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Ignition and combustion of diluted hydrogenmixtures in a flow past an array of catalytic wires
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
1Universidad Autónoma de la Ciudad de Méxicoe-mail: [email protected]
2Facultad de Ciencias, UNAMCiudad Universitaria, 04510 México D. F.
e-mail: [email protected] student, Facultad de Ingeniería, UNAM
Ciudad Universitaria, 04510 México D. F.e-mail: [email protected]
Key words: Combustion, fluidmechanics, heat and mass transfer
Abstract. In this paper we study the heat transfer and heterogeneous combustion prob-lem of the flow of a reacting mixture (in this case we address the case of hydrogen/oxygenmixtures) flowing through an array of catalytic wires. The fluid velocity, vorticity, tem-perature and species concentration of the reactants have been obtained for different flowReynolds numbers and for a Prandtl number of 0.72. The flow Reynolds number based onthe wire separation is assumed to be small but not larger than 40. We have obtained theignition temperature of the surface reactions as a function of the Peclet number for thecase of a wire radius of a = 0.02 cm. and a wire separation of l = 0.1 cm. The requiredwire temperature increases with the Peclet number, begining with a critical Peclet numberof 0.056 corresponding to the auto-ignition condition (ignition at room temperature).
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1 Introduction
The study of the flow dynamics of a gas through an array of wires represents an importantcontribution to the development in the design of thermal devices due to the constant needto maximize their efficiency and therefore to reduce the operation costs. The flow throughan array of catalytic wires has a number of important industrial applications, including themodeling of fibrous fibers, flow through porous media, design of catalytic converters andheat exchangers. The understanding of these processes helps to reduce the contact areabetween the fluid and the wire array, helps to minimize the pressure drop and thereforeincrease the efficiency of the system and coupled with the catalytic combustion (hydrogen-air), helps to reduce considerably the emission of pollutants to the atmosphere, speciallythe nitrogen oxides.The problem of flow across of a simple wire at uniform temperature and suspended in
an infinite medium has been studied experimentally and analytically in the last decades.Cole and Roshko1 employed the Oseen approximation coupled to the energy equation toobtain the heat transfer in a circular cylinder. The temperature field was obtained usingthe first terms of the Bessel function. Illingworth2 was able to obtain the next termsof the expansion using a similar technique. Hieber and Gebhart3 solved the problemusing asymptotic techniques and matching theory by modifying the Prandtl number andassuming that the Reynolds number tends to zero. Dennis et al.4 evaluated differentPrandtl numbers solving the complete form of the Navier-Stokes and energy equations.The precision of their calculations matches with the results obtained experimentally byCollins and Williams5. Recently, Kurdymov and Fernández6 found the heat transfer in atube immersed in an infinite medium at low Reynolds numbers, of order unity.All of the previous studies were done assuming that the wire is in an infinite medium.
The problem of an array of wires has not been studied as often as with the single wire.Gordon7, solves numerically the fluid field of the stream function and vorticity transportequations, using a Cartesian coordinate system and a finite difference scheme. Wung andCheng8−9 obtained the periodic solution of the fluid flow and fluid temperature usingfinite analytic methods. Wang10 found a series of solutions for an array of wires usingthe same method employed by Wung and Cheng, obtaining the evolution of the Nusseltnumber and the viscous stress over the surface of the wires. Along with the developmentin the dynamics of the fluid past an array of wires, the catalytic combustion process hasbeen studied in different configurations, such as plates, tubes, and different geometries.The catalytic ignition of fuel/air mixtures has received considerable attention in the
literature in the past few years, due to its role in the start-up in the automobile catalyticconverters and in the catalytic and catalytically assisted combustors11−15. Experimentaland theoretical studies of catalytic ignition have been published increasing our knowl-edge about several aspects related with this type of critical nonlinear process. Veserand Schmidt14 published experimental results of the catalytic ignition of different hydro-carbons on platinum using a stagnation-point flow configuration. They showed that for
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methane, the critical ignition temperature decreases as the mixture becomes richer. Fromthe theoretical point of view, the ignition process has been studied by either numericalsimulations using elementary chemistry13,16−19 or by large activation energy asymptoticanalyses using an one-step overall reaction mechanism20−24. The basic principles of het-erogeneous catalysis has been described elsewhere16,25. Williams et al.16 presented a modelfor the catalytic combustion of hydrogen at high temperatures. They presented the rateparameters of a detailed surface chemistry. Warnatz and co-workers17−18 studied in aseries of papers, the catalytic combustion and ignition of hydrogen using detailed kineticmechanisms for both surface and gas-phase reactions. They compared their results withpreviously reported data26. Deutschmann et al.13 studied the catalytic ignition of differentfuels on different catalyst materials. They indicated that the ignition process is an abrupttransition from kinetically controlled system to one controlled by mass transport and de-pends mainly on the adsorption - desorption reaction steps. In their numerical simulationsthey showed that one or the other reactant almost covered the surface prior to ignition.There is a need to obtain reduced kinetic schemes for the catalytic combustion, whichhelp to build a bridge between the full numerical works and the theories developed usingan overall one-step reaction for the surface kinetics. In a previous work by Treviño et al.27
an asymptotic analysis is presented for the catalytic ignition of hydrogen mixtures usinga simplified model for the heterogeneous chemistry. The critical conditions for ignitionhas been deduced and obtained in a closed form the parametric influence on this criticalprocess.The understanding of the catalytic combustion coupled to the dynamics of a gas past
an array of wires is a field that has received very little attention. Vera and Liñán28
described the diffusion controlled combustion of a reacting mixture flowing past a two-dimensional array of catalytic wires. Assuming first that the gas phase homogeneousreactions are frozen, the analysis provides the dependence of the downstream values ofthe temperature and the reactant mass fractions on the Peclet number, the Lewis numberof the reactants, the temperature of the wires, and the ratio of the wire radius to the wirespacing. The analysis includes the effect of the homogeneous reactions, showing that therate of fuel consumption in the gas phase grows with the ratio of the adiabatic laminarflame velocity to the upstream flow velocity, the product of the Zeldovich number and thePeclet number, and the nondimensional temperature of the wires. The objective of thiswork is to extend the results obtained by Vera and Liñán28 by including the heterogeneouskinetics for the hydrogen and oxygen mixtures and by increasing the Reynolds numbersup to 40.
2 Formulation
The physical model under study is shown in Fig. 1. A diluted premixed combustiblemixture of air-hydrogen, with mass concentrations denoted by YF0 and YO20, for the
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
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Figure 1: Schematics of the flow problem
hydrogen and oxygen, respectively, flows with a uniform velocity U0 and temperatureT0, perpendicular to an infinite array of catalytic (platinum) wires of radius a, with thespace between the center of neighbor wires denoted by l. The physical properties of thehighly diluted mixture such as density ρg, kinematic viscosity νg,specific heat at constantpressure Cpg, thermal conductivity λg as well as the thermal conductivity of the wire λw,for simplicity are assumed to be constants. The Reynolds number, Re = U0l/νg based onthe wire separation will be assumed to be of order unity or at least lower to 40, in orderto achieve a laminar steady flow. The governing equations are made nondimensionalusing the scales of l and U0 for the spatial coordinates and the velocity components,respectively. The pressure difference to the uniform upstream ambient pressure is scaledwith ρgU
20 . The nondimensional temperature is defined by ϕ = (T −T0)/(Te−T0), where
Te corresponds to the adiabatic temperature achieved by consuming completely the fuel,that is Te = T0 + YF0Q/CpgWF , where Q and WF are the heat release per unit of molof fuel consumed and the molecular weight of the fuel, respectively. The mass fractionsof the main species have been normalized with the corresponding values at the upstreamconditions, Y = YF/YF0 and YO = YO2/YO20. The resulting governing equations take theform
∂u
∂x+
∂v
∂y= 0, (1)
u∂u
∂x+ v
∂u
∂y= −∂p
∂x+1
Re
∙∂2u
∂x2+
∂2u
∂y2
¸, (2)
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u∂v
∂x+ v
∂v
∂y= −∂p
∂y+1
Re
∙∂2v
∂x2+
∂2v
∂y2
¸. (3)
u∂ϕ
∂x+ v
∂ϕ
∂y=1
Pe
∙∂2ϕ
∂x2+
∂2ϕ
∂y2
¸. (4)
u∂Y
∂x+ v
∂Y
∂y=
1
PeLF
∙∂2Y
∂x2+
∂2Y
∂y2
¸. (5)
u∂Yo∂x
+ v∂Yo∂y
=1
PeLO
∙∂2Yo∂x2
+∂2Yo∂y2
¸. (6)
In the above equations, the resulting nondimensional parameters are the Reynolds num-ber, the Peclet number, Pe = Re νg/αg, where αg denotes the thermal diffusivity of thecombustible gas. The Lewis numbers of both reactants are given by LF = αg/DF andLO = αg/DO, where DF and DO are the binary diffusion coefficients of the fuel and theoxidizer, respectively. Also in these equations the Cartesian coordinates are x normalto the array and y parallel to the array, with the origin placed in the symmetry planeand the line joining the centers of the wires (see Fig. 1). The nondimensional velocitycomponents are u and v along the x and y coordinates, respectively. The nondimensionalpressure difference is denoted by p.The nondimensional boundary conditions are given as follows
x→ −∞ : (u, v) = (1, 0), ϕ = Y − 1 = YO − 1 = p = 0 (7)
x→ +∞ :∂u
∂x=
∂v
∂x=
∂ϕ
∂x=
∂Y
∂x=
∂YO∂x
= 0 (8)
y → ±12: v =
∂u
∂y=
∂ϕ
∂y=
∂p
∂y=
∂Y
∂y=
∂YO∂y
= 0 (9)
At the wire surface, r = (x2 + y2)1/2 = a/l = , the following boundary condition apply
r = : (u, v) = (0, 0), ϕ− ϕw =∂Y
∂r− LF
LOφ=
∂YO∂r− = 0, (10)
where is the nondimensional reaction rate at the surface of the wire defined by
=sWOLOl
ρgαgYO20ω, (11)
s is the molar stoichiometric coefficient of the overall surface reaction F +sO2 →products+ Q, φ corresponds to the equivalence ratio of the mixture at the upstream conditions,φ = (sWO/WF ) (YF0/YO20), WO is the molecular weight of the oxidizer and ω is the
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
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dimensional reaction rate. The maximum possible value of , 0, is such that the fuelconcentration vanish at the outlet conditions (x→∞), that is
0 =PeφLO
2π. (12)
The difference between the fuel concentrations at the inlet and outlet conditions isrelated to the overall reaction rate as 1−Y∞ = δ, where Y∞ = limx→∞(1/2)
R 1/20
Y∞(x, y)dy
and δ = / 0 = 1/(π 0)R π0
( , β)dβ, are the mean values of the fuel concentration atthe outlet conditions and the reduced nondimensional reaction rate at the surface of thewire, respectively. β is the angle formed by the radial line from any point in the surfaceof the wire with the origin and the horizontal line (x axis). δ is therefore the normalizedDamköhler number, with 0 ≤ δ ≤ 1, thus measuring the overall conversion efficiency. Fromthe overall stoichiometry, the final normalized concentrations of both reactants are relatedby¡1− Y∞
¢φ = 1− YO∞. The overall energy conservation gives: ϕw = (Pe /2π Nu)ϕ∞,
where Nu is the mean value of the Nusselt number, Nu = Qw/2π λg(Tw − T0), where Qw
is the overall heat loss per unit length of the wire and finally, qE = ϕ∞ − δ, where qE isthe nondimensional externally added heat flux, defined by qE = QE/Pe ρgαgCpg(Te−T0),with QE being the added external heat flux per unit length of the wire. For not very leanmixtures, the catalytic reaction rate can be shown to be written as27
ω =2Γk2aK
2
(1 +K)2, (13)
where K =pk1d/(k1a − 2k2a), with
k1d = ΓA1d exp
µ− E1dRTw
¶(14)
and
kia =SipYiwW
ΓW3/2i
√2πRTw
, for i = 1(H2), 2(O2). (15)
Here Γ ' 1.6603 ·10−9 mol/cm2 is the surface molar concentration of active sites and R isthe universal gas constant. E1d and A1d are the activation energy and the preexponentialfactor of the desorption reaction for the adsorbed atomic hydrogen, respectively. Theseparameters can be found elsewhere27. The rates of the adsorption reactions, on the otherhand, are expressed in terms of sticking probabilities or accommodation coefficients, Si,which represent the fraction of the collisions with the surface that leads to successfuladsorption. The rate of collisions for species i is Zw = pi/
√2πmikT , from classical
kinetic theory, where pi and mi are the partial pressure and the mass of species i, and kis the Boltzmann constant, k = 1.38×1023 J/K. The rates of the desorption reactions areω1a = k1aθ
2V, ω2a = k2aθ
2V, and ω6a = k6aθV , where θV is the fraction of empty or vacant
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sites. This formulation is only valid for not very lean mixtures, with the adsorption rate ofhydrogen being very large compared with that of oxygen, that is k1a À 2k2a, everywherein the wire surface. The parametric values of the hydrogen mixtures are: LF = 0.3,LO = 1, WF = 2, WO = 32, Q = 2. 378 1× 105 J/mol, s = 1/2.
3 Numerical solution of the governing equations
It is preferable to introduce the stream function-vorticity formulation for the heat trans-fer and catalytic combustion problem, by defining the nondimensional vorticity Ω =∂v/∂x − ∂u/∂y and the stream function ψ such as u = ∂ψ/∂y and v = −∂ψ/∂x. Thenondimensional governing equations transform to
−Ω = ∂2ψ
∂x2+
∂2ψ
∂y2(16)
∂ψ
∂y
∂Ω
∂x− ∂ψ
∂x
∂Ω
∂y=1
Re
∙∂2Ω
∂x2+
∂2Ω
∂y2
¸(17)
∂ψ
∂y
∂θ
∂x− ∂ψ
∂x
∂θ
∂y=1
Pe
∙∂2θ
∂x2+
∂2θ
∂y2
¸. (18)
∂ψ
∂y
∂Y
∂x− ∂ψ
∂x
∂Y
∂y=
1
PeLF
∙∂2Y
∂x2+
∂2Y
∂y2
¸. (19)
∂ψ
∂y
∂Yo∂x− ∂ψ
∂x
∂Yo∂y
=1
PeLO
∙∂2Yo∂x2
+∂2Yo∂y2
¸, (20)
where θ = ϕ/ϕw, to be solved with the corresponding boundary conditions. The Cartesiancoordinate system (x, y) is not well suited for the studied problem. It is then convenientto transform the Cartesian physical coordinate system to a boundary-fitted coordinate,where the grid lines coincide with the body contour in the flow region. This new grid canprovide an accurate representation of the boundary conditions in the region of greatestsensitivity. Thompson et al.29,30 introduced a method for numerical generation of curvilin-ear coordinate systems with coordinate lines conformal with all boundaries of arbitrarilyshaped bodies in a two-dimensional flow region. In this grid generation technique, theCartesian coordinates (x, y) of the boundary-fitted grid points in the complex physicalspace are computed as solutions of an elliptic system of partial differential equationswith Dirichlet boundary conditions. They proposed Poisson equations for the coordinategenerating system, such as
∂2ξ
∂x2+
∂2ξ
∂y2= P (ξ, η) (21)
∂2η
∂x2+
∂2η
∂y2= Q (ξ, η) ,
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
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where P (ξ, η) and Q (ξ, η) are to be selected Since it is desired to execute al numericalcomputations in the uniform rectangular transformed plane, the roles of the dependentand independent variable must be interchanged in equation (21). This yields an ellipticsystem of non linear equations in the transformed plane
α∂2x
∂ξ2− 2β ∂2x
∂ξ∂η+ γ
∂2x
∂η2= −J2
µP (ξ, η)
∂x
∂ξ+Q (ξ, η)
∂x
∂η
¶α∂2y
∂ξ2− 2β ∂2y
∂ξ∂η+ γ
∂2y
∂η2= −J2
µP (ξ, η)
∂y
∂ξ+Q (ξ, η)
∂y
∂η
¶where α, β, and γ are the deformation coefficients
α =
µ∂x
∂η
¶2+
µ∂y
∂η
¶2β =
∂x
∂η
∂x
∂ξ+
∂y
∂η
∂y
∂ξ
γ =
µ∂x
∂ξ
¶2+
µ∂y
∂ξ
¶2and J denotes the Jacobian ot the transformation
J = xξyη − xηyξ (22)
Utilizing exponential functions to achieve the attraction of coordinate lines to the contourof the complex geometry
P (ξ, η) =X−aisign(ξ − ξi) exp(−ci |ξ − ξi|) (23)
Q (ξ, η) =X−bisign(η − ηi) exp(−di |η − ηi| (24)
employing the appropiate constants ai, bi, ci, and di, a nearly orthogonal boundary-fittedcoordinate system is obtained on the cylinder, while in the rest of the boundaries, thesystem of coordinates is orthogonal. Fig. 2 shows a typical near orthogonal grid generatedfor this problem.
3.1 Governing Equations in Boundary-Fitted Coordinate Sys-tems
Using the transformation in equation (22), the transport, energy and concentration equa-tions are, respectively
−τ ∂ψ∂ξ− σ
∂ψ
∂η= α
∂2ψ
∂ξ2+ γ
∂2ψ
∂η2−µ2β
∂2ψ
∂η∂ξ− J2Ω
¶(25)
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Figure 2: Nearly orthogonal grid structure for a value of ε = 0.2.
∙J2Re
∂ψ
∂η− τ
¸∂Ω
∂ξ+
∙−J2Re ∂ψ
∂ξ− σ
¸∂Ω
∂η= α
∂2Ω
∂ξ2+ γ
∂2Ω
∂η2− 2β ∂2Ω
∂η∂ξ(26)
∙JPe
∂ψ
∂η− τ
¸∂θ
∂ξ+
∙−J2Pe∂ψ
∂ξ− σ
¸∂θ
∂η= α
∂2θ
∂ξ2+ γ
∂2θ
∂η2− 2β ∂2θ
∂η∂ξ(27)
∙JPeLH
∂ψ
∂η− τ
¸∂Y
∂ξ+
∙−J2PeLH
∂ψ
∂ξ− σ
¸∂Y
∂η= α
∂2Y
∂ξ2+ γ
∂2Y
∂η2− 2β ∂2Y
∂η∂ξ(28)
∙JPeLo
∂ψ
∂η− τ
¸∂Yo∂ξ
+
∙−J2PeLo
∂ψ
∂ξ− σ
¸∂Yo∂η
= α∂2Yo
∂ξ2+ γ
∂2Yo∂η2
− 2β ∂2Yo∂η∂ξ
(29)
where the coefficients are given by
σ =1
J
µ∂y
∂ξDx −
∂x
∂ξDy
¶τ =
1
J
µ∂y
∂ηDx −
∂x
∂ηDy
¶Dx = α
∂2x
∂ξ2− 2β ∂2x
∂ξ∂η+ γ
∂2x
∂η2
Dy = α∂2y
∂ξ2− 2β ∂2y
∂ξ∂η+ γ
∂2y
∂η2
Considering that the equations of the transformation and the physical system areelliptic, only one method of solution can be employed. The system can be solved in animplicit form by discretizing using centered finite differences. The diffusion terms of theequations are used to iterate in order to obtain the convergence of the solution of thesystem.
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
1083
Figure 3: Numerical results of the stream function, vorticity and temperature fields forRe=40 and Pr=0.72.
4 Results and Conclusions
All the numerical calculations shown in this paper have been obtained for a wire radiusof a = 0.02 cm. Fig. 3 shows the results obtained for the nondimensional stream functionΨ, the vorticity Ω and the temperature θ obtained for a Reynolds number of Re = 40, aPrandtl number of Pr = 0.72 and a nondimensional wire radius of ε = 0.2. A recirculationbubble can be seen at the back of the wire. Using these profiles, the mass fractions for thehydrogen and oxygen can be obtained after solving the corresponding mass conservationequations for both species. For a given wire temperature we can compute the overallnondimensional surface reaction rate δ, the nondimensional heat loss per unit length ofthe wire, qw and the external heat per unit length of the wire, qE that must be addedto maintain the assumed wire temperature. Fig. 4 shows the nondimensional external
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300 400 500 600 700 800 900-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
qE
Wire temperature (K)
Ignitionsteady combustion
Figure 4: Nondimensional external heat flux per unit length of the wire as a function ofthe wire temperature.
heat flux per unit length of the wire qE as a function of the wre temperature, showing theignition condition (dqE/dTw) and the steady combustion condition with qE = 0. Finally,in Fig. 5 it is shown the ignition temperature as a function of the Peclet number. Thelower line corresponds to the wire temperature without considering the surface reactionheat release, while the upper is considering it. There is a minimum in the Peclet numberof 0.056 below which the catalytic ignition takes place at room temperature. As thePeclet number increases, the ignition temperature also increases, indicating the need ofexternal energy to heat up the wire to reach the required minimum wire temperature.The open rectangles are obtained using the asymptotic limit of low Peclet numbers. Thesolid quadrangles are obtained numerically using the techniques explained in this paper.
References
[1] Cole, J., and Roshko, A., 1954, “Heat Transfer From Wires at Reynolds Numbersin the Oseen Range”, Proceeding of Heat Transfer and fluid Mechanics Institute,University of California, Berkeley, CA, pp. 13-23.
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
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0.01 0.1 1 10 100300
310
320
330
340
350
360
370
380
390
400
Twig
T wig, T
w0 (K
)
Pe
Tw0
Pe*=0.056
Figure 5: Ignition wire temperature as a function of the Peclet number for a highly dilutedhydrogen/air mixture.
[2] Illingworth, C. R., 1963, “Flow at Small Reynolds Numbers”, in Laminar BoundaryLayers L. Rosenhead, ed., Claredon Press, Oxford.
[3] Hieber, C. N., and Gebhart, B., 1968, “Low Reynolds Number Heat Transfer from aCircular Cylinder”, J. Fluid. Mech.,Vol. 32, pp. 21-28.
[4] Dennis, S.C. R., Hudson, J.D., and Smith, N., 1968, “Steady Laminar Forced Con-vection From a Circular Cylinder at Low Reynolds Numbers”, Physics of Fluids, Vol.11, pp. 933-940.
[5] Collis, D. S., and Williams, M. J., 1959, “Two-Dimensional Convection From HeatedWires at Low Reynolds Numbers”, J. Fluid Mech. Vol. 6, pp. 357-384
[6] Kurdyumov, V. N., and Fernández, E., 1998, “Heat Transfer From a Circular Cylin-der at Low Reynolds Numbers”, J. Heat Transfer, Vol. 120, pp. 72-75.
[7] D. Gordon, Numerical Calculation on viscous flow fields through cylinder arrays,Computers and Fluids, vol. 6 pp.1-13, 1978.
[8] T.-S. Wung and C. J. Chen, Finite analytic solution of convective Heat Transfer fortube arrays in Cross£ow: Part I, Flow Field Analysis, J. Heat Transfer, vol. 111, pp.633-640, Aug. 1989.
MECOM 2005 – VIII Congreso Argentino de Mecánica Computacional
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[9] C. J. Chen and T.-S. Wung, Finite analytic solution of convective Heat Transfer fortube Arrays in Crossflow: Part II, Heat Transfer Analysis, J. Heat Transfer, vol. 111,pp. 641-648, Aug. 1989.
[10] Y.Q. Wang, L. A. Penner, and S. J. Ormiston, Analysis of laminar forced convectionof air for crossflow in bank of staggered tubes, Numerical Heat Transfer Part A. vol.38, pp.819-845, 2000.
[11] Rinnemo, M., M. Fassihi and B. Kasemo, ”The critical condition for catalytic igni-tion. H2/O2 on Pt”, Chemical Physics Letters, 211(1), 60 (1993).
[12] Fassihi, M., V. P. Zhdanov, M. Rinnemo, K.-E Keck and B. Kasemo, ”A theoreticaland experimental study of catalytic ignition in the hydrogen-oxygen reaction onplatinum”, Journal of Catalysis, 141, 438 (1993).
[13] Deutschmann, O., R. Schmidt, F. Behrendt and J. Warnatz, J., ”Numerical modelingof catalytic ignition”, Twenty-Sixth Symposium (International) on Combustion, TheCombustion Institute, 1747 (1996).
[14] Veser, G. and L. D. Schmidt, ”Ignition and extinction in the catalytic oxidation ofhydrocarbons over platinum”, AIChE Journal, 42(4), 1077 (1996).
[15] Bui, P.-A., D. G. Vlachos and P. R. Westmoreland, ”Homogeneous ignition ofhydrogen-air mixtures over platinum”, Twenty-Sixth Symposium (International) onCombustion, The Combustion Institute, 1763 (1996).
[16] Williams, W. R., C. M. Marks and L. D. Schmidt, ”Steps in the reaction H2+O2H2O on Pt: OH desorption at high temperatures”, J. Phys. Chem., 96, 5922 (1992).
[17] Warnatz J., Twenty-Fourth Symposium (International) on Combustion, The Com-bustion Institute, 553 (1992).
[18] Warnatz, J., M. D. Allendorf, R. J. Kee and M. Coltrin, ”A model of elementarychemistry and fluid mechanics in the combustion of hydrogen on platinum surfaces”,Combustion and Flame, 96, 393 (1994).
[19] Bui, P.-A., D. G. Vlachos and P. R. Westmoreland, ”Modeling ignition of catalyticreactors with detailed surface kinetics and transport: Oxidation of H2/O2 mixturesover platinum surfaces”, Ind. Eng. Chem. Res., 36, 2558 (1997).
[20] Treviño, C. and A. C. Fernández-Pello, ”Catalytic flat plate boundary layer ignition”,Combust. Sci. Tech., 26, 245 (1981).
[21] Treviño, C., Gas-phase ignition of premixed fuel by catalytic bodies in stagnationflow”, Combust. Sci. Tech., 30, 213 (1983).
J. J: Lizardi1, C. Treviño2, and L. Martínez-Suástegui3
1087
[22] Treviño. C., ”An asymptotic analysis of the catalytic ignition in a stagnation-pointflow”, submitted to Combustion Theory and Modelling (1998).
[23] Treviño, C. and F. Méndez, ”Ignition of Catalytic reactions in a vertical plate im-mersed in a combustible gas”, Twenty-Sixth Symposium (International) on Combus-tion, The Combustion Institute, 1797 (1996).
[24] Treviño, C. and N. Peters, ”Gas-Phase Boundary Layer Ignition on a Catalytic FlatPlate with Heat Loss”, Combust. Flame, 61, 39 (1985).
[25] Ertl, G., ”Chemical dynamics in surface reactions”, Ber. Bunsenges. Phys. Chem.,86, 425 (1982).
[26] Ljungström, S., B. Kasemo,A. Rosen, T. Wahnström and E. Fridell, Surf. Sci., 216,63 (1989).
[27] C. Treviño, A.Liñán and V. Kurdyumov, Autoignition in Hydrogen/Air mixturesby a thin catalytic wire, Proceedings of Combustion Institute, vol. 28 pp.1359-1364,2000.
[28] M.Vera and A. Liñan, Low Peclet number flow of reacting mixture past an array ofcatalytic wires, Combustion Theory and Modeling, vol. 8 pp. 97-121, 2004.
[29] Thompson, Joe F., Warsi, Z. U. A. and Mastin, C. W., "Boundary-Fitted Coordi-nate Systems for Numerical Solution of Partial Differential Equations — A Review",Journal of Computational Physics, 47, 1, 1982.
[30] Thompson, Joe F. (Ed.) Numerical Grid Generation, North-Holland 1982. (Alsopublished as Vol. 10 11 of Applied Mathematics and Computation, 1982).
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