AND Y. BAYAZITOGLU
laminar–turbulent transition begins at Reynolds number equal
to 1600 [11].
The Nusselt number variation with the Reynolds number for
fully developed laminar flow in a microchannel given by [14]380
is used. Table 2 includes each of the equations utilized for the
solution of this region.
Catalytic Reactor Region
This zone consists of chemically converting the superheated
vapor mixture of methanol and water into a mixture of hydrogen385
and carbon dioxide. The key parameter in this zone is the dwell
time of the vapor mixture in the presence of the Cu/ZnO catalyst.
Previous research has demonstrated that a period of 750 ms is
required to fully convert the mixture [16]. The length of the
channel in this section is governed entirely by having the fluid390
experience the necessary dwell time of 750 ms. However, the
fact that the mixture is changing chemical constituents results
in other varying physical properties such as density, speed of
sound, viscosity, and other properties, thus requiring an iterative
solution in this section also. The model is based upon a linear395
curve that transforms an equal part of the whole mass for each
fraction of time spent in contact with the catalyst.
The heat flux into the fluid throughout this section is gov-
erned by the amount of heat required to sustain the chemical
reaction, since the fluid has already reached the wall tempera-
ture by the time this zone begins. It may be possible to utilize 400
a catalyst operating at a lower temperature, which would per-
mit us to design a smaller and more efficient reformer. The
total time required to traverse the total channel length is impor-
tant for minimizing the startup time of the reformer. A shorter
startup time reduces the time required between turning a de- 405
vice on and the application of full power. This reactor utilizes a
copper–zinc oxide (Cu/ZnO) catalyst, which has been shown to
operate with greater than 88% conversion efficiency at 200◦C
[13]. This catalyst is deposited on the bottom surface of the
microchannel. 410
In this region of the microreformer, the effects of pressure
drop by slip flow could become significant. Additionally, an
exponential model of the catalytic reaction will be utilized for
the determination of effects on the overall fluid properties. The
exponential reaction model assumes that the reaction proceeds 415
exponentially, with the total reacted hydrogen gas reaching 99%
at 750 ms. The maximum and minimum fluid properties are
essentially unchanged by the use of either a linear or exponential
model, but some cumulative properties such as pressure drop are
affected by the use of one model over the other. From knowledge 420
of previous experiments [14], the exponential model is likely
to be more accurate. The general outline of the properties in
reactor region is displayed in Figure 3. All of the relations in
this region are equivalent to those of the superheat region (shown
in Table 2); however, the fluid properties are changing due to 425
the chemical conversion.
Figure 3 Flow Properties for four stages of microreformer.
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May 13, 2009 9:52 806 UHTE_A_397762
J. M. GERNAND AND Y. BAYAZITOGLU 7
RESULTS AND CONCLUSIONS
All quantities considered in this section are evaluated from
a minimum width of 20 µm to a maximum width of 400 µm.
In the preheat, phase change, and superheat regions the channel430
length is determined by the heat transfer coefficient, while the
length of the catalytic reactor is determined by the dwell time.
The necessary channel length varies from a maximum of 2244
meters for a 20-µm channel to a minimum of 1.6 m for a 400-
µm-wide channel. The overwhelming majority of the channel435
length is devoted to the catalytic reactor region. On average, less
than 1% of the total channel length is devoted to the preheat,
phase change, and superheat regions combined. The total chan-
nel length directly affects the total size of the device, but not in
a simple linear fashion. An equal length of spiral channel can440
be cut into both sides of the device. One can observe that the
packing efficiency of the spiral configuration is quite high, as
over 2200 m of channel can be held on a circular surface only
10 cm in diameter.
Another reason that the device diameter is important is that445
it affects the amount of heat lost to the environment, and thus
can decrease the efficiency of the reformer in providing more
power than it uses. The heat loss is calculated by considering the
device outer surface at an insulated temperature around 45◦C,
the maximum permitted for safe continuous skin contact [21].450
Using a typical free convection model for air, the values for heat
loss were derived. In reality, some of this heat could be used
to maintain the temperature of the fuel cell, or some heat could
be recaptured from waste heat given off by the supplied devices
electronics. But the results, as shown in Figure 4, should be con-455
sidered a good estimate of potential losses, although probably
at the high end.
As the fluid is heated it expands and loses density, especially
in its vapor form, and from that expansion the fluid must accel-
erate. As the channel size is decreased, the maximum velocity460
of the fluid increases. That continues without abatement until
Figure 4 Microreformer optimization displaying pressure drop, heat loss,
Mach number, and transit time.
the fluid in very small channels approaches the speed of sound.
However, since there is no nozzle to permit acceleration be-
yond that velocity, the flow is choked and the curve of resulting
properties takes a different path. 465
The complication to the Mach number calculation in the cat-
alytic reactor region is the changing chemical constituents of the
fluid. As methanol vapor, steam, hydrogen, and carbon dioxide
have different sonic values, the sonic value of the fluid account
must take into account what stage of the conversion is in ef- 470
fect for the particular cell being analyzed. Figure 4 displays the
maximum Mach number versus channel width for the microre-
former. A good rule of thumb to avoid compressibility effects
is to maintain the maximum Mach number below 0.15 [22]. In
order to comply with this criterion, the microreformer channel 475
width must be 85 µm or greater.
In addition to compressibility effects, the potential for turbu-
lence must be considered. The small channel sizes and high fluid
velocities have the potential to produce turbulence prior to the
normal flow transition point. Typically, the laminar–turbulent 480
transition point is said to begin around Re = 2300. However,
in microchannels, the transition can begin as early as Re =
1600 [11]. All channel widths produce flow conditions that are
expected to be entirely laminar. Due to this observation, no lim-
itations on the optimum channel width will be made so as to 485
avoid turbulent conditions.
In considering flows of thin gasses in very small channels,
one must also be aware of the effects of rarefied flow conditions.
While the gasses in this microreformer are not particularly thin,
the molecule size of methanol is rather large, and so the same 490
effects may be encountered in small channels as for thin gasses.
These rarefied flow conditions challenge the continuum assump-
tion made in most calculations. The Knudsen number provides
a measure of how applicable the continuum assumption is for
the flow being studied, with the assumption becoming less valid 495
as the Knudsen number increases. The highest Knudsen number
for each channel width was analyzed; for example, for a 20-µm
channel, it was 0.0022. This means that the continuum assump-
tion is valid for most channel widths, with only some small
effects becoming evident for channels narrower than 50 µm. 500
The total time fluid takes to traverse the entire device is of
importance to the operation of the microreformer. If an end user
has to wait for 10 s after turning a system on before it reaches
full power and becomes operational, that may be too long. The
transit time increases as the channel width increases, but this 505
quantity should be minimized for ideal operation. A maximum
transit value of 2 s is established, which limits the channel width
to less than 290 µm. Another quantity to consider is the avail-
able reactor surface area. By the present proposed method of
depositing a layer of catalyst on the bottom, the surface area in 510
the lower surface of the channel can be easily compared across
the possible geometries. Since a greater amount of catalyst re-
duces the possibility of fouling and increases the efficiency of
the conversion, this surface area quantity should be maximized.
That leads one to favor the smallest possible channel width 515
allowed by the other constraints.
heat transfer engineering vol. 30 no. 14 2009

May 13, 2009 9:52 806 UHTE_A_397762
8 J. M. GERNAND AND Y. BAYAZITOGLU
The total pressure drop of the device is equivalent to the
static pressure at the inlet required to maintain the necessary
mass flow rate through the device. Too much pressure drop,
and the device could become infeasible due to the large pump520
or pressure vessel required to force the fluid through the mi-
croreformer. Figure 4 plots the total pressure drop of the device
against the channel width. As would be expected, smaller chan-
nels require greater amounts of pressure than larger channels.
The linear and exponential models for the chemical reaction do525
produce some difference on cumulative flow properties, such
as total pressure drop, with the exponential model tending to
require slightly lower pressures than the linear model. This is
due to the fact that the end-product gases of hydrogen and car-
bon dioxide provide less flow resistance than input gases of530
methanol and water vapor. Collecting all of the criteria estab-
lished in this section and plotting those relevant criteria and the
applicable data on a single plot, as given by Figure 4, will give
us a good understanding of the optimal channel width to select
from these competing values. In addition, considerations of the535
reactor surface area lead one to minimize the channel width
to the extent possible. Treating the various factors equally, the
minimization of both transit time and heat loss occurs at their
point of intersection, which is nearest the channel width of
255 µm.540
Based on the data realized on this design from the simulation
model, we have calculated the maximum theoretical efficiency
considering the energy required to perform the reforming reac-
tion and the energy made available by that reaction as shown by
the equation below. That efficiency was found to be 70%. Based545
on the amount of insulation provided to prevent heat loss to the
environment, the actual efficiency would be lower. For example,
only reducing the exterior temperature to 40◦C, would result in
an efficiency of 42%.
Efficiency =
Total Potential Power from Reformed Hydrogen – Energy Required for Reforming – Heat Loss
Total Potential Power from Reformed Hydrogen
550
The microreformer design presented here has proven feasi-
ble based on the analyses performed to provide a safe, clean
hydrogen source for a micro fuel cell. The scale and power
requirements of this design are consistent with the needs of
small-scale personal electronic devices. The cost of the materi-555
als involved is low, as well as the required assembly tasks. The
flow conditions at each point of the microreformer have been
determined by a finite-element code developed especially to op-
timize the geometry and flow conditions of this design. This
analysis tool has demonstrated its value in that any changes560
to geometry, flow conditions, or thermal characteristics can be
quickly evaluated for their effect on the fluid at each point along
its travel and transformation process. While this design could
likely be implemented into a portable power system, the current
size and efficiency may only be sufficient for highly specialized565
portable electronic equipment for use by surveyors, military,
adventurers, and pipeline or power line inspectors.
NOMENCLATURE
A area (m2)
Bo boiling number 570
Cp specific heat at constant pressure (J/g-K)
Co convection number
D diameter (m)
EL effective length (m)
f friction factor 575
G mass flow rate for unit surface (kg/s-m2)
H height (m)
hfg enthalpy of vaporization (J)
h convection coefficient (W/m2-K)
kB Boltzmann’s constant (J/K) 580
k thermal conductivity (W/m-K)
Kn Knudsen number
L length (m)
m˙ mass flow rate (kg/s)
Nu Nusselt number 585
P pressure (Pa)
Pr Prandtl number
q heat flux (W)
R radius (m)
Re Reynolds number 590
s total arc length (m)
T temperature (◦C)
t thickness (m)
u fluid velocity (m/s)
V vapor portion of fluid 595
W width (m)
X vapor quality
Greek Symbols 600
β ratio of channel dimensions
ε area efficiency
θ angle (radians)
µ dynamic viscosity (N-s/m)
ρ density (kg/m3) 605
σ particle diameter (m)
φ two-phase multiplier
Subscripts
chem to sustain chemical reaction
e equivalent 610
h hydraulic
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May 13, 2009 9:52 806 UHTE_A_397762
J. M. GERNAND AND Y. BAYAZITOGLU 9
liq liquid
m mean value
n, n + 1 number of cell element
q quality615
sp single-phase
surf surface
tp two-phase
vv vapor portion
3 three-sided heating620
4 four-sided heating
Superscript
average
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Jeremy Gernand is a reliability engineer with
Northrop Grumman. He received his master’s degree
from Rice University, Houston, Texas, in 2007 and
his bachelor’s degree from Texas A&M University, 705
College Station, Texas, in 1998. He currently works
on predicting failures and analyzing risk in complex
systems.
Yildiz Bayazitoglu is H. S. Cameron Chair Profes-
sor of Mechanical Engineering at Rice University, 710
Houston, Texas. She received her bachelor’s degree
in mechanical engineering at Middle East Technical
University, Ankara, Turkey. She earned her master’s
and doctoral degrees in mechanical engineering at
the University of Michigan, Ann Arbor. She has over 715
150 publications in technical journals and reviewed
conference proceedings. She has been a keynote and
invited speaker, and is a reviewer of several journals
and government research funding agencies in the areas of heat transfer, fluid
flow, radiation, and energy. She is the editor-in-chief (Americas) of the Interna- 720
tional Journal of Thermal Sciences. Among others, her honors include SWE’s
Distinguished Educator Award and ASME’s Heat Transfer Memorial Award.
heat transfer engineering vol. 30 no. 14 2009