ANALYSIS OF THE EFFECT OF THE CHEMICAL SPECIES CONCENTRATIONS ON THE RADIATION HEAT TRANSFER IN PARTICIPATING GASES USING A MONTE CARLO METHODOLOGY

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1 Proceedings of the 11 th Brazilian Congress of Theral Sciences and Engineering -- ECIT 2006 Braz. Soc. of Mechanical Sciences and Engineering -- ABCM, Curitiba, Brazil,- Dec. 5-8, 2006 Paper CIT AALYSIS OF THE EFFECT OF THE CHEMICAL SPECIES COCETRATIOS O THE RADIATIO HEAT TRASFER I PARTICIPATIG GASES USIG A MOTE CARLO METHODOLOGY André Maurente Universidade Federal do Rio Grande do Sul Sarento Leite street, 425, Porto Alegre, RS, Brazil aurente@ecanica.ufrgs.br Francis H. R. França Universidade Federal do Rio Grande do Sul Sarento Leite street, 425, Porto Alegre, RS, Brazil frfranca@ecanica.ufrgs.br Horácio A. Vielo Universidade Federal do Rio Grande do Sul Sarento Leite street, 425, Porto Alegre, RS, Brazil vieloh@ecanica.ufrgs.br Abstract. This paper presents the application of the Monte Carlo ethod to solve the radiation heat transfer in an one-diensional syste fored by a gas ixture contained in a space between two infinite parallel plates. The proposed ethodology consists of the application of the Monte Carlo ethod to the absorption line blackbody (ALB) distribution function, a gas odel that allows a detailed evaluation of the dependence of the absorption coefficients of the absorbing species on the wavelength. The ethodology allows solving for gaseous ixtures that are non-hoogeneous and non-isotheral. In this work, the ethod is applied to the solution of heat transfer in a gas ixture fored with different concentrations of water vapor and carbon dioxide, two absorbing species, and non-participating species such as air or nitrogen. The results show that the concentration of the species have a strong effect on the heat transfer, and deonstrate the liitation of the conventional weighted-su-of-gray-gases (WSGG) odel, which relies on correlations that are valid for only a few concentrations of the absorbing species concentrations. The cases presented in the paper are related to gaseous ixtures resulting fro the cobustion of octane and ethane. Participating gases, wavelength dependence, Monte Carlo, absorption-line-blackbody distribution function, theral radiation 1. Introduction Radiation heat transfer is an iportant phenoenon in several processes in physics and engineering. In industrial cobustion systes, such as furnaces and engine chabers, theral radiation in participating edia is often the doinant heat transfer ode due to the high teperature of the gases generated in the cobustion process. Coputing radiation exchange in participating edia is in general a coplex task, a reason for this being the highly irregular dependence of the radiative edia properties with the wavelength. To siplify the radiation heat transfer coputations and so to reduce the coputation tie, several ethods have been proposed. The siplest odel is the gray gas ediu, which considers the absorption coefficient to be wavelength independent. Despite its strong departure fro the behavior of real gases, the odel can still be found in the solution of cobustion probles in the odern literature (Adas and Sith, 1994; Magel et al., 1996; Xue et al., 2001and Sijercic et al., 2001). In the Weighted-Su-of-Gray-Gases (WSGG) odel, first proposed by Hottel and Sarofi, (1967) the ediu is treated as hoogeneous and the entire spectru is odeled by a few bands. Each band corresponds to a gray gas, in which the absorption coefficient is assued unifor and teperature independent. The ediu teperature dependence is incorporated through the weighted contribution of each gray gas, corresponding to the fraction of blackbody energy in the spectru region where the absorption coefficient is correspondent to the gray gas. The absorption coefficients and the respective weighting functions are obtained fro fitting tabulated data, as those presented by Sith et al. (1982) for two hoogeneous edia coposed of water vapor, carbon dioxide and air. Perhaps the ajor liitation of the WSGG odel is relying on only a few gray gases and its inability to treat non-hoogeneous edia, but due to its siplicity it achieved wide application in treatent of coplex radiation heat transfer processes. There is, nowadays, database copiling characteristics related to the eission and absorption behavior of olecules, as HITRA and HITEMP. With the inforation provided by these databases, radiation heat transfer probles can be accurately solved by line-by-line (LBL) integration, which considers the eission and absorption of each individual spectral line. On the other hand, the LBL integration is difficult to ipleent and is coputationally expensive. To avoid the difficulties related to LBL integration, various band odels have been developed in late years. An extensive overview of these odels can be found in the Siegel and Howell (2002).

2 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT The WSGG odel can be applied to the general radiative transfer equation, as deonstrated by Modest (1991), allowing the solution of arbitrary radiation probles by any desired ethod replacing the spectral ediu by a sall nuber of gray gases with constant absorption coefficient. This iportant developent led to the rise of new WSGG odels, as the Spectral-Line-Based-Weighted-Su-of-Gray-Gases (SLWSGG) odel, as proposed by Denison and Webb (1993a), which allows one to obtain the weights of the gray gases fro detailed spectral database as HITRA and HITEMP. In later developents, the Absorption-Line Blackbody (ALB) distribution function was defined and applied to the SLWSGG odel, and nuerical correlations to deterine this function were presented for edia coposed of water vapor and air (Denison and Webb, 1993b) and carbon dioxide and air (Denison and Webb, 1995b). Appling the K-correlated assuption (Goody et al., 1989 and Goody and Yung, 1989), the ethod was extended to nonisotheral non-hoogeneous edia (Denison and Webb, 1995a). Finally, Denison and Webb (1995c) proposed an approxiated equation for the ALB distribution function for a ixture of two cheical species: water vapor and carbon dioxide. Further iproveents in the use of the SLWSGG ethod ay be possible with new inforation available in recent works (Wang and Modest, 2004, and Modest and Singh, 2004) on spectral band odels. The Monte Carlo ethod is a powerful technique for the solution of radiation probles Howell (1998), having the iportant advantage of easily dealing with geoetrical coplexities and/or directional radiation properties. The coputational cost of the ethod is becoing less prohibitive with the rapid rising of the coputer processing power. Thus, the Monte Carlo can be a copetitive alternative for the solution of coplex spectrally dependent radiation heat transfer probles. The ethod has already been applied to deal hoogenous isotherals edia in Modest (1992) and Cherkaoui et al.,1996). In order to consider the effects of the non-uniforities of the edia, Maurente et al. (2006) applied the Monte Carlo ethod to the ALB distribution function. The work deonstrated that the Monte Carlo ethod and the ALB distribution function can be cobined in a relatively siple way, and taking the advantage of incorporating all the late advances of the SLWSGG odel. In this work the Monte Carlo cobined to the ALB distribution function is used to solve the radiation heat transfer in a syste fored by a hoogeneous ediu contained between two infinite parallel walls. The ediu is a ixture of water vapor, carbon dioxide, two eitting absorbing cheical species, and nitrogen, a transparent ediu. Since the conventional WSGG odels are based on a few relations that are valid for only a liited nuber of cheical species concentrations, considering especially the stoichioetric cheical reaction, this work ais at deonstrating the errors that can incur fro applying those odels to copute radiation heat transfer for ixtures having different concentrations. 2. The used ethodology: Monte Carlo-Absorption-Line-Blackbody distribution function The Absorption-Line Blackbody (ALB) distribution function is defined (Denison and Webb, 1993b) as the fraction of the blackbody energy in the portions of the spectru where the high-resolution spectral absorption cross-section of the ediu, K, η, is less than a prescribed value K. For a single eitting absorbing species, it is given by: F 1 ( K T, T, P, Y ) = E ( η, T ) dη, b g T s 4 σ η b, η T i b i b (1) where Y s is the concentration of the single absorbing species s; T b is the source radiation teperature at which the blackbody eissive power is evaluated; T g is the ediu local teperature at which the ediu radiation properties are evaluated; P T is the total pressure of the gaseous ediu; η is the wavenuber; σ is the Stefen-Boltzann constant; and the sub-index i refers to the i th spectral segent. The absorption cross-section coefficient, K, η, is related with the absorption coefficient by K η = M s K,η (2) where M s is the olar concentration of the absorbing species s. When desiring to account for spectral behavior in radiation heat flux calculations the blackbody energy distribution function is used to assist in deterining the distribution of eitting absorbing energy along of the spectru. In the ost spectral odels the blackbody energy fraction within each considered spectral interval is calculated. However, as deonstrated by Denison and Webb (1993b, 1995b), the ALB distribution function can be used to obtain significant coputer tie savings by coputing at the sae tie the fraction of blackbody energy in several spectral intervals in which the absorption cross-section coefficient, K, η, presents the sae value. The fraction of the blackbody energy within spectral intervals corresponding to a high-resolution absorption cross-section interval K, j and K, j+1 can be obtained by ALB distribution function as [ K T Y P ), T ] F[ K ( T, Y, P T ] (3) F j = F, j ( g, s, T b, j+ 1 g s T ), b

3 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Different Monte Carlo ipleentation can be proposed to eploy the ALB distribution function for coputation of radiative heat transfer in spectrally dependent edia, depending for instance on how the nuber and the energy of the bundles are distributed along the spectru. Each choice will lead to a different cuulative distribution function. The ethodology used in this work was proposed having as guiding factors siplicity of ipleentation and coputational efficiency. According (Maurente et al, 2006), fro the definition of the ALB function, the eission rate fro a ediu volue in the spectru portions where the average absorption cross-section is K within an certain interval K can be approxiated by q 4 ( K ) T, K = 4M sk F σ (4) where the F (K ) is the difference between the ALB distribution functions evaluated at K + K /2 and K - K /2 around of a given K value and, according Eq. (2), the product M s K corresponds to the local absorption coefficient, where M s is the olar concentration of the absorption species s. In the Eq. (4) the ALB distribution function is coputed at the local conditions of the ediu volue, so the dependence of F on local teperature, absorbing species concentration and total pressure was dropped. Considering that the total nuber of bundles released fro volue is, It was proposed that the nuber of bundles that are released fro a spectral portion where the average absorption cross-section is K within an interval K be proportional to the aount of blackbody energy, at the ediu volue teperature, that is contained in that portion: = F, K K (5) by: It follows that the energy of a bundle eitted fro the portions where the absorption cross-section is K is given ( b) q, K q, K =, K 4 4M skσt = (6) which shows that the aount of energy of the bundle depends on the value of the absorption cross-section of the spectral portions fro where it is released. As deonstrated in (Maurente eat al, 2006) following the procedure outlined in (Siegel and Howell, 2002), the frequency of the bundles released fro the portions where the absorption cross-section is K is obtained by: f ( K, K FK ) = li = li = F' ( K) K K K 0 K 0 (7) The probability density function is defined as: P( K ) = K,ax K= 0 f ( K) = f ( ξ) dξ F' ( K ) [ F( K ) F( K = 0) ],ax = F' ( K ) (8) The above result follows fro the definition of the ALB distribution functions, in which F(K,ax ) =1 and F(K = 0) = 0. Finally, the cuulative function becoes: K K R( K) = P( ξ ) dξ = F'( ξ) dξ = F( K ) 0 (9) Equation (9) shows that for the Monte Carlo ipleentation based on Eq. (5), the cuulative distribution function R(K ), which governs the nuber of bundles that are released fro all the portions where the absorption cross-section is less than K, is equivalent to the ALB distribution function. Turning to the bundles eitted fro the wall boundaries, the energy that is eitted by a gray wall eleent having area A and total eissivity ε w can be approxiated by: q 4 A, K = ε w A FK σt (10)

4 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Although there are no ediu involved in the wall eission, the fraction of the eitted blackbody energy is given by ALB distribution function which is a function of arbitrary values of K. It assists in coputing the edia absorption of the bundles provided fro walls. As done for the ediu eission, it was proposed that the nuber of wall eleent bundles that are released fro the portions where the absorption cross-section is K, within the interval K, be proportional to the fraction of blackbody energy (at the wall eleent teperature, T A ) of these portions, that is: A, K = FK A (11) where A is the total nuber of bundles released fro the wall eleent. It follows that the energy of each bundle is given by: q ( b) A, K ε w Aeb ( T = A A ) (12) Thus, the bundles released fro the wall eleents have all the sae aount energy, and does not depend on the selected portions of spectru. As well as for eission fro the ediu, Eq. (9) can also be applied to the wall eleents. As deonstrated by Denison and Webb (1995c) the ALB distribution function for edia coposed for tow eitting absorbing species can be obtained by the following adequate approxiation: F ( K K ) F ( K ) F ( K ) (13) s1,, s, 1, s1, s1, where the sub-index s 1 and s 2 refer to the both eitting absorbing species present in the ediu. The absorption coefficient to the ediu coposed by these both eitting absorbing species is K = M s K + M K (14) 1, s1, For to deterine the energy carried out for the bundles eitted fro an unifor volue eleent,, by Eq. (6), it is necessary to prescribe the nuber of eitted bundles,, and to know the value of absorption cross-section, K, related to the spectral interval of bundle energy. Using the Monte Carlo ethod the K is obtained fro the cuulative distribution function. For so uch, the Eq. (9) is rewritten as K = K( R) = K( F) (15) The final procedure in deterining K is to generate a rando nuber for the ALB distribution function, F, once it is equivalent to the cuulative distribution function, R, in this case. According Siegel and Howell (2002), the length traveled, l, before absorption of a bundle in a ediu of constant absorption coefficient, K = M s K, is l = ln( Rl ) /( M s K ) (16) where R l, is a rando nuber. The Monte Carlo equations above presented were obtained to local conditions of ediu and wall eleents whose teperature and properties are unifor, however, these equations can be used to non-isotheral non-hoogeneous edia. The nuerical procedure to copute radiation heat transfer in a ediu of non constant absorption coefficient consist basically in to discrete the path length in sall segents of unifor properties. For each segent of different properties ust be found the respective absorption cross section, K, and subsequent absorption coefficient of the ediu, K, relative to the spectral interval of the eitted energy. The K of the ediu in each traveling path segent can be related with spectral interval of eitted energy applying a K-correlated hypothesis, as deonstrated by Denison and Webb (1995a). Although there are no K involved in the gray walls eission, for each bundle eitted fro a wall it is necessary to generate a rando nuber for F to relate the spectral interval of the bundle energy with the ediu properties and so proceed as well as to copute the ediu absorption of the bundles eitted for volue eleents. Finally, the radiation heat exchange in the doain of a given approached proble can be evaluated accounting all the bundles (and its respective carried energy) eitted and absorbed by the ediu and the walls.

5 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Results and discusion Theral radiation in participating gases is in general the doinant heat transfer ode in cobustion systes such as furnaces, stea generators and engines. However, odeling of this coplex process is not liited to theral radiation, for it also involves cheical reactions of cobustion, turbulent fluid flow and convective heat transfer. The application of the ore advanced gas radiation odels in this proble is one of the ost challenging on-going researches in the field. Due to its siplicity, the conventional weighted-su-of-gray-gases (WSGG) odel is probably the ost coonly applied odel to such probles. However a few approxiations are necessary to apply this ethod. It is postulated that the total eittance and absorptance of the gas can be represented by a weighted average of gray gases eittances and absorptances, where the absorption coefficients are constant and the weights are solely dependent on the teperature. In addition, the gas is assued hoogeneous. The data presented in Sith et al. (1982) for the gray gases absorption coefficients and the polynoials weighting functions has been widely eployed, but they are valid for only two different gas ixtures having water vapor and carbon dioxide as the eitting absorbing cheical species. Those gas ixtures correspond to the products of the stoichioetric cobustion of ethane and fuel oil, and they differ only in the water vapor fractions: 20% against 10% for the cobustions of the ethane and of fuel oil, respectively. In both cases, the concentration of the carbon dioxide is 10 %. The reaining species in the ixtures can be either nitrogen or air, which are non-participating species. In contrast to the hoogeneous stoichioetric products of ethane and oil cobustion, the gaseous products that are present in cobustion systes are often non-hoogenous and the copositions can differ fro those related to stoichioetric cheical reaction. In actual cobustion process, it is coon practice to use ore air than the stoichioetric aount to enhance the possibility of coplete cobustion or to control the teperature of the cobustion chaber. For coplete cobustion of the hydrocarbon fuels, the gaseous products contain only water vapor, carbon dioxide, which are absorbing species, and inert (non-participating) gases such as nitrogen and oxygen, this last one occurring in the case of cobustion with excess of air. Aiing at investigating the departure of the WSGG odel when using the data liited to stoichioetric cobustion reactions, as the one presented in Sith et al. (1982), the Monte Carlo cobined to the ALB distribution function is used to solve for theral radiation in gases with different concentrations. As a siple exaple case, it is considered the radiation heat transfer in a gas ixture contained between two infinite parallel black walls. Gas ixtures originated fro the cobustion of two different fuels, octane and ethane, are considered. The geoetry of all the solved cases consists of two parallel black walls that are 1.0 departed fro each other. The syste is shown in Fig. 1. The nuerical solutions involved the division of the doain into 30 (thirty) equal-sized eleents in the x-direction. Figure 1. Gas layer between infinite parallel walls Octane fuel Most failiar fuels consist priarily of hydrogen and carbon. They are called hydrocarbon fuels. For a coplete stoichioetric cobustion of hydrocarbon fuels, the gaseous product is coposed of water vapor, carbon dioxide and nitrogen, and their concentrations are fixed by the cheical reaction balance. The concentrations however are dependent on the any different types hydrocarbon fuels. The available data for the conventional WSGG odel is liited to a few hydrocarbon fuels. In the widely cited work of Sith et al., 1982, data is only presented for gas ixtures having 10% H 2 O and 10% CO 2 (fuel oil cobustion) and 20% H 2 O and 10% CO 2 (ethane oil cobustion), so using this odel for different concentrations will probably lead to significant errors.

6 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT The octane is the ain hydrocarbon found in the gasoline. The stoichioetric cobustion of octane leads to a gas ixture that is coposed of 14% H 2 O and 12.5% CO 2, the reaining species being non-participating. To evaluate the effect of the absorbing species concentration, it is also considered a gas ixture having 10% H 2 O and 10% CO 2, the closest concentration that is found in Sith et al., For the two gas ixtures, the radiative heat transfer in the above referred geoetry was coputed using the ethodology presented in Section 2. The gas teperature was taken as the adiabatic of flae, obtained according the procedure outlined in Çengel and Boles (2002), which is 2304 K. The walls, assued black, are at the a teperature of 300 K. Figure 2 presents the voluetric radiative heat rate, in kw/ 3, in the gas for the two ixtures. Figure 2. Voluetric radiative heat rate and heat flux on the walls for two different gaseous ixtures. In both cases, the gas teperature is 2304 K, and the reaining species in the ixture is non-participating. As can be observed in Fig. 2, there is a significant difference between the voluetric radiative heat rate results, which was even greater near the walls. The radiative heat fluxes on the walls are shown on the top of the figure. As indicated in the figure, the heat flux on the wall for the for the gaseous ixture coposed of 10% H 2 O and 10% CO 2 is 16.6% lower than for the ixture coposed of 14% H 2 O and 12.5% CO 2, that is kw/ 2 against kw/ 2. This result is in agreeent with the voluetric radiative heat rate being larger for the later ixture, a straightforward consequence of the energy conservation. Accordingly, the integral of the voluetric radiative heat rate is about 16.6% greater for the second gas ixture than for the first one. According to the adopted convention, negative voluetric radiative heat rate indicates that the zone eits ore than absorbs. As seen in the figure, the aount of energy lost by the gas increases with the proxiity of the wall. The oscillations that appear in the Fig. 2 are expected fro the statistical nature of the Monte Carlo ethod and can becoe less iportant if the nuber of bundles be increased. A total of eight illion ( ) energy bundles were released fro each wall and gas zones for the gaseous ixture coposed of 10% H 2 O and 10% CO 2 ; as for the gaseous ixture coposed of 14% H 2 O and 12.5% CO 2, a total of five illion ( ) energy bundles were released fro the wall and gas zones Methane fuel Different fro the octane, there are correlations in Sith at al., 1982, for the weighting factors related to a gaseous ixture resulting fro the stoichioetric cobustion of ethane (20% H 2 O and 10% CO 2 ). However in real cobustion systes, the cobustion processes usually do not occur following the stoichioetric balance, but with excess of air, leading to different products concentrations. To evaluate its effect on the radiative heat transfer, two cobustion reactions differing in the excess of air were considered. The cobustion reaction with 50% of excess of air generates a ediu whose eitting absorbing species are 13.1% H 2 O and 6.55% CO 2. The radiative heat transfer was coputed for this ediu at the adiabatic flae teperature, which is 1780 K. The walls, assued black, are again kept at a teperature of 300 K. The voluetric radiation heat rate and the wall radiative heat fluxes are shown in Fig. 3. For coparison, this figure also shows the results for a gas ixture at the sae teperature generated in the stoichioetric cobustion of the ethane, coposed of 20% H 2 O and 10% CO 2. For an excess of air of 100%, the gas resulting fro the cobustion process is coposed of

7 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT % H 2 O and 5% CO 2. Figure 4 shows the voluetric radiative heat rate for this gas ixture at the adiabatic flae teperature of 1476 K. The figure shows also the result when the concentrations of H 2 O and CO 2 are taken at the stoichioetric values of 20% and 10%, respectively. Figure 3. Voluetric radiative heat rate and heat flux on the walls for gas ixtures having concentrations of 20% H 2 O and 10% CO 2 and of 13.1% H 2 O and 6.55% CO 2. Gas ixtures teperatures of 1780 K. Figure 4. Voluetric radiative heat rate and heat flux on the walls for gas ixtures having concentrations of 10% H 2 O and 10% CO 2 and of 10% H 2 O and 5% CO 2. Gas ixtures teperatures of 1476 K. For both cases in Figs. 3 and 4, a total of three illion ( ) energy bundles were released fro each wall and gas zones. To reduce the statistical oscillations, it was taken an arithetic average between the values obtained for both sides of syetry line of the probles. In real cobustion systes, the ediu is non-isotheral. To illustrate this situation, the Monte Carlo cobined to the ALB distribution function was applied to solve the radiative heat transfer in two non-isotheral gaseous ixtures, differing in the fractions of the eitting absorbing species. For both gases, the teperature varies, according to the below relation, fro 1476 K on the walls to 2327 K in the center position between the plates:

8 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT T ( x) = 3404 x x (17) These iniu and axiu teperatures are the adiabatic flae teperature in the stoichioetric ethane cobustion with 100% of excess of air. One of the gas ixtures has the concentration of the ethane stoichioetric cobustion (20% H 2 O and 10% CO 2 ), while the other has the concentration of a gas ixture resulting fro the cobustion process with 100% of excess of air: 10% H 2 O and 5% CO 2. Figure 5 presents the voluetric radiative heat rate for the two gaseous ixtures. As seen, the discrepancy in the two cases was the greatest in the iddle of the enclosure (x = 0.5 ), where teperatures are higher, and near the walls (x = 0 ). The heat fluxes on the walls are presented on the top of the figure, showing a considerable difference between the results. The stoichioetric gaseous ixture loses 52% ore energy (70.3 kw/ 2 ) to the walls than the gas ixture coposed of 10% H 2 O and 5% CO 2 (46.2 kw/ 2 ). For this case, the Monte Carlo solution was obtained for a total of four illion ( ) bundles being released fro each gas and wall zone. Figure 5. Voluetric radiative heat rate and heat flux on the walls for gas ixture having concentrations of 20% H 2 O and 10% CO 2 and of 10% H 2 O and 5% CO 2. The gas ixtures teperatures are given by Eq. (17). 4. Conclusions This work presented the application of the Monte Carlo ethod to the absorption line blackbody (ALB) distribution function to solve the radiation heat transfer in gas ixtures coposed of different concentrations of carbon dioxide and water vapor. The absorption line blackbody (ALB) distribution function is a gas odel that allows a detailed evaluation of the dependence of the absorption coefficients of the absorbing species on the wavelength. In addition, it enables the consideration of different concentrations of the absorbing species, an iportant advance with respect to the WSGG odel, which relies on liited data for a few specific concentrations. As shown in the work, the Monte Carlo can be ipleented so that its cuulative distribution function becoes equal to the ALB distribution function, which leads to a direct coupling between the ethods. The ethodology was applied to a few exaple cases aiing at deonstrating the effect of the concentrations of water vapor and carbon dioxide on the radiation heat transfer. The syste was an one-diensional gas layer contained between two infinite parallel black walls. The ediu coposition was chosen to relate to the gas ixtures that can be fored in the cobustion of octane and ethane. The results for both the voluetric radiative rate in the gas and for the heat flux on the wall deonstrated the iportance of the concentrations of the absorbing species on the radiative heat transfer, indicating the need of ore advanced gas odels than the conventional WSGG odel.

9 Proceedings of ECIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Acknowledgeent The authors thank the financial support fro CAPES-Brazil through a doctorate scholarship grant to the first author. 5. References Adas BR, Sith PJ., 1994, Modeling effects of soot and turbulence-radiation coupling on radiative transfer in an industrial furnace, ASME Radiative Heat Transfer: Current Research, HTD-Vol. 276, pp Çengel Y. A., Boles M. A., 2002, Therodyaics: An Engineering Approach, Fourth Edition, McGraw-Hill, ew York. Cherkaoui M., Dufresne J. L, Fournier R, Grandpeix JY, Lahellec, 1996, A. Monte Carlo siulation of radiation is gases with a narrow-band odel and a net-exchange forulation, Journal of Heat Transfer, Vol. 118,pp Denison M. K., Webb B. W., 1993, A spectral line-based weighted su-of-gray-gases odel for arbitrary RTE solvers, Journal of Heat Transfer, 1993, Vol. 115, pp Denison M. K., Webb B. W., 1993, An absorption-line blackbody distribution function for efficient calculation of total gas radiative transfer, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 50, pp Denison M. K., Webb B. W., 1995, Developent and application of an absorption-line blackbody distribution function for CO 2, International Journal of Heat and Mass Transfer, Vol. 38, pp Denison M. K., Webb B. W.,1995, The spectral line-based weighted su-of-gray-gases odel in nonisotheral nonhoogeneous edia, Journal of Heat Transfer, Vol. 117, pp Denison M. K., Webb B. W., 1995, The spectral line-based weighted su-of-gray-gases odel for H 2 O/CO 2 ixtures, Journal of Heat Transfer, Vol. 117, pp Goody R, West R, Chen L, Crisp D., 1989, The correlated-k ethod for radiation calculations in nonhoogeneous atospheres, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 42, pp Goody R. M., Yung Y. L., 1989, Atospheric Radiation, ew York: Oxford University Press. Hottel H. C., Sarofi A. F., 1976, Radiative Transfer, ew York: McGraw-Hill Book Copany. Howell, J. R. The Monte Carlo in Radiative Heat Transfer. Journal of Heat Transfer, 1998; 120: Magel HC, Schnell U, Hein KR., 1996, Siulation of detailed cheistry in a turbulent cobustor flow, Twenty-Sixth Syposiu (International) on Cobustion/The Cobustion Institute, pp Maurente A., Vielo H. A., França F. H. R., 2006, A Monte Carlo Ipleentation to Solve Radiation Heat Transfer in on-unifor Media with Spectrally Dependent Properties, Subitted for JQSHT. Modest M. F., 1991, The weighted-su-of-gray-gases Model for Arbitrary Solution Methods in Radiative Transfer, Journal of Heat Transfer, Vol. 113, pp Modest M. F., 1992, The Monte Carlo ethod applied to gases with spectral line structure, uerical Heat Transfer, Part B, Vol. 22, pp Modest M. F., Zhang H., 2002, The full-spectru correlated-k distribution for theral radiation for olecular gasparticulate ixtures, Journal of Heat Transfer, Vol. 124, pp Modest M. F., Singh V., 2004, Engineering correlations for full spectru K-distribution of H 2 O fro the HITEMP spectroscopic databank. In Radiation Transfer: Gas Mixtures. Fourth International Syposiu on Radiative Transfer, Istanbul Turkey, Siegel R., Howell, J. R., 2002, Theral Radiation Heat Transfer, ew York: Taylor & Francis. Sijerčić M, Stevanović Z, Belošević S., Modeling of non-confined turbulent flow of two coaxial streas under cobustion conditions, Mechanical Engineering, 1, pp Sith T. F., Shen Z., F., Friedan, J.., 1982, Evaluation of coefficients for the weighted su of gray gases odel, Journal of Heat Transfer, Vol. 104, pp Xue H, Ho JC, Cheng YM, 2001 Coparison of different cobustion odels in enclosure fire siulation, Fire Safety Journal, 36, pp Wang A., Modest M. F., 2004, High-accuracy copact database of narrow-band K-distributions for water vapor and carbon dioxide, In: Radiation Transfer: Gas Mixtures. Fourth International Syposiu on Radiative Transfer, Istanbul Turkey, Copyright otice The author is the only responsible for the printed aterial included in his paper.