Fuel 89 (2010) 1736–1742

Contents lists available at ScienceDirect

Fuel

journal homepage: www.elsevier .com/locate / fuel

Parametric investigations of premixed methane–air combustion in two-sectionporous media by numerical simulation

Hui Liu a, Shuai Dong b, Ben-Wen Li b,*, Hai-Geng Chen a

a Thermal Engineering Department, Material and Metallurgy College, Northeastern University, Shenyang 110004, Chinab Key Laboratory of National Education Ministry for Electromagnetic Processing of Materials, P.O. Box 314, Northeastern University, Shenyang 110004, China

a r t i c l e i n f o

Article history:Received 28 April 2009Received in revised form 1 June 2009Accepted 2 June 2009Available online 21 June 2009

Keywords:Porous mediaPremixed combustionNumerical simulation

0016-2361/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.fuel.2009.06.001

* Corresponding author. Tel.: +86 24 83681756; faxE-mail addresses: heatli@hotmail.com, heatli@epm

a b s t r a c t

Motivated by detailed designs of industrial porous burners published in patents, the combustion of meth-ane–air mixtures in a two-section porous burner has been studied numerically. The software FLUENT isused to solve a two-dimensional transient mathematical model of the combustion. In order to reveal thereality of the combustion in porous media, the user defined function (UDF) is used to extend the ability ofFLUENT and enable two-dimensional distributions of temperature and velocity to be obtained. Someoperating or property parameters, which mainly affect the functions and quality of the industrial burnerdesign, such as the inlet velocity of the reactants, the equivalence ratio, the extinction coefficient and thethermal conductivity of porous media, have been investigated. The results show that the contours of tem-perature and velocity change considerably at the interface of the porous media and near the wall, the gastemperature at the low inlet velocity limit is higher than that for the high velocity limit, the thermal con-ductivity in the upstream section has more influence on the temperature than that in the downstreamsection and finally, the temperature profiles of both the gas and the porous skeleton vary considerablywith changes of the radiative extinction coefficient of the large-pore porous media.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Flame within a porous medium differs from flame in the openbecause its presence causes different heat transfer mechanisms,since, for the same volume, the emissive and absorptive power ofthermal radiation of the porous media are much higher than thoseof gas. Early in 1971, Weinberg [1] suggested that heat recircula-tion without dilution in a burner was the way to increase efficiencyand reduce emission. Inspired by the work of Weinberg, Takenoand Sato [2] proposed inserting a porous solid of high conductivityinto the flame to transfer the post flame enthalpy and aid preheat-ing of the fresh mixture.

Many researchers have performed experiments following theseearly attempts and the models of combustion within porous burn-ers have steadily become more sophisticated as computationalcapabilities have been improved. Echigo et al. [3] theoreticallyand experimentally studied the combustion within porous media.They modeled the combustion as a one-dimensional problem withspatially dependent heat generation and their analytical modelachieved good agreement with measured solid temperature pro-files. Tong et al. [4] studied radiative heat transfer within porous

ll rights reserved.

: +86 24 83681758..neu.edu.cn (B.-W. Li).

media. Their results showed that, to maximize radiant output,the porous layers should be optically thick and the porous mediumof the layer should be highly back-scattering. Hsu et al. [5–7] ex-tended the modeling work of Chen et al. [8] by adding detailedchemical kinetics and using the YIX method, which solves the exactintegral equations of spatial-angular integration form, for radiativetransfer. The name of YIX was given simply because the three char-acters I, X and Y, which look like the integration point distributionswith 2, 4 and 3 angular points in two-dimensional case. For de-tailed description on YIX, one can refer Ref. [9]. The works of Hsuet al. appeared to be very detailed for the one-dimensional modelsfor submerged flames. Using a one-dimensional transient approachthat included the complete chemistry of methane combustion, Bar-ra et al. [10–12] completed a computational study of a two-sectionporous burner. Their results showed that the heat recirculationefficiency decreased with the increase of the equivalence ratio,and the heat recirculation to the incoming fuel–air mixture wasdominated by either solid conduction or radiation, depending onthe equivalence ratio and inlet flow velocity.

Different from the works of Barra et al. [10–12], a two-dimen-sional transient mathematical model is presented in present work,and detailed temperature distributions under different conditionsand the two-dimensional velocity contours and vectors are ob-tained. Methane is used as the fuel instead of the syngas to reducethe computational cost. The software FLUENT is used to solve atwo-dimensional transient mathematical model of the combustion.

H. Liu et al. / Fuel 89 (2010) 1736–1742 1737

2. Physical and mathematical models

2.1. Physical model

The two-section porous burner studied in this paper is an axi-ally symmetric cylinder; half of the computational domain of theburner is shown in Fig. 1. The computational region, which is6.05 cm long, includes a small-pore porous ceramic 3.5 cm longin the upstream section and a large-pore porous ceramic 2.55 cmlong in the downstream section. The diameter of the cylinder is7 cm. The premixed methane–air is preheated in the upstream sec-tion, and reacts in the downstream section. A two-dimensionalphysical model is presented here.

2.2. Assumptions

To simplify the model, the assumptions used in the model are asfollows [5]:

(1) The porous ceramics act as gray homogeneous media.(2) The wall is no slip, adiabatic, and radiative gray.(3) Gas radiation is not considered.(4) Potential catalytic effects of the solid at high temperature

are ignored.(5) The Dufour effect, ‘‘bulk” viscosity, and body forces are

ignored.(6) The reactants and the products are treated as incompressible

ideal gases.

2.3. Governing equations

The two-dimensional model, which includes the effects of solid-and gas-phase conduction, solid radiation, solid-to-gas heat trans-fer, species diffusion, and chemistry [13–20], is expressed as:

(1) Continuity equation

@ðeqgÞ@t

þr � ðeqguÞ ¼ 0 ð1Þ

where qg is the density of gas; u is the velocity vector of thegas; e is the porosity of the solid.

(2) Momentum equation

@ðeqguuÞ@t

þr � ðeqguuÞ ¼ �erpþr � ðesÞ þ R ð2Þ

where R ¼ � la þ

C2qg

2 juj� �

u represents viscosity resistance andinertial resistance produced by the viscosity effect and theshape effect of the porous medium when the fluid passesthrough it, a is the viscosity resistance factor, C2 is the inertialresistance factor and s is the viscosity stress tensor.

(3) Species conservation equation

@ðeqYiÞ@t

þr � ðeqguYiÞ ¼ �r � ðeqgYiViÞ þ e _xWi ð3Þ

where Yi is the mass fraction of the ith species, Vi ¼ ui � u is thediffuse velocity of the ith species, ui is the velocity compared to

Inlet

Downstreamsection

Upstreamsection

Premixed gas

Axis 0 3.5 6.05 cm

Products

Outlet

Fig. 1. Diagram of the physical model.

the stationary coordinate system of the ith species, _xi is thereaction rate of the ith species and Wi is the molecular massof the ith species.

(4) Gas phase energy equation

@ðeqgCgTgÞ@t

þr � ðeuðqgCgTg þ pÞÞ

¼ hvðTs � TgÞ þ r � ½eðkg þX

i

qgiCgiDTiÞrTg

� ðeX

i

hiqYiðui � uÞÞ þ eðsuÞ� þ e _Q ð4Þ

where p is the pressure, _Q is the heat release rate of the chem-ical reactions, _Q ¼

Pi

_xihiWi, Cg is the specific heat of the gasmixture, kg is the thermal conductivity of the gas mixture, DTi

are the thermal diffusion coefficients which use the empiri-cally-based composition-dependent expression in FLUENT,

DTi ¼ �2:59� 10�7T0:659 W0:511i XiPN

i¼1W0:511

i Xi

� Yi

� ��PN

i¼1W0:511

i XiPN

i¼1W0:489

i Xi

� �hv is

the volumetric heat transfer coefficient between the porousmedia and the gas, hi is the molar enthalpy of the ith speciesand Tg is the temperature of the gas.

(5) Solid phase energy equation

@½ð1� eÞqsCsTs�@t

¼ r � ðkserTsÞ þ hvðTg � TsÞ ð5Þ

where kse ¼ kc

e þ kre is the heat transfer coefficient of the porous

medium, kceis the thermal conductivity of the porous medium

and kre is the radiation heat transfer coefficient. The

radiation heat transfer can be approximated by qr ¼�ð16rT3

s =3rsÞdTs=dx, where r=5.67 � 10�8W/m2 K4 is theStefan–Boltzmann constant, rs is the extinction coefficient ofthe porous medium, qs is the density of the solid, Cs is the spe-cific heat of the solid and Ts is the temperature of the solid.

(6) State equation

qg ¼WpRTg

ð6Þ

where W is the mean molecular weight and R is the universalgas constant.

For the chemical kinetics, a one-step chemical mechanism isused for the methane–air combustion in this study. Here, thepre-exponential factor is 2.119e + 11, the activation energy is2.027e + 08 J/kmol and the temperature exponent is zero.

CH4 þ 2O2@CO2 þ 2H2O ð7Þ

2.4. Property data of the porous media

The small-pore porous material in the upstream section is PSZ(Partially Stabilized Zirconia) [10], and the large-pore material inthe downstream section is aluminum oxide. First to validate themodel, the empirical properties of the porous media [6] used inthe computations are summarized in Table 1. Even using the sameporous media (PSZ in upstream section and alumina in downstreamsection in our work) the properties can be changed in very wideranges. The term ‘‘PPC” in Table 1 means ‘‘pores per centimeter”.

In Table 1, the constants C and m are used to determine the vol-umetric Nusselt number, from which the convective coefficient canbe obtained.

Nuv ¼ CRem ð8Þ

hv ¼Nuvkc

e

l2cð9Þ

where lc is the mean pore diameter.

Table 1Property parameters of porous media.

Upstream Downstream

Porous media type 25.6 PPC 3.9 PPCPore diameter d 0.029 cm 0.152 cmPorosity e 0.835 0.87Thermal conductivity Kc

e 0.2 W/m K 0.1 W/m KExtinction coefficient rs 1707 m�1 257 m�1

C 0.638 0.146m 0.42 0.96

0.025 0.030 0.035 0.040 0.045

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Tem

pera

ture

(K)

x(m)

10.1s20.1s72.1s

solid

gas

Fig. 2. Temperature profiles at t = 10.1 s, 20.1 s, and 72.1 s.

0.025 0.030 0.035 0.040 0.045

200

400

600

800

1000

1200

1400

1600

1800

2000

gassolid

Tem

pera

ture

(K)

x(m)

Ref.[10] present

Fig. 3. Comparison of temperature profiles.

1738 H. Liu et al. / Fuel 89 (2010) 1736–1742

2.5. Boundary and initial conditions

At the inlet, for the gas phase

T0 ¼ 300 K;Yi ¼ Yi;in; u ¼ uin;v ¼ 0: ð10Þ

For the solid phase

kce@Ts

@x¼ �erðT4

s;in � T40Þ ð11Þ

At the exit, for the gas phase

@u@x¼ @v@x¼ @Tg

@x¼ @Yi

@x¼ 0 ð12Þ

and for the solid phase

kce@Ts

@x¼ �erðT4

s;out � T40Þ ð13Þ

On the axis of symmetry line

@u@y¼ v ¼ @Ts

@y¼ @Tg

@y¼ @Yi

@y¼ 0 ð14Þ

Initially, the fluid velocity of the computational region is specifiedaccording to the inlet velocity of the gas mixture and the tempera-ture profile in the solid is specified as having a peak temperature of1500 K, in order to initiate the reaction [7].

3. Numerical method

Using commercial software FLUENT, stable solutions are ob-tained by solving the transient governing equations. In FLUENT,only the single temperature model could be used to solve the en-ergy equations in porous media, i.e., assuming the solid and thegas are in thermal equilibrium. The application of the single tem-perature model cannot reveal the true situation. Therefore, UDFis necessary to modify the single temperature model to give atwo-temperature model, one for gas and the other for solid. TheUDF is also used to define the property data of the porous media,which change with temperature so cannot be defined by the origi-nal property parameter model of FLUENT.

The SIMPLE (Semi-Implicit Method for Pressure-Linked Equa-tions) algorithm has been employed to solve the pressure–velocitycoupling momentum equation. The convective terms are approxi-mated by the first-order upwind scheme, and the diffusion termsare approximated by the central difference scheme. The under-relaxation iteration is used to solve the stiff problem in chemicalreactions.

4. Results and discussions

Two-dimensional distributions of temperature and gas velocityhave been studied, and the effects of inlet velocity, equivalence ra-tio, extinction coefficient and thermal conductivity on the temper-ature profiles are presented.

4.1. Validations of the computations

First the definition of equivalence ratio is given. The equiva-lence ratio is defined as / ¼ ðF=OÞactual

ðF=OÞstoich, where ðF=OÞactual is the mass

ratio of the fuel to the oxidant and ðF=OÞstoich is the stoichiometricmass ratio of the fuel to the oxidant. Fig. 2 shows the temperatureprofiles of the gas and the solid at /=0.65, uin=0.6 m/s and at timest = 10.1 s, 20.1 s, and 72.1 s. The temperature profiles of the gas andthe solid at t = 20.1 s almost completely coincide with those att = 72.1 s. This means that the flame tends to be stable till t = 20.1 s.

Fig. 3 shows comparisons of the temperature profiles betweenthe present results and those from Ref. [10] at the same conditions/=0.65, uin=0.6 m/s. The trends of temperature show mostly goodagreement with the numerical results from Ref. [10]. As the flam-mable gas mixture flows through the porous media, the reactionproducts heat the ceramic matrix by convection and radiation. Be-cause of the high emissivity of the porous media in comparisonwith the gas, radiation from the high temperature post flame zoneserves to heat the pre-flame zone of the porous media, which, inturn, radiatively and convectively heats the incoming reactants,so the methane–air mixture is preheated effectively.

Fig. 3 also shows the disagreement between the present resultsand those from Ref. [10]. Compared with the temperature profile ofthe gas from Ref. [10], our result reaches a peak near the interfacein the downstream section, and the temperature on this peak is

1 744

176 7

178 9

183 3

187819001922196777

655

0

325

x/m

y/m

0.025 0.03 0.035 0.04 0.045 0.05 0.0550

0.01

0.02

0.03

Fig. 4. Contours of the gas temperature (unit: K).

H. Liu et al. / Fuel 89 (2010) 1736–1742 1739

some 150 K higher than that of Ref. [10]. However, within a veryshort distance, about 3 mm, both gas temperature profiles tendto be the same. In contrast, the temperature of the solid in the pres-ent work reaches its largest value after a somewhat longer distancecompared with that of Ref. [10]. The reasons for these disagree-ments may come from the different numerical methods, differentchemical mechanisms or different dimensions of the models.

4.2. Two-dimensional distributions of temperature and gas velocity

Fig. 4 shows the temperature contours of the gas. The tempera-ture of the gas increases rapidly from 550 K to 1900 K near theinterface between the two sections. The temperature gradient nearthe interface is sharp and somewhat higher than that of Ref. [10]because a one-step chemical mechanism is used in the presentstudy instead of a multi-step one, which is very expensive for com-putation. Clearly, the temperature contours show that the temper-ature is slightly lower near the wall than in the center. Because theno-slipping wall assumption is imposed, the gas velocity is zero atthe solid surface and the reaction slows down as well.

Plots (a) and (b) of Fig. 5 show the axial velocity vectors andcontours of the gas, respectively. The velocity increases sharply

(a

(b

x/

y/m

0.025 0.03 0.035 0.0

0.01

0.02

0.03

Fig. 5. (a) Vectors of the axial velocity component; (b) C

and reaches a peak near the interface, due to the reaction. Becauseof the no-slipping wall assumption, the velocity contours are closertogether and the velocity decreases to zero at the wall.

Plots (a) and (b) of Fig. 6 show the radial velocity vectors andcontours of the gas, respectively. The values and gradients of theradial velocity of the gas in the upstream section are very smalland very difficult to observe. Near the interface, the radial veloci-ties clearly increase because of the reaction. In the downstreamsection, the radial velocities increase gradually from the axis ofsymmetry to the wall, while they decrease abruptly to zero atthe wall because of the no-slipping wall assumption.

4.3. Effect of the inlet velocity

Fig. 7 shows the temperature profiles of the gas for the stableoperating limits at /=0.65. The operating range means the differ-ence between the minimum inlet velocity (the minimum stableburning rate) and the maximum inlet velocity (the maximum sta-ble burning rate) for the same equivalence ratio. The result showsthe same trend as in Ref. [10]. The flame at the low inlet velocitylimit stabilizes just upstream of the interface. The flame at the highinlet velocity limit stabilizes just downstream of the interface.

)

)

m04 0.045 0.05 0.055

3.6m/s

ontours of the axial velocity component (unit: m/s).

(a)

(b)

x/m

y/m

0.025 0.03 0.035 0.04 0.045 0.05 0.0550

0.01

0.02

0.03

0.016m/s

Fig. 6. (a) Vectors of the radial velocity component; (b) Contours of the radial velocity component (unit: m/s).

1740 H. Liu et al. / Fuel 89 (2010) 1736–1742

These results also indicate that the gas temperature at the low inletvelocity limit is higher than that at the high inlet velocity limit, be-cause, at the same equivalence ratio, the lower inlet velocity leadsto a longer preheat time and higher preheat temperature of thereactants. Close to the outlet of the burner, the final temperaturedifference between the gas and the solid with the low inlet velocityis larger than that for the high inlet velocity. The reason is likely tobe that the convective heat transfer between gas and solid is en-hanced with the increase of inlet velocity.

4.4. Effect of the equivalence ratio

The stable operating ranges for an equivalence ratio intervalfrom 0.55 to 0.9 are obtained. The results are shown in Fig. 8, to-gether with the computational results of Ref. [10] and the experi-ment results of Ref. [21]. Clearly, the present results lie between

0.025 0.030 0.035 0.040 0.045250

500

750

1000

1250

1500

1750

2000 gas

solid

Tem

pera

ture

(k)

x(m)

0.25m/s 0.63m/s

Fig. 7. Temperature profiles for different inlet velocities at an equivalence ratio of0.65.

them and show the same trends. The stable operating range willenlarge and shift to larger values when the equivalence ratio in-creases. The present results are higher than the experimental datain Ref. [21] due to the neglect of radial heat losses, as occurs in Ref.[10], while our results are lower than the computational results ofRef. [10] and the minimum stable burning rates are close to theexperimental data of Ref. [21]. The reason for this may be thatthe thermal dispersion correlation adopted in the present work isdifferent from the thermal dispersion correlation being used inRef. [10] and the stable operating limits depend strongly on thedispersion correlations [22].

4.5. Effect of the extinction coefficient of porous media

Figs. 9 and 10 present the effect of the extinction coefficient ofthe porous media on the temperature profiles of the gas and solid.

0.6 0.7 0.8 0.9

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6 present Ref. [10] Ref. [20]

φ

Vmax

Vmin

inle

t vel

ocity

(m/s

)

Fig. 8. Comparisons of stable operating ranges for different equivalence ratios.

0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

200

400

600

800

1000

1200

1400

1600

1800

x(m)

Solid

Tem

pera

ture

(K)

Fig. 10. Temperature profiles of the solid for different extinction coefficients.

0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

200

400

600

800

1000

1200

1400

1600

1800

2000

x(m)

Gas

Tem

pera

ture

(K)

Fig. 9. Temperature profiles of the gas for different extinction coefficients.

Table 2Extinction coefficients of each case.

Case I (m�1) Case II (m�1) Case III (m�1) Case IV (m�1)

Upstream section 1707 1707 2407 2407Downstream

section257 557 257 557

0.025 0.030 0.035 0.040 0.045

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Gas

Tem

pera

ture

(K)

x(m)

Fig. 11. Temperature profiles of the gas for different thermal conductivities.

0.025 0.030 0.035 0.040 0.045

200

400

600

800

1000

1200

1400

1600

1800

Solid

Tem

pera

ture

(K)

x(m)

Fig. 12. Temperature profiles of the solid for different thermal conductivities.

Table 3Thermal conductivities of each case.

Case i(W/m K)

Case ii(W/m K)

Case iii(W/m K)

Case iv(W/m K)

Upstream section 0.2 1 0.2 1Downstream section 0.1 0.1 0.5 0.5

H. Liu et al. / Fuel 89 (2010) 1736–1742 1741

The extinction coefficients of four cases for comparison are listed inTable 2. The results of cases I and III show that the extinction coef-ficient, as well as the radiation of the upstream section, has littleeffect on the temperature profiles of the gas and solid, since thegas and the solid are almost at the temperature of the environmentin the upstream section. As shown in cases I and II, when theextinction coefficient of the upstream section remains invariantand the extinction coefficient of the downstream section increases,the reaction region moves downstream. The temperature peak ofthe gas decreases, while the temperature peak of the solid in-creases. In comparing case I with case IV, where there is an in-crease of extinction coefficients of both the upstream anddownstream sections, the temperature peak of the gas has de-creased, the temperature peak of solid has changed a little, andthe reaction region clearly moves downstream. The explanationfor this is that, with the increase of the extinction coefficient ofthe porous media, which corresponds to the decrease of the pore

diameter, the premixed gas velocity increases and the start pointof reaction consequently moves downstream.

4.6. Effect of the thermal conductivities of porous media

Figs. 11 and 12 present the effect of the thermal conductivitiesof the porous media on the temperature profiles of the gas and so-lid. The thermal conductivities for four cases are listed in Table 3.Compared with case i, the thermal conductivity of downstreamsection is increased in case iii, while its upstream section valueremains fixed. This will lead to enhanced heat transfer in thedownstream section, hence an increase in this region of the tem-perature of the gas and solid and also increases of temperatureof the gas and solid in the upstream area close to the interface.Again, compared with case i, we increase the thermal conductivityin both upstream and downstream sections of case iv, but onlyin the upstream section of case ii. Since increasing the upstream

1742 H. Liu et al. / Fuel 89 (2010) 1736–1742

conductivity serves to enhance the heat recirculation from down-stream to upstream, the solid temperature downstream near theinterface decreases, while the solid temperature of the remainingsolid and the gas temperature in both the upstream and down-stream sections all increase.

5. Conclusions

Using a two-dimensional model, the combustion of methane–air mixture in a porous burner is studied numerically. The two-dimensional model is validated. The temperature and velocity con-tours, which cannot be observed by using a one-dimensional mod-el, are obtained. The results of stable operating ranges show closertrends to the experiments than the results in reference. The tem-perature profiles are significantly affected by the stable operatinglimits, extinction coefficient and thermal conductivity of the solid.The change of the extinction coefficient of the porous media willalso lead to movement of the reaction region, which should be seri-ously considered in industrial application of porous burner.

In the future, the combustion of industrial syngas will benumerical simulated using a detailed chemical reactionmechanism.

Acknowledgements

This work was supported by the Fundamental Research Pro-gramme of China (2006CB601203). The corresponding authorgratefully acknowledges Prof. Akira Tomito for his great effort toimprove the quality of this paper.

References

[1] Weinberg FJ. Combustion temperatures: the future. Nature 1971;233:239–41.[2] Takeno T, Sato K. An excess enthalpy flame theory. Combust Sci Technol

1979;20:73–84.[3] Echigo R, Yoshizawa Y, Hanamura K, Tominura T. Analytical and experimental

studies on radiative propagation in porous media with internal heatgeneration. In: Proceedings of the eighth international heat transferconference, vol. 2; 1986; p. 827–32.

[4] Tong TW, Lin WQ, Peck RE. Radiative heat transfer in porous media withspatially-dependent heat generation. Int Commun Heat Mass 1987;14:627–37.

[5] Hsu PF, Evans WD, Howell JR. Experimental and numerical investigation ofpremixed combustion within nonhomogeneous porous inert media. CombustSci Technol 1993;90:149–72.

[6] Hsu PF. Analytical and experimental study of combustion in porous inertmedia. PhD thesis. The University of Texas at Austin; 1991.

[7] Hsu PF, Matthews RD. The necessity of using detailed kinetics in models forpremixed combustion within porous inert media. Combust Flame 1993;93:457–67.

[8] Chen YK, Matthews RD, Howell JR. The effect of radiation on the structure of apremixed flame within a highly porous inert medium. Radiat Phase ChangeHeat Transfer Thermal Syst 1987;81 of HTD:35–42.

[9] Tan ZQ, Howell JR. New numerical method for radiation heat transfer inparticipating media. J Thermophys Heat Transfer 1990;4:419–24.

[10] Barra AJ, Diepvens G, Ellzey JL, Henneke MR. Numerical study of the effects ofmaterial properties on flame stabilization in a porous burner. Combust Flame2003;134:369–79.

[11] Barra AJ. Computational study of a two-section porous burner. MS thesis. TheUniversity of Texas at Austin, Austin, TX; 2002.

[12] Barra AJ, Ellzey JL, Henneke MR. A computational study of heat recirculation inporous burners. In: Proceedings of the Central States/The Combustion Institute2003 Spring Meeting, B22, March 2003, Chicago.

[13] Martin AR, Saltiel C, Chai J, Shyy W. Convective and radiative internal heattransfer augmentation with fiber arrays. Int J Heat Mass Transfer 1998;41:3431–40.

[14] Mital R, Gore JP, Viskanta R. A study of the structure of submerged reactionzone in porous ceramic radiant burners. Combust Flame 1997;111:175–84.

[15] Talukdar P, Mishra SC, Trimis D, Durst F. Combined radiation and convectionheat transfer in a porous channel bounded by isothermal parallel plates. Int JHeat Mass Transfer 2004;47:1001–13.

[16] Talukdar P, Mishra SC, Trimis D, Durst F. Heat transfer characteristics of aporous radiant burner under the influence of a 2-D radiation field. J QuantSpectrosc RA 2004;84:527–37.

[17] Lammers FA, De Goey LPH. The influence of gas radiation on the temperaturedecrease above a burner with a flat porous inert surface. Combust Flame2004;136:533–47.

[18] Tong TW, Li W. Enhancement of thermal emission from porous radiantburners. J Quant Spectrosc RA 1995;53(2):235–48.

[19] Lacroix C, Bala PR, Feidt M. Evaluation of the effective thermal conductivity inmetallic porous media submitted to incident radiative flux in transientconditions. Energy Convers Manage 1999;40:1775–81.

[20] Leonardi SA, Viskanta R, Gore JP. Radiation and thermal performancemeasurements of a metal fiber burner. J Quant Spectrosc RA 2002;73:491–501.

[21] Khanna V. Experimental analysis of radiation for methane combustion withina porous medium burner. MS thesis, Mechanical Engineering Dept., Universityof Texas, Austin; 1992.

[22] Henneke MR. Simulation of transient combustion within porous inert media.PhD thesis. The University of Texas at Austin; 1998.