Axial heat conduction and heat supply effects on methanol-steam reforming performance in micro-scale reformers

International Journal of Heat and Mass Transfer 55 (2012) 3029–3042

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Axial heat conduction and heat supply effects on methanol-steam reforming performance in micro-scale reformers Reiyu Chein a, Yen-Cho Chen b, J.N. Chung c,⇑ a

Department of Mechanical Engineering, National Chung Hsing University, Taichung City 402, Taiwan Department of Energy Engineering, National United University, Miaoli City 360, Taiwan c Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6300, USA b

a r t i c l e

i n f o

Article history: Received 11 May 2011 Received in revised form 2 February 2012 Accepted 2 February 2012 Available online 22 March 2012 Keywords: Methanol-steam reforming (MSR) Microscale tubular reformer Heat supply Axial conduction parameter

a b s t r a c t The methanol-steam reforming (MSR) performance in micro-scale tubular reformers made by various materials is numerically studied. The physical domain considered includes an inlet section for methanol-steam mixture supply, a reformer section packed with CuO/ZnO/Al2O3 catalyst particles and an outlet section for reformed gas collection. The heat transfer effect with three different heat supply mechanisms on the MSR performance is addressed. For heat supplies from the applied heat fluxes at the reformer outer wall surface and from internal heat generation in the reformer wall, it is found that the axial conduction plays an important role in both heat transfer characteristics and MSR performance. It is suggested that the reformer have a small axial conduction parameter for high MSR performance which can be achieved by designing the reformer with low wall thermal conductivity, thin wall thickness and a small reactants feed rate. It is also found that an excess heat supply can be obtained when the axial conduction parameter is small. This excess heat supply enhances the MSR performance compared with the infinitely-thin walled reformer. For the reformer with a constant wall outer surface temperature, the wall material effect on the MSR performance is insignificant due to uniformly distributed reformer wall temperature. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction In past studies on mini or micro-scale fuel reformers for hydrogen production, the focus was on fuel conversion and carbon monoxide (CO) production [1,2]. Due to the endothermic nature of the reaction, a catalytic steam reformer requires that heat energy be transferred from an external heat source to the reaction site. By considering the reformer and external heat source as a heat exchanging system, the heat transfer from the external heat source to the reaction site plays an important role in fuel reforming performance [3–6]. Based on the catalyst arrangement the reformer can be classified as packed-bed and plate types. In packed-bed reformers such as the tubular reformer, catalyst pellets are packed inside a tube [7]. In plate type reformers such as the micro-channel reformer [8], the catalyst is coated directly onto the channel wall. The heat supply to the reformer may be achieved in various ways. In the process of developing a new catalyst, the reformer used in the catalyst characterization test is usually placed inside an electric oven ⇑ Corresponding author. Tel.: +1 352 392 9607; fax: +1 352 392 1071. E-mail address: jnchung@ufl.edu (J.N. Chung). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2012.02.022

with constant elevated temperature [9]. In practical applications, the reformer may be heated externally by wrapping an electric heater around the reformer wall [10,11] or internally by placing a heat source inside the reformer [12]. Several studies recently proposed integrating a catalytic combustor with the reformer as the heat supply [13–15]. The general feature of these heat supply mechanisms is that heat is transferred to the reformer through the reformer wall. From the classical forced convection heat transfer in a duct [16], it is well known that the heat transfer in the duct wall can generally be neglected because the wall thickness is usually very small compared to the duct hydraulic diameter. Conversely, in most microscale thermal devices, the transverse section area of the solid material perpendicular to the flow direction is comparable to the channel cross-section area. As a consequence, the heat transfer in the solid wall cannot often be disregarded. Several studies reported that the experimentally measured heat transfer coefficient for the micro-channel flow will be underestimated if the wall effect is neglected [17–19]. Moreover, the flow rate in micro-scale thermal devices is usually small and the convective heat transfer due to fluid flow is less effective. As a consequence, conduction heat transfer along the duct wall becomes significant as compared with

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Nomenclature A1 B1 A2 CD CF cp CR CWGS Dij DTi dp ER ED EWGS h1 K Keq kD kR

jWGS Lb mcat Mi mi NG n_ i p Q qc qi q00w0 qw i00

constant in reforming reaction rate, 1.15  106 m3 s1 kg1 constant in reforming reaction rate, 9.41  105 m3 s1 kg1 constant in decomposition reaction rate, 7.09  107 mol s1 kg1 correction factor for decomposition reaction rate, 5.5 Forchheimer drag coefficient gas specific heat (J kg1 K1) correction factor for reforming reaction rate, 5.5 correction factor for water gas shift reaction rate, 11.2 binary molecular diffusion coefficient (m2 s1) thermal diffusion coefficient of species i (m2 s1) catalyst particle diameter (m) activation energy for reforming reaction, 84,100 J mol1 activation energy for decomposition reaction, 111,200 J mol1 activation energy for water gas shift reaction, 70,000 J mol1 ambient heat transfer coefficient (W m2 K1) catalyst bed permeability (m2) equilibrium constant in water gas shift reaction rate constant of decomposition reaction (mol s1 kg1) rate constant of reforming reaction (m3 s1 kg1) rate constant of water gas shift reaction (mol m3 s1 Ka Pa2) reformer length (m) catalyst weight (kg) molecular weight of species i (g mol1) mass fraction of species i number of species in the gas mixture molar flow rate of species i (mol s1) pressure (Pa) volumetric flow rate (m3 s1) energy source term due to the chemical reaction (J m3) input electric power (W) heat flux at reformer wall outer surface (W m2) heat flux at reformer wall inner surface (W m2)

the heat transfer due to fluid flow. In micro-scale heat exchangers [20,21], significant heat conduction in the tube wall was shown to reduce the effectiveness of the heat exchanger. It is expected that problems encountered in mini or micro-scale heat exchangers such as the size effect, wall material and flow rate should also appear in a micro-scale reformer-external heat source system. The wall effect on the heat transfer characteristics and fuel reforming performance should be addressed. In this study, we focus on the heat transfer between the heat source and reformer and its effect on the reformer performance. Particularly, special attention is paid to the reformer wall axial conduction effects that have not been focused previously. Fuel conversion, hydrogen yield and CO production in reformers made of various materials and subject to various heat supply mechanisms are numerically examined and discussed. Because of advantages such as high hydrogen to carbon ratio, liquid form at ambient condition, low reforming temperature (200–350 °C) and low CO formation [22,23], methanol-steam reforming (MSR) has been widely adopted as the fuel supply in proton exchange membrane fuel cells for portable devices. The MSR reformer is used for carrying out the evaluation of heat transfer effects on the reforming performance in this study.

q00z q00V R Rb ri rR rD rWGS SCO T tr ~ V Vb xi Y H2

axial conduction heat flux at reformer wall inner surface (W m2) volumetric heat generation rate (W m3 s1) universal gas constant, 8.314 J mol1 K1 reformer radius (m) molar generation rate of species i (mol m3 s1) reforming reaction rate (mol m3 s1) decomposition reaction rate (mol m3 s1) water gas shift reaction rate (mol m3 s1) CO selectivity temperature (K) reformer wall thickness (m) velocity (m s1) catalyst bed volume (m3) molar fraction of species i hydrogen yield

Greek symbols a temperature exponent d molar steam/CO ratio DHD heat of decomposition reaction (J mol1) DHR heat of reforming reaction (J mol1) DHWGS heat of reforming reaction (J mol1) e catalyst layer porosity g methanol conversion K axial conduction parameter k thermal conductivity (W m1 K1) l viscosity (kg m1 s1) / molar ratio of water to methanal q density (kg m3) Subscript c in m out s w

reformer wall inlet gas mixture outlet catalyst wall outer surface

2. Physical and mathematical models 2.1. Physical domain To carry out the study of heat transfer characteristics and MSR performance, a cylindrical reformer proposed by Suh et al. [7] is adopted. As shown in Fig. 1(a), the reformer has diameter db (=2Rb) = 1 mm and length Lb = 10 mm. Gaseous methanol–water mixture with feed rate Qin, temperature Tin, and steam to methanol molar ratio / is introduced into the reformer. CuO/ZnO/Al2O3 catalyst particles are packed inside the reformer. In the study by Suh et al. [7], the reformer wall was assumed to be infinitely thin and an elevated wall temperature Tw was specified for the heat supply. Practically the reformer wall can be made of various materials with a finite wall thickness. We therefore extend the model shown in Fig. 1(a) to consider that the reformer has a wall with thickness tr as shown in Fig. 1(b). In addition to the reformer section, an inlet section connecting to the methanol–water mixture supply line and an outlet section connecting to Gas Chromatography (GC) for product analysis are also included in the physical domain. The lengths of the inlet and outlet sections are both chosen to be L = 2 mm. At the reformer outer wall an elevated temperature Tw may be specified to emulate the heat supply from a high temperature

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(a)

r, v CH3OH+H2O mixture

Rb

Catalyst Bed

z, u

uin , Tin Lb (b)

outer wall with qw0 or Tw

inlet

outlet

L

tr

Lb

L

Fig. 1. (a) Physical domain used in the study by Suh et al. [7]. (b) Physical domain considered in the present study.

environment such as an electric oven or a constant heat flux q00wo to emulate the heat supply from an electric heater wrapped around the reformer. For a reformer made by electrical conducting material, thermal power may be generated by applying electric current directly to the wall. The generated thermal power may be viewed as an internal heat source with volumetric heat generation rate q000 V and serves as another way to supply heat to the reformer. 2.2. Mathematical model

(1) All species in the gas mixture are ideal gases. (2) The gas flow in the reformer is assumed to be weakly compressible, axisymmetric, steady and laminar. (3) The catalyst particles are assumed to be spherical with a diameter dp and the catalyst bed is treated as a homogeneous porous medium with porosity e and permeability K. (4) The catalyst bed is in local thermal equilibrium with the surrounding gas mixture. Based on the above assumptions, the governing equations for the mass conservation, fluid flow, energy transport and species transport for the gas mixture can be written as,

VÞ ¼ 0 r  ðeq~

e

2

ð1aÞ 

$

V~ VÞ ¼ r  p I þ r  ðq~

(

r

Vmi  qmi eq~



* * lm ~ 2l $ ðrV þ ðr V ÞT Þ  m I r  V þ SU e 3

ð1bÞ

NG  X



Dij rxi þ ðxi  mi Þ

j¼1

ð2Þ 

rp p



DTi

rT T

) ¼ ri ð3Þ

Eq. (1) is used to describe the gas mixture flow through the porous medium with source term SU. For the source with the form,

SU ¼ 

Transport phenomena in the reformer-heat supply system can be described by the conservation equations of mass, momentum, energy and species leading to a set of non-linear partial differential equations. To simplify the analysis, the following assumptions are made:

1

r  ðeqcp ~ VTÞ ¼ r  ðke rTÞ þ qc

lm K

* qC F * * V þ pffiffiffiffi j V j V K

ð4Þ

Eq. (1) is then known as the Brinkman-Darcy-Forchheimer model for the fluid flow in a porous medium with a homogeneous porosity. Note that in the pure fluid region (inlet and outlet sections), K = 1, e = 1, and SU = 0. In Eq. (1), q is the mass-weighted density defined as,

q¼

NG p X xi M i RT i¼1

ð5Þ

The permeability K and Forchheimer drag coefficient CF for a packed bed with spherical particles can be written as [24], 2

K ¼ dp e3 =ð150ð1  eÞ2 Þ;

pffiffiffiffiffiffiffiffiffi C F ¼ 1:75=ð 150e3=2 Þ

ð6Þ

Eq. (2) is the energy transport in the reformer. qc is the energy source due to chemical reaction. Similar to gas mixture flow, qc = 0 in the pure fluid regions. In Eq. (2), cp is the mass-weighted specific heat defined as,

cp ¼

NG X

mi cpi

ð7Þ

i¼1

ke is the effective thermal conductivity of the catalyst bed defined as,

ke ¼ ekm þ ð1  eÞks

ð8Þ

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where ks is the thermal conductivity of the catalyst particle and km is the gas mixture thermal conductivity. Eq. (3) is known as the Maxwell–Stefan species transport equation. Dij and DTi are the binary molecular diffusion coefficient and thermal diffusion coefficient of the ith species, respectively. ri is the production rate of the ith species due to chemical reaction. In these equations, the gas mixture transport properties (lm, km ; Dij and DTi ) can be evaluated based on the Chapman–Enskog theory [25]. Since there is no fluid flow in the reformer wall, the temperature distribution is simply governed by the heat conduction,

r  ðkc rT c Þ þ

q000 V

¼0

ð9Þ

where kc is the thermal conductivity of reformer wall and q000 V is the volumetric heat generation rate inside the reformer wall. Note that q000 V only appears in the case for heat generation inside the reformer wall. All governing equations were written in a cylindrical coordinate system (r, h, z). Utilizing the symmetry in the h coordinate we can recast the problem as an axisymmetric two-dimensional model (r, z). The fluid velocity components in the r and z-directions for the reactant flow are u and v, respectively. 2.3. Chemical reaction model Using CuO/ZnO/Al2O3 as the catalyst the chemical reactions taking place during the MSR are [26,27],

Table 1 Temperature-dependent heat reaction. Reforming

DHR ¼ 4:95  104 þ ðcpCO2 þ 3cpH2  cpCH3 OH  cpH2 O ÞðT  298Þ

Decomposition

DHD ¼ 9:07  104 þ ðcpCO þ 2cpH2  cpCH3 OH ÞðT  298Þ

Water gas shift

DHWGS ¼ 4:912  104 þ ðcpCO2 þ cpH2  cpH2 O  cpCO ÞðT  298Þ

 K eq ¼ exp

4577:8  4:33 T

 ð20Þ

where jWGS and Keq are the rate constant and the equilibrium constant of the WGS reaction, respectively, pi (i = CO, H2O, CO2, H2) is the partial pressure of the ith species, a is a constant determined by the experiments and d is the molar ratio of water to CO. Based on the study of Chen et al. [30], a and activation energy EWGS are specified as 8.0 and 70 kJ/mole, respectively. Similar to the models for reforming and decomposition reactions proposed by Suh et al. [7], we introduced a correction factor CWGS accounting for the catalyst activity and effectiveness for the WGS reaction. To match the experimental data reported by Suh et al. [12], CWGS is chosen to have a value of 11.2 in this study. Based on the reaction models described above, the production rate of each species and energy source can be written as,

rCH3 OH ¼ rR  rD

ð21aÞ

rH2 O ¼ r R  r WGS

ð21bÞ

rCO2 ¼ r R þ r WGS

ð21cÞ

rCO ¼ rD  r WGS

ð21dÞ

For the packed-bed reformer, Suh et al. [7] proposed semi-empirical kinetic models for the steam reforming and decomposition reactions as,

rH2 ¼ 3r R þ 2r D þ rWGS

ð21eÞ

qc ¼ r R DHR  r D DHD þ r WGS DHWGS

ð21fÞ

r R ¼ ð1  eÞqs kR C CH3 OH

ð13Þ

r D ¼ ð1  eÞqs kD

ð14Þ

where DHR, DHD, and DHWGS are the heat of reactions for the reforming, decomposition and WGS reactions, respectively. Temperature-dependent heats of reaction of these reactions are listed in Table 1 [31].

Steam reforming : CH3 OH þ H2 O ! 3H2 þ CO2

ð10Þ

Decomposition : CH3 OH ! 2H2 þ CO

ð11Þ

Water gas shift ðWGSÞ : CO þ H2 O ! H2 þ CO2

ð12Þ

where C CH3 OH is the molar concentration of methanol. In Eqs. (13) and (14), where qs, kR and kD are catalyst density, and rate constants for reforming and decomposition reactions defined as,

qs ¼

mcat mcat ¼ Vb pR2b Lb

ð15Þ

kR ¼ C R ½A1 þ B1 ln u expðER =RTÞ

ð16Þ

kD ¼ C D A2 expðED =RTÞ

ð17Þ

2.4. Boundary conditions The boundary conditions must be specified to complete the mathematical model. Referring to Fig. 1, the boundary conditions are specified as follows, (1) reformer inlet (z = 0, 0 < r < Rb)

u ¼ uin ; In Eq. (15), mcat is the catalyst weight and Vb is the catalyst bed volume. In Eqs. (16) and (17), A1, A2 and B1 are constants given in the study by Amphlett et al. [28]. ER and ED are the activation energies for the reforming and decomposition reactions, respectively. R and T are the universal gas constant and gas mixture temperature, respectively. CR and CD are the correction factors for the reforming and decomposition reactions accounting for the catalyst activity and effectiveness and their values are chosen as 5.5 [12]. Based on the studies of Purnama et al. [29] and Chen et al. [30], the chemical reaction model for the WGS reaction can be written as,

r WGS ¼ C WGS jWGS ðpCO pH2 O  pCO2 pH2 =K eq Þ 

jWGS ¼ 1:78  1022 ð1  0:154d þ 0:008d2 ÞT a exp 

EWGS RT

v ¼ 0;

T ¼ T in ; mCH3 OH ¼ mCH3 OH;in ; mH2 O

¼ mH2 O;in ; mH2 ¼ 0; mCO2 ¼ 0; and mCO ¼ 0

ð22aÞ

(2) reformer outlet (z = Lb + 2L, 0 < r < Rb)

@~ V @T @mi ¼ ¼ ¼0 @z @z @z

ð22bÞ

(3) reformer wall at inlet (z = 0, Rb < r < Rb + tr)

T c ¼ T in

ð22cÞ

(4) reformer wall at outlet (z = Lb + 2L, Rb < r < Rb + tr)

@T c ¼0 @z

ð22dÞ

ð18Þ

(5) outer walls of inlet and outlet sections (0 < z < L, Lb < z < Lb + L, r = b + tr)

ð19Þ

@T c ¼0 @r



ð22eÞ

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(6) inner walls of inlet and outlet sections (0 < z < L, Lb < z < Lb + L, r = Rb)

~ V ¼ 0;

T ¼ Tc;

km

@T @T c ¼ kc ; @r @r

@mi ¼0 @r

ð22fÞ Y H2 ¼

(7) inner wall of reformer (L < z < Lb, r = Rb)

~ V ¼ 0;

T ¼ Tc;

@T @T c ¼ kc ; @r @r

ke

@mi ¼0 @r

Hydrogen yield characterizes the performance of the reformer with respect to the hydrogen production. It is the ratio of the produced hydrogen to the theoretical maximum amount of hydrogen [32],

ð22gÞ

(8) along reformer centerline (0 < z < Lb þ 2L; r ¼ 0)

n_ H3 n_ CH3 OH;in

ð24Þ

CO selectivity defines the molar fraction between produced CO and the molar fraction of all carbon-containing gas phase species which are CO and carbon dioxide (CO2) in MSR. It is an indicator for the effectiveness of CO production and is defined as [32],

*

@T @mi @ V ¼ ¼ ¼0 @r @r @r

ð22hÞ

SCO ¼

n_ CO n_ CO þ n_ CO2

ð25Þ

(9) reformer wall outer surface (L < z < Lb, r = Rb + tr)

@T c ¼ q00wo ; @r

4. Results and discussion

q000 V ¼ 0

@T c ¼ 0; q000 V –0 @r ðiiiÞT c ¼ T w ; q000 V ¼ 0 ðiiÞ

ð22iÞ

In Eq. (22a), uin ¼ Q in =ðpðR2b Þ and mi are the inlet velocity and mass fractions of each species, respectively. The Neumann boundary conditions are specified for the reformer outlet flow velocity, temperature and species concentrations as indicated in Eq. (22b). At the inlet, the reformer wall is assumed to have the same temperature as that of the fed methanol-water mixture, as described in Eq. (22c). For the outlet, the reformer wall is assumed to be insulated as indicated in Eq. (22d). In Eq. (22e) we assumed that the inlet and outlet outer wall sections are insulated. Referring to Fig. 1(b) the conditions for no slip gas flow, continuous heat transfer and no species deposition at the inner walls of the inlet and outlet sections, as indicated in Eq. (22f). The same conditions were also applied at the reformer inner wall as described in Eq. (22g). In Eq. (22h), the axisymmetric condition is specified along the reformer centerline. Eq. (22i) shows the various boundary conditions at the reformer outer wall. Case (i) emulates the heat supply from an electric heater wrapped around the reformer outer wall. Case (ii) emulates the heat supply from the volumetric heat generation rate inside the reformer wall. Case (iii) emulates the heat supply when the reformer is placed in a high temperature environment.

The numerical model used in this study was verified by comparing the methanol conversion and CO concentration results computed from the present numerical model with those reported by Suh et al. [7] and Lee et al. [33] under the same reformer geometry

1 0.9

(a)

Suh et al. [7] present study

0.8

mcat=25 mg

0.7 0.6

η

ðiÞ  kc

16 mg

0.5 0.4 0.3

5 mg

0.2 0.1 0 200

210

220

230

240

o

Tw ( C)

3. Numerical methods

 n_ CH3 OH n_ g ¼ CH3 OH;in n_ CH3 OH;in

ð23Þ

2000 1800

(b)

T w=210 oC, experiment [33] T w=220 oC, experiment [33] o T w=230 C, experiment [33] present study

1600

CO (ppm)

All of the governing equations along with the boundary conditions were solved simultaneously using COMSOL multi-physics (Comsol Inc., version 4.01). Multiphysics modules of weakly compressible Navier–Stokes, general heat transfer, and Maxwell–Stefan were applied for solving the velocity, temperature and species concentration distributions in the reformer. Because the numerical solution accuracy strongly depends on the mesh size, a refined mesh is necessary in the region where the dependent variable gradients are pronounced. Finer meshes were used to capture the subtle changes in velocity, temperature and species concentration in the inlet, outlet, and fluid-wall interface regions. The solution independence of the mesh size was carefully studied before reporting the final results. The numerical results show that the solutions become mesh-independent when the element number exceeds approximately 5000. Hence, more than 5000 meshes were used for the results presented in this study. Important characteristics for MSR are methanol conversion, hydrogen yield, and CO selectivity. Methanol conversion is defined as the ratio between converted methanol at a position along the reformer and the inlet methanol flux [32],

1400

Tw=230 oC

1200 1000

Tw=220 oC 800

Tw=210 oC

600 400 0.5

1

1.5

2

2.5

3

3.5

mcat/Q in [mg/(μl/min)] Fig. 2. Comparisons of (a) methanol conversion and (b) CO concentration predicted from the numerical model used in this study with the results reported in the study by Suh et al. [7] and Lee et al. [33]. For methanol conversion, Qin = 10 ll/min and Tin = Tw are used.

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reported by Lee et al. [33] is presented. It is seen that the model used in the present study under predicts the CO production slightly, but we note that the trends are consistent between the measurement and calculated data. The discrepancy may be caused by both the assumptions adopted in the water–gas shift (WGS) reaction model and the experimental uncertainty. For working in microscale heat and fluid flow, it is very important to check the validity of the continuum model and evaluate possible rarefied gas flow effects. In this study, the Knudsen number can be defined as the ratio of the molecular mean free path of reformed gas to the reformer diameter. The molecular mean free path of the reformed gas in the 250–350 °C range has been evaluated by Arzamendi et al. [34] with the values between 93 and 115 nm. The corresponding Knudsen numbers are then between 9.3  105 and 1.15  104 for our case. These values are smaller than 0.001 [35] which assures the validity of the continuum model, so the governing equations for the MSR considered in this work are

Table 2 Thermophysical property of the wall material. Material

Density [kg/m3]

Thermal conductivity [W/mK]

Specific heat [kJ/kg K]

Thermal capacity [kJ/m3 K]

Chromium alloy Silica glass Steel (AISI4340) Copper

8400 2203 7850 8700

11.3 1.38 44.5 400

450 703 475 385

3.78  106 1.54  106 3.72  106 3.35  106

and catalyst bed parameters (e = 0.35 and ks = 20 W/mK). Under the conditions of Qin = 10 ll/min, / = 1.1 and Tin is equal to the wall temperature Tw, Fig. 2(a) shows that a good agreement was obtained between our predictions and those by Suh et al. [7] for the methanol conversion. In Fig. 2(b), a comparison of CO concentration obtained by the present model with the experimental data

(a)

0.8

(b) 0.7

H2

molar fraction xi

0.6

H 2O 0.5

CH 3OH 0.4 0.3

CO2

0.2 0.1

CO

0 0

2

4

6

8

10

12

14

z/db Fig. 3. (a) Typical temperature and species concentration distributions in the silica glass made reformer. qi = 0.5 W, Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (b) Species concentration variations along the reformer centerline corresponding to the results shown in (a).

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1

1.5

(a)

(d)

silica glass

silica glass

0.8

infinite-thin wall

1

η

" q "wi/q w0

0.6

infinite-thin wall

0.4 0.5

steel

0.2

steel

copper

copper

0

0 1.5

0

(e)

silica glass

(b)

-10

silica glass 1

-20

copper

-30

infinite-thin wall

Y H2

q "z /q w0

steel

0.5

-40

steel

-50

copper 0

-60 300

100

(f)

(c) silica glass

silica glass

10-1

250

infinite-thin wall infinte-thin wall steel

200

-2

steel

S CO

T ( oC )

10

10-3

150 10-4

copper

100

0

2

4

6

8

z/db

10

12

14

10-5

copper

0

2

4

6

8

10

12

14

z/db

Fig. 4. Effect of wall material on the heat transfer characteristics and MSR performance with constant heat flux applied at the reformer outer wall as the heat supply. qi = 0.5 W, Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (a) Heat flux along the reformer inner wall (r = Rb), (b) axial conduction heat flux along the reformer inner wall (r = Rb), (c) gas mixture temperature along the reformer centerline (r = 0), (d) methanol conversion along the reformer centerline (r = 0), (e) hydrogen yield along reformer centerline (r = 0), and (f) CO selectivity along the reformer centerline (r = 0).

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0.7

0.5

(a)

(d)

tr=0.1 mm

0.6

0.4

tr=0.1 mm 0.3

0.4

η

q "wi/q "wo

0.5

0.2 mm

0.3

0.2

0.2 mm

0.2 0.1

0.4 mm

0.1

0.4 mm 0

0

0.8

0

(e)

(b) 0.7

-10

tr=0.1 mm 0.6

-20 0.5

tr=0.1 mm

-30

Y H2

q "z /q "w0

0.2 mm

0.4 mm -40

0.4 0.3

-50

0.2

-60

0.1

-70 250

10-1

0.2 mm

0.4 mm

0

(c)

(f) tr=0.1 mm tr=0.1 mm

10-2

0.2 mm 200

T ( oC )

0.2 mm

S CO

0.4 mm

10-3

0.4 mm

150 10-4

100 0

2

4

6

8

z/db

10

12

14

10-5 0

2

4

6

8

10

12

14

z/db

Fig. 5. Effect of wall thickness on the heat transfer characteristics and MSR performance in steel made reformer with constant heat flux applied at the reformer outer wall as the heat supply. qi = 0.5 W, Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (a) Heat flux along the reformer inner wall (r = Rb), (b) axial conduction heat flux along the reformer inner wall (r = Rb), (c) gas mixture temperature along the reformer centerline (r = 0), (d) methanol conversion along the reformer centerline (r = 0), (e) hydrogen yield along reformer centerline (r = 0), and (f) CO selectivity along the reformer centerline (r = 0).

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0.5

0.5

(d)

(a)

0.4

0.4

Qin=600 μL/hr Qin=1200 μL/hr

0.3

900 600

0.2

900

η

q "wi/q "w0

0.3

0.2

1200 0.1

0.1

0

0 0.6

0

(b)

(e)

Q in=600 μL/hr

0.5 -10 0.4

900

Y H2

q "z /q "w0

-20

-30

0.3

1200

0.2

Q in=600 μL/hr -40

0.1

900 1200

0 -50 250

10

-1

(f)

(c)

Qin=600μL/hr

10-2

200

S CO

T ( oC )

900 1200

900 150

100

0

2

4

10-3

Q in=1200 μL/hr

600

6

8

z/db

10

12

14

10-4

0

2

4

6

8

10

12

14

z/db

Fig. 6. Effect of methanol-steam mixture feed rate effects on the heat transfer characteristics and MSR performance in steel made reformer with constant heat flux applied at the reformer outer wall as the heat supply. qi = 0.5 W, Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (a) Heat flux along the reformer inner wall (r = Rb), (b) axial conduction heat flux along the reformer inner wall (r = Rb), (c) gas mixture temperature along the reformer centerline (r = 0), (d) methanol conversion along the reformer centerline (r = 0), (e) hydrogen yield along reformer centerline (r = 0), and (f) CO selectivity along the reformer centerline (r = 0).

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1

1.5

a

0.9

d

0.8 0.7 1 0.6

chromium alloy

η

q "wi/q "w0

chromium alloy 0.5 0.4 0.5

0.3

steel

steel

0.2 0.1

copper 0

0

0

1.5

e

b chromium alloy

-10

1

chromium alloy

Y H2

-20

q "z /q "w0

copper

-30

0.5

-40

steel

steel

-50

copper

copper 0

-60 300

10-1

f

c

chromium alloy 250

10-2

chromium alloy

S CO

T ( oC )

steel steel

200

10-3

10-4

150

copper

copper

10-5

100 0

2

4

6

8

10

12

14

z/db

0

2

4

6

8

10

12

14

z/db

Fig. 7. Heat transfer characteristics and MSR performance using internal heat generation as heat supply in chromium alloy, steel, and copper reformers. qi = 0.5 W, Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (a) Heat flux along the reformer inner wall (r = Rb), (b) axial conduction heat flux along the reformer inner wall (r = Rb), (c) gas mixture temperature along the reformer centerline (r = 0), (d) methanol conversion along the reformer centerline (r = 0), (e) hydrogen yield along reformer centerline (r = 0), and (f) CO selectivity along the reformer centerline (r = 0).

valid. Based on the comparisons and justifications described above, the present numerical model can then be extended to study the

heat transfer characteristics and MSR performance in a reformer with the physical domain described in Fig. 1(b).

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3

1

a 2.5

d

0.9

silica glass steel copper

0.8 0.7

2

1.5

η

q "wi/q "wo

0.6 0.5 0.4 1

0.3 infinite-thin wall silica glass steel copper

0.2 0.5

0.1 0

0 1.5

0

e silica glass

steel -500

b

-1000

copper

Y H2

q "z /q "w0

1

-1500

0.5

infinite-thin wall silica glass steel copper

-2000

0

-2500

100

c

250

f 10-1

S CO

T (o C )

200

150

infinite-thin wall silica glass steel copper

2

4

6

8

10

infinite-thin wall silica glass steel copper

10-3

100 0

10-2

12

14

z/db

10-4 0

2

4

6

8

10

12

14

z/db

Fig. 8. Heat transfer characteristics and MSR performance under constant wall temperature Tw = 250 °C applied at the reformer outer wall. Qin = 900 ll/hr, tr = 0.2 mm, and Tin = 120 °C. (a) Heat flux along the reformer inner wall (r = Rb), (b) axial conduction heat flux along the reformer inner wall (r = Rb), (c) gas mixture temperature along the reformer centerline (r = 0), (d) methanol conversion along the reformer centerline (r = 0), (e) hydrogen yield along reformer centerline (r = 0), and (f) CO selectivity along the reformer centerline (r = 0).

In order to focus on the wall effect on the heat transfer and MSR performance, the feed rate and temperature of the methanol–water mixture are fixed as Qin = 900 ll/hr and Tin = 120 °C. The catalyst

mass is fixed as mcat = 16 mg. Other catalyst bed parameters are the same as those used for the result shown in Fig. 2. For / = 1.1, the inlet mass fractions of methanol and water are mCH3 OH;in ¼

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R. Chein et al. / International Journal of Heat and Mass Transfer 55 (2012) 3029–3042 1 0.9 0.8 0.7

η,out

0.6

qi=0.7W

0.5 0.4

0.5W 0.3 0.2

0.3W

0.1

(a) 0

0

500

1000

1500

2000

Q in (μL/hr) 1.5

1

YH2,out

qi=0.7W

0.5W

0.5

0.3W (b) 0

K¼

0

500

1000

1500

2000

Q in (μL/hr) 0.3

(c) 0.25

SCO,out

0.2

0.15

qi=0.7W 0.1

0.5W 0.05

0.3W 0 0

0:62 and mH2 O;in ¼ 0:38; respectively. We first examine the heat transfer characteristics and MSR performance under a constant heat flux applied at the outer wall using a silica glass made reformer (Case i in Eq. (22i)). The thermophysical property of the silica glass is listed in Table 2. The reformer wall thickness is taken as 0.2 mm. For the input electric power of qi = 0.5 W, the heat flux applied at the reformer outer wall is q00w0 ¼ qi =ð2pRb Lb Þ ¼ 1:1368 kW=m2 . For this heat flux, gas temperature and species molar fraction distributions for the silica glass made reformer are shown in Figs. 3. From Fig. 3(a), it is seen that the methanol–water mixture temperature increases as it flows to the reformer downstream due to the heat supply from the applied heat flux. Because of the increased temperature, the methanol concentration decreases while the hydrogen and CO concentrations increase along the reformer length. The corresponding concentration variations for each species in the gas mixture along the reformer centerline are shown in Fig. 3(b). Under this heat flux supply and reformer wall material used the methanol conversion is approximately 0.92 at the reformer outlet. Using the same operating conditions and wall thickness described in Fig. 3, the heat transfer characteristics and MSR performances of steel and copper made reformers are computed and compared with the silica glass made reformer as shown in Fig. 4. The thermophysical properties of steel and copper are listed in Table 2. In addition to these three reformers, the results for an infinitethin walled reformer are also shown in Fig. 4. As shown in Fig. 4, the MSR performances for the steel and copper made reformer were much lower than that of the silica glass made reformer. The reason for this result is attributed to the axial heat conduction effect along the reformer wall. From the classical heat exchanger theory, the significance of axial conduction on heat exchanging performance can be justified using the axial conducting parameter [16,20–21]. For convective heat transfer in ducts, the axial conduction parameter is the ratio of the heat conduction loss in the duct wall to the convective heat loss in the fluid flow inside the duct. For the present study, the axial conduction parameter can be defined as,

500

1000

1500

2000

Q in (μL/hr) Fig. 9. Overall MSR performance with constant heat flux applied at the outer wall of a 0.2 mm-thick steel made reformer. Tin = 120 °C. (a) Averaged methanol conversion at reformer out let, (b) averaged hydrogen yield at reformer outlet, and (c) averaged CO selectivity at reformer outlet.

kc Ac

qav e Q in cp;av e Lb

ð26Þ

where Ac ¼ p½ðRb þ t r Þ2  R2b  is the cross-sectional area of the reformer wall, qave is the averaged gas mixture density, and cp,ave is the averaged gas mixture specific heat. Using qav = 0.5 kg/m3 and cp,av = 2000 J/kg K [3], the values of K are 0.42, 13.42, and 120.64 for silica glass, steel and copper made reformers, respectively. Since the axial conduction parameters are large, axial heat conduction along the reformer wall cannot be neglected and the actual heat flux supplied to the reformer will be less than the input heat flux. The actual heat flux supply to the MSR can be evaluated using the heat flux along the reformer inner wall denoted as q00wi . As shown in Fig. 4(a), it is clearly seen that q00wi decreases as K increases. For the steel and copper made reformers, a large portion of the heat supply is conducted away along the reformer wall and results in high axial conductive heat flux q00z along the reformer wall as indicated in Fig. 4(b). Note that q00z is evaluated along the reformer inner wall. The negative value of q00z indicates that the heat conduction is in the direction opposite to the gas mixture flow. Because of heat loss due to the axial conduction, the gas mixture temperature cannot be raised to a high value in steel and copper made reformers, as shown in Fig. 4(c). Because the MSR performance strongly depends on the reaction temperature, lower methanol conversion, hydrogen yield and CO selectivity are obtained for the steel and copper made reformers as compared to the silica glass made reformer, as indicated in Figs. 4(d)–(f), respectively. Note that the gas mixture temperature, methanol conversion, hydrogen yield and CO selectivity shown in Fig. 4 are evaluated along the reformer centerline. Both

R. Chein et al. / International Journal of Heat and Mass Transfer 55 (2012) 3029–3042

the methanol conversion and hydrogen yield increase along the reformer length due the increase in temperature. Based on the definition of CO selectivity indicated in Eq. (25), SCO cannot be defined at the inlet section where no reaction occurs. Therefore, the SCO variation shown in Fig. 4(f) starts from the reformer section (z/db = 2). It is seen that SCO decreases in the region near the inlet section and then increases along the reformer length. The reduction in SCO in the reformer entrance zone is due to the forward WGS reaction that converts CO into CO2 which is favorable when the temperature is low. As the temperature increases in the reformer downstream, SCO increases because of the reversed WGS reaction which is favorable when the temperature is high [29,36–37]. An interesting feature can be observed from Fig. 4 is that the MSR performance in the silica glass made reformer is better than that for the infinite-thin walled reformer. This can be explained by the q00wi variation shown in Fig. 4(a). Fig. 4(a) shows that q00wi is greater than q00w0 for the silica glass made reformer in the reforming section. This means that the actual heat flux supply to the reformer is somehow greater than the input heat flux at the outer reformer wall. This phenomenon can be explained from the temperature distribution in the wall. As shown in Fig. 3 for the gas mixture temperature distribution in the reformer wall, temperature gradient exists in both axial and radial directions. Since a high temperature is produced in the downstream wall, the temperature gradient in the wall is large. This high temperature gradient produces a heat flux in the negative r-direction which serves as an excess heat source for the heat supply. Because of the excess heat flux, the MSR performance in the silica glass made reformer is better than that for the infinite-thin walled reformer, as shown in Figs. 4(d)– (f). Besides the thermal conductivity, the feed rate, wall thickness and reformer length also affect the axial conduction, as indicated in Eq. (26). The wall thickness and feed rate effects on the heat transfer characteristics and MSR performance using steel made reformers are shown in Figs. 5 and 6, respectively. The increase in wall thickness implies more significant axial conduction and results in a decrease in q00wi and increase in q00z , as shown in Figs. 5(a) and (b). Because of the low heat supply, a high gas mixture temperature cannot be expected as shown in Fig. 5(c). As a result, the corresponding MSR performance is degraded as shown in Figs. 5(d)– (f). In Fig. 6 the methanol-water mixture feed rate effect on the heat transfer characteristics and MSR performance are shown. Although the axial conduction would become more significant when the feed rate is reduced, as shown in Figs. 6(a)–(c), better MSR performance still results as shown in Figs. 6(d)–(f) when compared with the high feed rate case. This is because the low feed rate requires less energy for the reaction. Although a high feed rate can reduce the axial conduction, more heat supply is needed to have good MSR performance. Based on the results shown in Figs. 4–6, it is believed that the reformer length effect on the MSR performance will have the same characteristics as those of thermal conductivity, wall cross sectional area and feed rate. It can be expected that an increased reformer length will reduce the axial wall conduction and result in better MSR performance. In Fig. 7 the heat transfer characteristics and MSR performance with a volumetric heat generation rate of q00V as the heat source are shown for reformers made of chromium alloy, steel, and copper (Case ii in Eq. (22i)). The same input electric power qi = 0.5 W is used for the three reformers studied. This corresponds to the volumetric heat generation rate of q00V ¼ qi =ðpLb ½ðRb þ tr Þ2  R2b Þ ¼ 6:63  103 kW=m3 . Note that the chromium alloy will require the lowest electrical current input for generating such thermal power because it has the lowest electrical conductance among the materials studied. As shown in Fig. 7, axial conduction also plays an important role under such heat supply mechanism. Because of low thermal conductivity, the chromium alloy made reformer

3041

had the lowest axial conduction. Compared with the steel and copper made reformers, this results in higher actual heat supply to the reformer, as shown in Fig. 7(a), lower axial conduction shown in Fig. 7(b), and higher gas mixture temperature shown in Fig. 7(c). Note that the heat fluxes shown in Figs. 7(a) and (b) are normalized by q00w0 which is the heat flux applied at outer reformer with the same input electric power as discussed in Figs. 4–6. Because of the excess heat flux produced by the wall temperature distribution, the actual heat supply for MSR can be higher than q00w0 for the chromium alloy reformer. The higher gas mixture temperature for the chromium alloy reformer creates higher corresponding MSR performance over steel and copper reformers as shown in Figs. 7(d)–(f). With Tw = 250 °C (Case iii in Eq. (22i)), the heat transfer characteristics and MSR performance are shown in Fig. 8 for an infinitelythin walled, silica glass, steel, and copper made reformers. The wall thickness for the finite-thickness walled reformers is 0.2 mm. Using the heat flux q00w0 as the base for comparison, there is no significant difference in the actual heat supply to the reformer for the three finite-thickness walled reformers, as shown in Fig. 8(a). Although there is a significant axial conductance for the copper reformer at the inlet-reformer junction, as shown in Fig. 8(b), it produces no significant effect on the resulting gas temperature, as shown in Fig. 8(c). As a result, the MSR performance shown in Figs. 8(d)–(f) are almost identical for all four reformers studied. The reason for the results shown in Fig. 8 may be explained as follows. For this case, the reformer wall outer surface that is exposed to the outside heating environment is assigned a constant surface temperature of Tw. This boundary condition is simply to simulate a situation where the reformer is placed in a high temperature oven or in a combustor such that the outer wall surface is uniformly heated by an intense heat flux to attain a uniform high surface temperature of Tw. Fig. 8(c) shows the reformer inside gas mixture axial temperature distributions. The gas mixture temperatures for the four cases are all approaching the wall temperature Tw = 250 oC near the end of the reactor (outlet) but they are still lower than Tw. In this case, the effect of wall material on the heat transfer and MSR performance is insignificant. Next, we examine the input electric power qi effect on the overall MSR performance using a 0.2 mm-thick steel reformer with heat supplied from an electric heater wrapped around the reformer (Case ii in Eq. (22i)). The averaged methanol conversion, hydrogen yield and CO selectivity at the reformer outlet as functions of Qin and qi are used to quantify the overall MSR performance. The results are shown in Fig. 9. As shown in Fig. 9(a), the methanol conversion increases with the increase in qi and decrease in Qin. Although axial conduction becomes more significant as the feed rate is low, high methanol conversion can still be obtained. As discussed above, this is because less heat supply for the reaction is required when the feed rate is low. Although the axial conduction is less significant as the feed rate increases, low methanol conversion occurs. When feed rate is high, high heat supply for the reaction is required in order to obtain high methanol conversion. In Fig. 9(b), the averaged hydrogen yield at reformer outlet is shown. Since the hydrogen production is proportional to the methanol conversion, the variation trend in hydrogen yield is about the same as that for methanol conversion. Similar to the hydrogen yield, CO production is also related to the methanol conversion and has the same variation trend as the methanol conversion and hydrogen yield, as shown in Fig. 9(c).

5. Conclusion We numerically examined the heat transfer characteristics and MSR performance in microscale cylindrical packed bed reformers.

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Three heat supply mechanisms: constant heat flux at the reformer outer wall, internal heat generation in the reformer wall and constant temperature at the reformer outer wall were examined. Special focus was placed on the axial wall conduction effect along the reformer wall. For heat supplies from the heat flux applied at the reformer outer wall and internal heat generation in the reformer wall, it was found that the axial heat conduction in the reformer wall played an important role for both the heat transfer and MSR performance. The significance of axial conduction was justified using the axial conduction parameter which depends on the gas mixture feed rate, wall conductivity, wall cross sectional area, reformer length and gas mixture specific heat. The actual heat supply for the MSR was reduced as the axial conduction parameter increases. As a result, the gas mixture temperature cannot be raised to a high temperature and MSR performance is poor. Our results also showed that when the reformer was made by low thermal conductivity materials, there was an excess heat flux supply for the MSR because of the temperature distribution in the wall. As a result, MSR performance was better than that for infinite-thin walled reformers. For the heat supply with an elevated reformer wall temperature, the axial conduction effect on the heat transfer and MSR performance was insignificant due to uniformly distributed wall temperature. Based on our numerical results, it is suggested that the material for micro-scale reformer fabrication should have low thermal conductivity, small thickness and low electrical conductance. Acknowledgment This work was partially supported by the National Science Council of Taiwan, R.O.C., under the grant NSC 96-2313-B-239 -001. References [1] J.D. Holladay, Y. Wang, E. Jones, Review of developments in portable hydrogen production using microreactor technology, Chem. Rev. 104 (2004) 4767–4790. [2] J.D. Holladay, J. Hu, D.L. King, Y. Wang, Review – an overview of hydrogen production technologies, Catal. Today 139 (2009) 244–260. [3] A. Karim, J. Bravo, A. Datye, Nonisothermality in packed bed reactors for steam reforming of methanol, Appl. Catal. A 282 (2006) 101–109. [4] P.A. Erickson, C. Liao, Heat transfer enhancement of steam reformation by passive flow disturbance inside the catalyst bed, ASME J. Heat Transfer 129 (2007) 995–1003. [5] K. Shah, R.S. Besser, Understanding thermal integration issues and heat loss pathways in a planar microscale fuel processor: demonstration of an integrated silicon microreactor-based methanol steam reformer, Chem. Eng. J. 135 (2008) 46–56. [6] R. Chein, Y. Chen, L. Chen, J.N. Chung, Heat transfer effects on the methanolsteam reforming with partially filled catalyst layer, Int. J. Hydrogen Energy 34 (2009) 5398–5408. [7] J. Suh, M. Lee, R. Greif, C.P. Grigoropoulos, A study of steam methanol reformer in a micro-reactor, J. Power Sources 173 (2007) 458–466. [8] T. Kim, S. Kwon, Design, fabrication and testing of a catalytic microreactor for hydrogen production, J. Micromech. Microeng. 16 (2006) 1760–1768. [9] W. Ehrfeld, V. Hessel, H. Lowe, Microreactors, Germany, Wiley-VCH, Weinheim, 2000. [10] Y. Kawamura, N. Ogura, T. Yamamoto, A. Igarashi, A miniaturized methanol reformer with Si-based microreactor for a small PEMFC, Chem. Eng. Sci. 61 (4) (2006) 1092–1101.

[11] A.V. Pattekar, M.V. Kothare, A microreactor for hydrogen production in micro fuel cell applications, J. Microelectromech. Sys. 13 (1) (2004) 7–18. [12] J. Suh, M. Lee, R. Greif, P. Costas, C.P. Grigoropoulos, Transport phenomena in a steam-methanol reforming microreactor with internal heating, Int. J. Hydrogen Energy 31 (2009) 314–322. [13] J. Won, H. Jun, M. Jeon, S. Woo, Performance of microchannel reactor combined with combustor for methanol steam reforming, Catal. Today 111 (2006) 158– 163. [14] T. Kim, Micro methanol reformer combined with a catalytic combustor for a PEM fuel cell, Int. J. Hydrogen Energy 34 (2009) 6790–6798. [15] J.H. Lee, G.S. Do, H.J. Moon, O.C. Kwon, An annulus-type micro reforming system integrated with a two-staged micro-combustor, Int. J. Hydrogen Energy 35 (2010) 1819–1828. [16] A.F. Mills, Heat Transfer, Prentice Hall, Englewood cliffs, NJ, 2001. [17] Z.G. Liu, S.Q. Liang, M. Takei, Experimental study on forced convective heat transfer characteristics in quartz microtube, Int. J. Thermal Sci. 46 (2007) 139– 148. [18] G.P. Celata, M. Cumo, V. Marconi, S.J. McPhail, G. Zummo, Microtube liquid single-phase heat transfer in laminar flow, Int. J. Heat Mass Transfer 49 (2006) 3538–3546. [19] I. Tiselj, G. Hetsroni, B. Mavko, A. Mosyak, E. Pogrebnyak, Z. Segal, Effect of axial conduction on the heat transfer in microchannels, Int. J. Heat Mass Transfer 47 (2004) 2551–2565. [20] R.B. Peterson, Numerical modeling of conduction effects in microscale counterflow heat exchangers, Microscale Thermophys. Eng. 3 (1999) 17–30. [21] T. Stief, O.U. Langer, K. Schubert, Numerical investigations of optimal heat conductivity in micro heat exchangers, Chem. Eng. Tech. 22 (1999) 297–303. [22] D. Palo, R. Dagle, J. Holladay, Methanol steam reforming for hydrogen production, Chem. Rev. 107 (2007) 3992–4021. [23] F. Joensen, J.R. Rostrup-Nielsen, Conversion of hydrocarbons and alcohols for fuel cells, J. Power Sources 105 (2002) 195–201. [24] H.S. Fogler, Elements of Chemical Reactor Engineering, Prentice-Hall, Englewood cliffs, NJ, 1986. [25] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed., Wiely, New York, 2002. [26] B. Peppley, K. Amphlett, L. Kearns, R. Mann, Methanol-steam reforming on Cu/ ZnO/Al2O3. Part 1, the reaction network, Appl. Catal. A 179 (1999) 21–29. [27] B. Peppley, K. Amphlett, L. Kearns, R. Mann, Methanol-steam reforming on Cu/ ZnO/Al2O3catalysts. Part 2, A comprehensive kinetic model, Appl. Catal. A 179 (1999) 31–49. [28] J. Amphlett, K. Creber, J. Davis, R. Mann, B. Peppley, D. Stokes, Hydrogen production by steam reforming of methanol for polymer electrolyte fuel cells, Int. J. Hydrogen Energy 19 (1994) 131–137. [29] H. Purnama, T. Ressler, R.E. Jentoft, H. Soerijanto, R. Schlogl, R. Schomacker, CO formation/selectivity for steam reforming of methanol with a commercial CuO/ZnO/Al2O3 catalyst, Appl. Catal. A 259 (2004) 83–94. [30] W.H. Chen, M.R. Lin, T.L. Jiang, M.H. Chen, Modeling and simulation of hydrogen generation from high temperature and low-temperature water gas shift reactions, Int. J. Hydrogen Energy 33 (2008) 6644–6656. [31] V.K. Vadlamudi, S. Palanki, Modeling and analysis of miniaturized methanol reformer for fuel cell powered mobile applications, Int. J. Hydrogen Energy 36 (2011) 3364–3370. [32] M.J. Stutz, D. Poulikakos, Effects of microreactor wall heat conduction on the reforming process of methane, Chem. Eng. Sci. 60 (2005) 6983–6997. [33] M.T. Lee, R. Greif, C.P. Grigoropoulos, H.G. Park, F.K. Hsu, Transport in packedbed and wall-coated steam-methanol reformers, J. Power Sources 166 (2007) 194–201. [34] G. Arzamendi, P.M. Dieguez, M. Montes, M.A. Centeno, J.A. Odriozola, L.M. Gandia, Integration of methanol steam reforming and combustion in a microchannel reactor for H2 production: A CFD simulation study, Catal. Today 143 (2009) 25–31. [35] G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press Inc., New York, 2003. [36] J. Agrell, H. Birgersson, M. Boutonnet, Steam reforming of methanol over a catalyst: a kinetic analysis and strategies for suppression of CO formation, J. Power Sources 106 (2002) 249–257. [37] J.K. Lee, J.B. Ko, D.H. Kim, Methanol steam reforming over catalyst: kinetics and effectiveness factor, Appl. Catal. A 278 (2004) 25–35.