Transport Phenomena Coupled by Chemical Reactions in Methane Reforming Ducts

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1 I. J. Trans. Phenomena, Vol. 11, Rerints available directly from the ublisher Photocoying ermitted by license only 009 Old City Publishing, Inc. Published by license under the OCP Science imrint, a member of the Old City Publishing Grou. Transort Phenomena Couled by Chemical Reactions in Methane Reforming Ducts J. Yuan 1 *, X. Lv, D. Yue and B. Sundén 1 1 Deartment of Energy Sciences, Faculty of Engineering, Lund University, Box 118, 100 Lund, SWEDEN Marine Engineering College, Dalian Maritime University, Dalian 11606, China Mass, heat and momentum transort rocesses are strongly couled with catalytic chemical reactions in a methane steam reforming duct. In this aer, a three-dimensional calculation method is develoed to simulate and analyze reforming reactions of methane, and the effects on various transort rocesses in a steam reforming duct. The results show that the design and oerating arameters groued as characteristic ratios have significant effects on the transort henomena. Keywords: transort henomena, chemical reactions, reformer, CFD, analysis, characteristic arameters. INTRODUCTION Methane is usually converted into H, CO and CO by emloying Ni as a catalyst suorted by alumina in the reformers. Such reformers have been develoed during last years. In general, technologies to roduce hydrogen from methane are based on one of the following conventional rocesses: steam methane reforming (SMR), artial oxidation (POX), autothermal reforming (ATR) [1]. There is an increasing interest worldwide in the develoment of innovative fuel rocessing technologies for fuel cell systems, for instance, comact reformer (CR hereafter) for a variety of alications. The basic idea of the CR is, by alying thin coatings of catalyst, to catalytically activate both sides of a comact heat exchanger one side for combustion to rovide heat for the other side to sustain steam reforming of methane and roduce hydrogen. In this configuration, the thin coating results in small thermal conduction and secies diffusion ath lengths that largely eliminate heat and mass transfer restrictions associated with conventional reformers, and an imroved utilization of the intrinsic reforming catalyst kinetics is allowed to achieve an efficient transfer of thermal energy. The comact reformer concet and its *Corresonding author: Jinliang.yuan@energy.lth.se 39

2 40 J. Yuan et al. otential high ower density could lead to major alication in fuel cell systems for stationary and transortation alications [ 4]. For instance, couling of steam reforming and catalytic combustion in adjacent ducts received attention recently, and an excellent review can be found in [5] regarding the CR concet alication and new design develoment. However, literature review shows that the research on the kinetic reaction erformance and effects on the transort rocesses are very limited. In this study, a three-dimensional comutational rocedure is develoed to simulate and analyze steam reforming of methane in a comosite domain consisting of a orous active layer, a gas flow duct and solid lates. The reformer conditions such as the combined thermal boundary conditions (heat flux on the active solid wall and thermal insulation on the other solid walls), mass balances associated with the reforming reactions and gas ermeation to/from the orous catalyst layer are alied in the analysis. Momentum and heat transort together with fuel gas secies equations have been solved by couled source terms and variable thermo-hysical roerties (such as density, viscosity, secific heat, etc.) of the fuel gas mixture. It should be mentioned that various transort henomena couled by the chemical reactions of methane in the reformer is concentrated and resented in this aer. Problem statement and Mathematical Modeling A three-dimensional comutational fluid dynamics (CFD) code is emloyed for a methane reforming duct from a tyical comact reformer, as shown in Fig. 1. The U, V, and W are the velocity comonents in the x, y, z directions, resectively. In this study, the orous catalyst layer is assumed to be homogeneous and characterized by effective arameters and the fuel in the orous layer is in thermal equilibrium with the solid matrix. The reforming reactions are within the orous catalyst layer. A constant flow rate U = U in with mole fractions of the mixed fuel is secified at the inlet of the fuel flow duct, while U = 0 is secified at the inlet for the solid walls and the orous catalyst layer. Only half of the duct is considered by imosing symmetry conditions on the mid-lane, as shown in Fig. 1. There are several transort rocesses (such as mass, heat and momentum transort) together with chemical reactions aearing in multifunctional reactors. It is often found that endothermic and exothermic reactions are strongly couled by heat exchange in the reactors, such as hydrocarbon cracking, steam reforming and dehydrogenation. In a catalytic reformer, there are many reactions taking lace. It is a fact that [1, 5 6] the Figure 1 Scheme of an investigated duct of steam reforming reactors.

3 Transort henomena couled by chemical reactions in methane reforming ducts 41 steam reforming, water gas-shift, and reverse methanation reactions of methane are the major ones with significant reaction rates, while other side reactions include cracking of methane and carbon monoxide to carbon deosition, and gasifying carbon by steam with very low reaction rates. The above mentioned side reactions can then be ignored and only the following major chemical reactions are included in this study: Methane steam reforming: Water gas-shift: CH + H O CO + 3 H, h = 6000 kj/kmol Reverse methanation: 4 (98K) CO + H O CO + H, h = kj/kmol (98K) CH4 + HO CO + 4 H, h = kj/kmol (98K) (1) () (3) It is clear that the above rocesses in Eqs. (1) and (3) are endothermic and the overall balance of the reactions requires net heat inut by the catalytic combustion in the adjacent ducts. This heat suly is reresented by a heat flux q b in this study. The governing equations to be solved are the general ones including continuity, momentum, energy and secies equations. These equations together with secific source terms have been documented in, e.g., [7], and are not reeated here. It should be mentioned that the inclusion of the source term in the momentum equation allows it to be valid for both the orous catalytic layer and the fuel gas flow duct. For the fuel (or gas) flow duct, the source term becomes zero and this equation then reduces to the regular Navier- Stokes equation. For the orous layer, the source term is not zero, and the momentum equation with nonzero source term can be regarded as a generalized Brinkman-Forchheimer-extended Darcy model. For more details, see [8, 9] and the references included there. It accounts for the macroscoic inertial effects and shear stresses, and microscoic inertial effects as well. Based on the thermal equilibrium assumtion, only one set energy equation is solved to balance the convected energy, the heat conduction through the solid and the gas mixture, the energy due to fuel gas secies diffusion, and a source term S T. The heat source term is associated with the steam reforming, water gas-shift and reverse methanation reactions, S = R h T i reaction, i i (4) where R i is the reaction related mole fluxes, and h reaction,i is the reaction enthaly. The secies mass conservation equations are formulated in a general form as well for H, CH 4, CO and H O, resectively, i.e., for n-1 secies where n is the total number of secies involved in the fuel gas mixture. The last secies (CO ) can be solved because the sum of the mass fractions equals one. It is a fact that mass diffusion is a rocess leading to equalization of substance concentration or establishing an equilibrium gas distribution that results from random migration of the secies. Molecular diffusion occurs as a result of thermal motion of the molecules, and the flux of the secies i is roortional to the concentration gradient and diffusion coefficient. One of the significant challenges in fuel reforming modelling is in determining the rate at which the secies diffuse and gases convect in the fuel flow ducts and orous catalytic areas. The Stefan-Maxwell model is more commonly used in multi-comonent system, as in this study. The diffusion coefficients of secies i in the fuel gas flow duct are calculated by the exression based on the binary coefficients [10] D A, gm 1- X A = X / D + X / D +... B AB C AC (5) where D A,gm is the diffusion coefficient of the comonent A in the mixture with B, C,, X A, X B, X C are the molar fraction of the aroriate secies, and D AB and D AC are the diffusion coefficients in the AB and AC binary system, resectively. It is clear that for an n comonent system, n(n-1)/ binary diffusivities are required. There exist various reaction kinetics and rate/equilibrium constants reorted in the literature for the reactions. In this study, the following reaction rates are emloyed to exress the kinetic rates of absortion or

4 4 J. Yuan et al. roduction of the gas secies, based on artial ressure, temerature and secies comositions for the chemical reactions (1)-(3): 3 k 1 H CO.5 CH 4 HO - H K e,1 3 R1 = m, kmol/(m s) cl ( Den) k H CO CO HO - H K e, 3 R = m, kmol/( m s) cl ( Den) R k 4 H CO CH 4 HO - K e,3 3 m, kmol/( m s) ( Den) H 3 = cl (6) (7) (8) in which, m cl is the catalyst loading (kg cat /m 3 ), and Den = 1+ KCO CO + KH H + K CH / 4 CH + K 4 HO HO H. The values of the re-exonential factors, activation energies, equilibrium constants, and heat of adsortion are given in Table 1 and Table, resectively. In the secies mass conservation equations, the source terms S s,i read: Table 1 Kinetic Parameters and equilibrium constants [5] Reaction Steam reforming Water gas-shift Reverse methanation Table Adsortion constants K i [5] Kinetic rate constant k i (kmol/kg cat h) Equilibrium constant K ej e (-40100/RT) e (-11476/RT), bar e (-67130/RT) e (4639/RT) e (-43900/RT) e (-1646/RT), bar Secies CH 4 CO H H O K i e (-3880/RT), bar e (-70650/RT), bar e (-8900/RT), bar e (88680/RT), - Ss,H = (3R 1+ R + 4 R3) M H ; Ss,CH =- ( R 4 1-R3) M CH ; 4 Ss,HO=- ( R 1-R-R3) M HO; S = ( R -R ) M s,co 1 (9) Based on the reforming reaction function, the thermal and fuel gas mass concentration/flux boundary conditions at the walls are secified as follows. At the bottom wall (y = 0): T U = V = W = 0; qb = - keff ; Ji y Yi =- ρeff Di, eff ( i= H, CO, HO and CH 4) y at the to and side walls: at the mid-lane (z=a/): Numerical Solution Methodology (10) (11) (1) A three-dimensional comutation fluid dynamics (CFD) code is alied to solve the governing equations together with the boundary conditions (10 1). The emloyed code is a general urose one and based on the finite-volume technique with boundary fitted coordinates for solving the differential equations. The Cartesian coordinate system in the hysical sace is relaced by a general non-orthogonal coordinate system. The momentum equations are solved for the velocity comonents on a non-staggered grid arrangement. The Rhie-Chow interolation method is used to comute the velocity comonents at the control volume faces. Algorithms based on the TDMA and a modified SIP are emloyed for solving the algebraic equations. In this study, the convective terms are treated by the QUICK scheme, while the diffusive terms are treated by the central difference scheme. The SIMPLEC algorithm handles the linkage between velocities and ressure. More details can be found in, e.g., [7]. CO U= V= W= 0, q= 0, J i = 0 U V T Y = = W = = i = 0 z z z z

5 Transort henomena couled by chemical reactions in methane reforming ducts 43 As shown in [7], the equations to be calculated are couled by temerature, artial ressure/concentration of gas secies via source terms and thermal-hysical roerties. It should be mentioned that no gas flow is resent in the solid lates. Only the heat conduction equation, derived from the energy equation, is solved for this domain. The thermal-hysical roerties of the gas mixture are variables. These arameters deend on the osition in the duct, and the secies mass fraction and/or temerature as well. Fuel gas mixture density, viscosity and secific heat are then calculated and udated during the calculations. In this investigation, a uniform grid oint distribution in the cross section is alied. To obtain finer meshes in the entrance region of the duct, a non-uniform distribution of grid oints with an exansion factor is imlemented for the main flow direction. Various values of the exansion factor have been checked and 1.01 was found to be sufficient to achieve grid indeendent solutions. Results and Discussion Parameters of a tyical reforming duct are alied as a base case in this study, while the arameter studies are conducted for various duct configuration and oerating conditions to comare with. The base geometry arameters are shown in Table 3. For the orous layer, the arameters are chosen as: orosity ε = 0.5, ermeability β = m, and catalyst loading mcl = 0.1g cat /cm 3. The binary diffusion coefficients of the fuel secies are shown in Table 4 [11]. Fuel inlet temerature T in = 650 o C; inlet mole concentration H : CH 4 :CO:H O:CO = 0.06:0.470:0:0.7145:0.015 with U in = 5 m/s. It should be noted that all the results for the base case was resented in [7], and are not reeated in this aer. Table 3 Geometries of the reforming reaction duct (cm) Length (x) Deth (y) Width (z) Overall Duct Fuel Flow Duct Porous Catalytic Layer Table 4 Binary diffusivity of the ith fuel gas secies i/j Di,j (m /s) i/j Di,j (m /s) CH 4 /CO 3.47e-05 CO/H 11.9e-05 CH 4 /H O 4.30e-05 CO/CO.59e-05 CH 4 /H 11.04e-05 H O/H 14.10e-05 CH 4 /CO.88e-05 H O/CO 3.38e-05 CO/ H O 4.15e-05 H /CO 10.3e-05 Three characteristic ratios, having significant effects on various transort rocesses and chemical reactions as discussed later in this aer, are defined in this study. These are the hydraulic diameter ratio D hr (ratio of the orous layer diameter to the flow duct diameter), the ermeation length ratio PL r (ratio of the fuel flow duct width to the orous catalyst layer width), and the ermeation rate ratio PR r (ratio of the entrance ressure gradient to ermeation resistance). D = D / D hr h hd PLr = a / b PRr = ρ U h µ U β = ( ρβ U ) / ( µ h ) ( in / )/( in / i ) i in (13) (14) (15) D h in Eq. (13) is the hydraulic diameter of the orous catalyst layer (D h = 4bh /((b + h ))), D hd the hydraulic diameter of the fuel flow duct (D hd = 4ah d / ((a + h d ))); a in Eq. (14) is the width of gas flow duct, b the width of the orous catalyst layer; h in Eq. (15) is the thickness of the orous layer. It is clear that both diameter ratio D hr and ermeation length ratio PL r are related to the fuel flow duct and catalytic orous layer configurations, to account for the characteristics of the ermeation area and length, resectively. The ermeation rate ratio PR r considers the characteristics of the catalytic orous material (such as the ermeability β i ) and duct oeration arameter (such as the inlet velocity U in ). To investigate effects of the diameter ratio on the transort henomena and reformer erformance, the

6 44 J. Yuan et al. height of fuel flow duct h d was varied. Figure shows velocity contours for the cases of D hr = 1.17 (h d = 3.5 mm) and D hr = 0.99 (h d = 4.5 mm). As shown by dashed lines, the base case (D hr = 1.07, h d = 4 mm) is resent as well in Fig.. It should be noted that the height of the uer solid late was changed accordingly to kee the total height of the uer solid late and the fuel flow duct constant. As shown in Fig., the velocity contours for big or small D hr have a similar trend as that of the base case, i.e., there is no symmetry of the axial velocity and the osition of the maximum values shifts away from the hysically central lane. This effect is more significant for the big D hr case (Fig. a), if comared to the one with small D hr (Fig. b). More critically, more fuel is ermeated to and ket in the orous reaction region, as shown in Fig. a with smaller velocity contours than those in Fig. b. This may be due to the fact that the fuel flow duct in Fig. a is small if comared to the orous catalyst layer. Effects of the ermeation length ratio have been investigated as well by varying the width of the fuel flow duct a, while other ratios were ket constant. Permeation length ratios PL r = 0.6 (a = 3 mm) and PL r = 0.9 (a = 4.5 mm) were emloyed, and the redicted erformance is comared with that of the base case (PL r = 0.8, a = 4 mm). From Fig. 3, it is found that the cross-section velocity rofiles are similar to each other for different ermeation length ratios. Moreover, the steam reforming reaction rate for the case with small ermeation length ratio (Fig. 4a) is almost in the same order as that achieved in the case with big ermeation length ratio (Fig. 4b). The effects of the ermeation rate ratio on the fuel gas flow are shown and discussed in the following section. It is noted from Fig. 5a that, by increasing the ermeability, fuel gas ermeation to the orous layer is big, i.e., the length having a axial velocity in the orous layer close to the fuel flow duct is longer, if comared to the case with a small ermeability shown in Fig. 5b. This is so because the ermeability is a term used for the conductivity of the orous medium with resect to ermeation by a fluid. It is known that a big ermeability of a orous layer allows more gas to ass at the same ressure gradient. Consequently, more fuel gas is ermeated from the fuel flow duct, and the gas convection can be found with bigger velocities in the orous layer close to the fuel flow duct at the entrance region. Certain imacts on the change of the axial velocity distribution are exected Figure Velocity contours for the cases of: a) D hr = 1.17; b) D hr = 0.99.

7 Transort henomena couled by chemical reactions in methane reforming ducts 45 Figure 3 Distribution of velocity contours at the inlet cross section for the cases of: a) PL r = 0.6; b) PL r = 0.9. Figure 4 Distribution of steam reforming reaction at the inlet cross section for the cases of: a) PL r = 0.6; b) PL r = 0.9. for both the fuel flow duct and the orous catalytic layer, when the ermeability is large. Effects of inlet velocity on the reforming erformance are shown in Figs. 6 and 7. Permeation rate ratios PR r = 0.01 (U in =.5 m/s) and PR r = (U in = 10 m/s) have been emloyed to comare with each other, i.e., PR r = 0.04 and U in = 5 m/s. It is revealed that, in the entrance region, small PR r has a

8 46 J. Yuan et al. Figure 5 Effects of the ermeation rate ratio (ermeability) on the dimensionless axial velocity contours at: a) PR r = 0.40 (β = m ); b) PR r = (β = m ). Figure 6 Effects of the ermeation rate ratio (inlet velocity) on the steam reforming reaction distribution at inlet velocity of: a) PR r = 0.01 (U in =.5 m/s); b) PR r = (U in = 10 m/s). small steam reforming reaction rate in Fig. 6a comared to the case in Fig. 6b with a big inlet velocity case. It is because the fuel gas ermeation to the orous catalyst layer is small as revealed in [9]. Big inlet velocity on the other hand has more significant effects not only on the fuel gases ermeation to the orous catalyst layer for the reactions, but also on the convection (the fuel flow rate) in the gas flow duct. It is then

9 Transort henomena couled by chemical reactions in methane reforming ducts 47 Figure 7 Effects of the ermeation rate ratio (inlet velocity) on the H distribution at inlet velocity of: a) PR r = 0.01 (U in =.5 m/s); b) PR r = (U in = 10 m/s). Figure 8 Effects of the ermeation rate ratio (thickness of the orous layer) on the H distribution. a) PR r = (h =.0 mm); b) PR r = (h = 1.0 mm). noted from Fig. 7a that the exit H mole fraction is high even the reforming reaction rate is small comared to the case in Fig. 7b. It means that the H yield is controlled by the combined effects of the reforming reactions in the orous catalyst layer and convective flow (the fuel flow rate) along the flow direction downstream the fuel gas flow duct. As exected, thickness of the orous catalyst layer is one of the most imortant arameters. To investigate effects of the orous layer thickness on the gas

10 48 J. Yuan et al. Figure 9 Effects of the thickness of the orous reforming layer on distribution of steam reforming reaction rate. a) PR r = (h =.0 mm); b) PR r = (h = 1.0 mm). flow and the reformer reactions, the height of orous layer h was varied while other arameter ratios were ket constant. It should be mentioned that the thickness of the lower solid late was changed accordingly to kee the total height of the orous catalyst layer and the lower solid late constant. It is noted that the ducts emloying thin orous layers (thickness h =.0 and 1.0 mm, resectively, vs. 4.0 mm) redict very similar H mole fraction rofiles, as shown in Fig. 8. However for the case of the thinner orous catalyst layer (Fig. 8b), a smaller H mole fraction is found in the corner of the orous catalyst layer close to the exit and the bottom solid late. It is clear that the distribution of steam reforming reaction rates in Fig. 9 holds a similar trend, i.e., strong steam reforming reaction aears in the interface region of the orous catalyst layer close to the fuel flow duct. On the other hand, weak reaction (with small reaction rate value) can be found in the remaining areas as well for the thin orous catalyst layers shown in Fig. 9. The reforming reaction erformance achieved in the case of PR r = (h =.0 mm) is smaller than the one for the case PR r = (h = 1.0 mm) (Fig. 9b). Figure 10 shows the temerature distribution to reveal the orous layer thickness effects. It is found that the reforming ducts emloying thin orous layers have high temeratures in both the fuel flow duct and the orous catalyst layers. For instance, the maximum temeratures aearing in the active late corner (the bottom late in Fig. 1) at the exit are 779 o C and 769 o C for thin orous layers, comared to o C for the base condition (not shown). It is so because the thin orous catalytic layers are emloyed to have reforming reactions, where the less heat is consumed. As discussed above, it is clear that the thickness of the orous catalytic layer has various roles in the chemical reaction rates and the transort rocesses. It is due to the fact that the thickness of the orous catalyst layer is involved in both the diameter ratio and ermeation rate ratio, i.e., a thin orous layer generates a smaller diameter ratio D hr, however a bigger ermeation rate ratio. Further study is needed to find an otimal thickness of the orous catalytic layer, in conjunction with the catalyst loading and distribution. Conclusions In this aer, a fully three-dimensional calculation method has been further develoed to study the design

11 Transort henomena couled by chemical reactions in methane reforming ducts 49 Figure 10 Effects of the orous catalytic layer thickness on temerature distribution. a) PR r = (h =.0 mm); b) PR r = (h = 1.0 mm). and oerating arameter effects on transort henomena couled by the chemical reactions in a comosite duct relevant for a comact reformer. The model offers the ossibilities of determining temerature and fuel gas fraction/velocity rofiles by taking into account the methane steam reforming, water gas-shift and reverse methanation reactions. The imortant variables based on reformer duct configurations and oerations are groued into three characteristic ratios. The transort rocesses are then evaluated based on these ratios. Big diameter ratio and the ermeation length ratio have significant effects to yield high methane reforming efficiencies at the exit of the duct. For big ermeation rate ratio (high inlet velocity and ermeability, and small thickness of the orous catalyst layer) induces big steam reforming and reverse methanation reaction rates. The orous layer thickness has comlex effects and no simle conclusion can be drawn for the effects on the transort henomena and overall reforming reaction erformance. Acknowledgment The Swedish Research Council (VR) financially suorts the current research. Nomenclature a width of fuel flow duct, m b width of orous catalyst layer, m c secific heat, J/(kg K) D diffusion coefficient of secies, m /s D h hydraulic diameter, m D hr hydraulic diameter ratio h overall height of the duct, m; enthaly, kj/mole h d height of the fuel flow duct, m h thickness of orous catalyst layer, m h r thickness ratio (h /h) J reaction related molar flux, mol/(m s) k thermal conductivity, W/(m K); kinetic rate constant, kmol/(kg cat h) K e equilibrium constants, Pa L reformer length, m m cl catalyst loading, kg cat /m 3 m mass diffusion flux, kg/(m s) n molar diffusion flux, mol/(m s) M molecular weight of secies, kg/mol P ressure, Pa PL r ermeation length ratio PR r ermeation rate ratio q heat flux, W/(m )

12 50 J. Yuan et al. R reaction rate, kmol/(m 3 s) R gas constant, kj/(mol K) r e effective radius, m Re Reynolds number (UD h /ν) S source term T temerature, o C V velocity vector, m/s V i velocity comonents in x, y and z directions, resectively, m/s x, y, z Cartesian coordinates X molar fraction of fuel secies Y mass fraction of fuel secies Greek Symbols β ermeability of orous layer, m ε orosity µ dynamic viscosity, kg/(m s) ν kinematic viscosity, m /s ρ density, kg/m 3 τ tortuosity Suerscrits + forward reaction - reverse reaction Subscrits di eff f form gm CH 4 CO CO H H O in k m diffusion effective arameter fuel gas mixture formation fuel gas mixture methane carbon monoxide carbon dioxide hydrogen water inlet Knudsen diffusion mass transfer ermeation r re s References steam reforming reaction reverse methanation reaction solid wall; shift reaction Hoang, D.L. and Chan, S.H. (004) Modeling of a Catalytic Autothermal Methane Reformer for Fuel Cell Alications, Alied Catalysis A: General 68, Samanta, I., Shah, R.K. and Wagner, A. (004) Fuel Processing for Fuel Cell Alication, Fuelcell , in: R.K. Shah and S.G., Kandlikar (eds.), Proceedings of Fuel Cell Science, Engineering and Technology, ASME, New York. Farrauto, R., Hwang, S., Shore, L., Ruettinger, W., Lamert, J., Giroux, T., Liu, Y. and Ilinich, O. (003) New Material Needs for Hydrocarbon Fuel Processing: Generating Hydrogen for the PEM Fuel Cell, Annual Review of Material Research 33, 1 7. Dicks, A.L., Goulding, P., Jones, S.L., Judd, R. and Ponton, K. (001) Assessment of Advanced Catalyst Performance and Fabrication Otions for a Comact Steam Reformer, ETSU F/0/00180/REP, DTI PUB URN 01/1163, UK. Zanfir, M. and Gavriilidis, A. (003) Catalytic Combustion Assisted Methane Steam Reforming in a Catalytic Plate Reactor, Chemical Engineering Science 58, Kirillov, V.A., Kuzin, N.A., Kulikov, A.V., Fadeev, S.I., Shigarov, A.B. and Sobyanin, V.A. (003) Thermally Couled Catalytic Reactor for Steam Reforming of Methane and Liquid Hydrocarbons: Exeriment and Mathematical Modeling, Theoretical Foundations of Chemical Engineering 37, Yuan, J., Ren F. and Sundén, B. (007) Analysis of Chemical Reaction Couled Mass and Heat Transort Phenomena in a Methane Reformer Duct for PEMFCs, Int. J. Heat Mass Transfer, 50, Yuan, J. and Sundén, B. (004) A Numerical Investigation of Heat Transfer and Gas Flow in Proton Exchange Membrane Fuel Cell Ducts by a Generalized Extended Darcy Model, International Journal of Green Energy 1, Yuan, J., Rokni, M. and Sundén, B. (003) Three-Dimensional Comutational Analysis of Gas and Heat Transort Phenomena in Ducts Relevant for Anode-Suorted Solid Oxide Fuel Cells, International Journal of Heat and Mass Transfer 46, Ferguson, J.R., Fiard, J.M. and Herbin, R. (1996) Three-dimensional Numerical Simulation for Various Geometries of Solid Oxide Fuel Cells, Journal of Power Sources 58, Ackmann, T., Haart, L.G.J., Lehnert, W. and Thom, F. (000) Modelling of Mass and Heat Transort in Thick-Substrate Thin- Electrolyte Layer SOFCs, in: Proc. 4 th Euroean Solid Oxide Fuel Cell Forum, Lucerne /Switzerland,

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