Proceeings o the 5 th ASME/JSME Joint hermal Engineering Conerence March 15-19, 1999, San Diego, Caliornia CONDENSAION HEA RANSFER OF ACUAL FLUE GAS ON HORIZONAL UBES Masahiro OSAKABE, ugue IOH an Kiyoyuki YAGI okyo University o Mercantile Marine -1-6 Etchujima, Koutou-ku, okyo 135-8533, Japan Phone +81-3-545-744, FAX +81-3-545-7336 E-Mail osakabe ipc.tosho-u.ac.jp Keywors: Boiler, Actual lue gas, Heat an mass transer, Conensation AJE99-6397 ABSRAC In orer to improve the boiler eiciency, latent heat recovery rom an exhaust lue gas is a very important concept. Conensation heat transer on horizontal stainless steel tubes was investigate experimentally using an actual lue gas rom a natural gas boiler. he experiment was conucte at ierent air ratios an steam mass concentrations o the lue gas, an in a wie range o tube wall temperature. he conensation pattern was similar to the ropwise conensation near the ew point. As the wall temperature was ecrease, the wall region covere with a thin liqui ilm increase. he heat an mass transer behavior were well preicte with the simple analogy correlation in the high wall temperature region. But in the low wall temperature region, the total heat transer rate was higher than that preicte by the simple analogy correlation. At a high steam mass concentration artiicially generate with steam injection, the total heat transer rate was higher than that preicte by the simple analogy correlation. he analogy correlation using the moiie Sherwoo number taking account o the mass absorption eect was propose. he moiie correlation gave a goo preiction o the heat lux at the high steam mass concentration. EXPERIMENAL APPARAUS AND MAJOR RESULS Water coole test tubes o SUS316L were installe at a transparent polycarbonate test section o which cross-section was 16mm 11mm. hree tubes o 1.7mm iameter were arrange horizontally at pitch o 33.7mm. Sheathe K-type thermocouples o.5 mm iameter were imbee at 15 circumerential locations o tubes to obtain the average wall temperature. he steam an SO concentrations in the lue gas can be controlle with steam an SO injections upstream o the test section. he experiments were conucte at the ierent wall temperature, lue gas low rate an properties. Shown in Fig.A-1 is the relation between the heat lux an the average wall temperature in a lue gas o air ratio 1.9 where the steam mass concentration was approximately.1. he soli an ashe lines are preictions by the simple analogy correlation. he conensation heat lux was obtaine by the amount o conense water collecte an measure with multiple suction pipes. he total heat lux an the conensation heat lux were well preicte with the simple analogy correlation at the high wall temperature an the low steam mass concentration. q w (kw/m ) 4 otal Con. otal Conensation 5 1 ( w ) ave. Fig. A-1 Relation between heat lux an average wall temperature 1
NOMENCLAURE C: mass concentration per lui o a unit volume [kg/m 3 ] C p : speciic heat [kj/kg] : outer iameter o tube [m] D: mass iusivity(m /s) h V : heat transer coeicient [kw/(m K)] h C : mass transer coeicient [m/s] K : moiie Nusselt number L W : latent heat [kj/kg] m S : injecte steam low rate [kg/s] Nu: Nusselt number( = hv / λ ) P: pressure [Pa] q: heat lux [kw/m ] Pr: Prantl number( = ν / κ ) Re: Reynols number( = u / ν ) R: relative humiity o air Sh: Sherwoo number ( = h c / D) Sc: Schmit number ( = ν / D ) : temperature [ C] u: velocity at minimum low area [m/s] V: volumetric low rate [m 3 N /s] w: mass concentration per lui o an unit mass [kg/kg] x: low-irectional istance [m] y: istance rom wall [m] κ: thermal iusivity ( = λ /( ρc P )) λ: heat conuctivity [W/(mK)] µ: air ratio ν: kinematic viscosity [m /s] ρ: ensity [kg/m 3 ] subscript a: atmosphere, C: conensation, COX: carbon ioxie an monoxie, : ry gas, F: uel, : lue gas, i: conensation surace, V: convection, W: wall, N: stanar conition at C an atmospheric pressure, sat: saturate conition o steam, sub: subcooling, wt: wet gas INRODUCION he most part o energy losses in a boiler is ue to the heat release by the exhaust lue gas to atmosphere. he release heat consists o sensible an latent one. Recently, or a biological an environmental saety, a clean uel such as a natural gas is wiely use in the boiler. As the clean uel inclues a lot o hyrogen instea o carbon, the exhaust lue gas inclues a lot o steam accompanying with the latent heat. So the latent heat recovery rom the lue gas is very important to improve the boiler eiciency. For the latent heat recovery rom a boiler, conensation heat transer experiments have been conucte by using steam-air mixtures(aniguchi et. al., 1987; Kanzaka et. al., 199 an Kawamoto et. al., 1995). hese experiments yiel ierent opinions on the analogy or heat an mass transer. Furthermore, conensation in actual lue gas is more complex an least unerstoo. So it was iicult to preict the accurate thermo-lui behavior o an actual conensing heat exchanger using an actual lue gas. Conensation heat transer on horizontal stainless steel tubes was investigate experimentally by using the actual lue gas rom a natural gas boiler. he experiment was conucte at ierent air ratios an steam mass concentrations o the lue gas in a wie range o tube wall temperature. EXPERIMENAL APPARAUS AND MEHOD Shown in Fig.1 is a schematic o experimental apparatus. he lue gas rom a natural gas test boiler was coole rom 7 C to 1 C by a heat exchanger without the conensation. he steam an SO concentrations in the lue gas can be controlle with steam an SO injections systems upstream o the test section. Flue gas Boiler Water F P 9 45 13A gas Heat exchanger Drain Hot water F Col water P : : hermocouple hermocouple P: P: Pressure Pressure gage gage F: F: Flow Flow meter meter Steam or SO Straitening pipes est section 85 Extraction Atmosphere Blower Fig. 1 Schematic o experimental apparatus 18 11 Water 135.5 8 16 1 est tube 1 Extraction Fig. est tubes an extraction system Mixing cell 3
he steam was supplie rom another steam boiler an measure with a vortex-sheing low meter. he error was within ±% o the measure value. he low rate an pressure o the natural gas uel supplie to the test boiler were measure. he error o the low rate was within ±.5%. he lue gas temperatures just above an below the test tubes were measure with sheathe K-type thermocouples o.5 mm in iameter. Water coole test tubes o SUS316L were installe in a transparent polycarbonate uct with the cross-section o 16mm 11mm as shown in Fig.. he water low rate was measure with a turbine low meter within ±%. he connecting pipes outsie the test section were thermally insulate with a glass wool. hree tubes o 1.7mm in iameter were arrange horizontally at a pitch o 33.7mm. he pitch to iameter ratio p/ was 1.55. Sheathe K-type thermocouples o.5 mm in iameter were imbee at circumerential locations o, 45, 9, 135 an 18 rom the top o 3 tubes to obtain the average wall temperature. he inlet an outlet water temperature o the test tubes were measure also with the sheathe K-type thermocouples o.5 mm in iameter. he outlet temperature was measure at a mixing chamber to obtain a well-mixe bulk temperature. he temperature ierence o the cooling water through the tubes was kept approximately at 1 4 K. he heat lux o the test tubes was calculate with the low rate an the temperature ierence o cooling water through the tubes. he measurement error o the heat lux was estimate to be % as the maximum in the non-conensation region an 5% as the minimum in the conensation region. he thermocouple signals were transerre to a personal computer with a GPIB line an analyze. he measurement error o the temperature in this stuy was within ±.1 K. he conensate generate on the test tubes was collecte with an extraction system as shown in Fig.. he multiple stainless-steel tubes o 1 mm inner iameter were attache to a heaer piping o 6 mm in iameter which le to a vacuum pump. he conensate hanging to the tube bottom was immeiately extracte to a measuring pot with the multiple tubes an the amount collecte uring 5 to 1 minutes perio was measure. By using the collecte amount an the latent heat o steam in the lue gas, the conensation heat lux was estimate. It was conirme that the extraction i not aect the conensation heat lux an the steam mass involve in the extracte gas was negligibly small. he ph value o the conensate at 5 C was measure with an electric-conuctivity ph sensor. able1. Composition o natural gas uel(13a) CH 4 88. % C H 6 5.8 C 3 H 8 4.5 C 4 H 1 1.7 Preicte sat 8 75 Measure by capacitance type sensor Error less than 7 7 75 8 Measure sat Fig. 3 Preicte an measure ew points he composition o natural gas uel use in the test boiler are shown in able.1. Volumetric concentrations o N, CO, O an CO in the ry gas were measure by a gas analyzer. he measurement error was within ±1 % or CO, within ±.7 % or O an within ±15 % or CO. By using the measure concentration, the air ratio µ is calculate as N µ = (1) 79. N ( O 5. CO) 1. he molar raction o the carbon in the uel o 1 mol can be calculate as, CCR = 1. 88 +. 58 + 3. 45 + 4. 17 mol By using the volumetric low rate o the uel V F, the volumetric low rate o the carbon ioxie an monoxie, V COX, is V = V CCR () COX F he volumetric low rate o ry gas V is, V COX V = (3) CO + CO he molar raction o the hyrogen corresponing to CO X o 1 mol can be calculate as, CHR = ( 4. 88 + 6. 58 + 8. 45 + 1. 17 ) / CCR mol Consiering that the air low rate necessary or the combustion o the uel is V N /.79, the volumetric raction o H O in the lue gas can be estimate as ( CO + CO) CHR / + N R P sat / ( P a 79. ) + m S 4. / ( 18 V ) H O = 1 + ( CO + CO) CHR / + N R P sat / ( P a 79. ) + m S 4. / ( 18 V ) (4) where P sat is the saturation pressure o steam in the air. Shown in Fig.3 is a comparison o the preicte ew points by using Eq.(4) an the measure ones with a capacitance-type humiity sensor. he measurement error o the ew points was 3
± C in the experimental conition in Fig.3. he calculate ew points by Eq.(4) agree well with the measurement. he volumetric low rate o wet gas, V wt, is V V wt = (5) 1 H O When the lue gas temperature is C, the steam mass concentration C per unit volume o lue gas is, able. Low velocity experimental conition Experiment No. L-1 L- L-3 Air ratio 1.9 1. 1.33 Flow rate V wt (m 3 N /h) 3. 33.6 36.3 Gas temp. ( C) 145 167 19 Steam conc. w (kg/kg).111.18.97 Dew point sat ( C) 57.1 56.4 54.4 able3. High velocity experimental conition Exp. No H-1 H- H-3 H-4 H-5 H-6 H-7 Air ratio 1.9 1. 1. 1.19 1.19 1. 1.18 V wt (m 3 N /h) 1 34 34 46 49 68 55 ( C) 14 118 118 118 118 116 1 m S (kg/h) 31 34 43 46 51 53 w (kg/kg).13.16..49.6.63.79 sat ( C) 55.5 7.4 71. 73. 74.3 74.4 75.6 1 K 1 1 Zukauskas Low velocity test High velocity test K =.6Re.6 1 1 3 Re 1 4 Fig. 4 Moiie Nusselt number uner non-conensing conition H O 18 7315. C = (6). 4 7315. + he steam mass concentration W per unit mass o lue gas is H O w = 18 HO 18 + ( 1 H O )( CO 44 + CO 8 + N 8 + O 3) (7) wo series o experiments with low an high lue gas velocities were conucte. he lue gas velocity at the minimum low area o the test section was approximately 3.5m/s in the low velocity experiment an approximately 15m/s in the high velocity experiment, respectively. In the low velocity experiment, the boiler was operate at three kins o air ratios by controlling the rotational spee o the blower with an inverter. In the high velocity experiments, steam concentration o the lue gas was controlle by injecting a steam into the lue gas. he experimental conitions or the low an high velocity experiments are shown in ables. an 3, respectively. EXPERIMENAL RESULS AND DISCUSSIONS Low velocity experiment he maximum inner wall temperature o the polycarbonate test section was 1 C. he maximum contribution ratio o the raiation heat lux rom the inner wall to the test tubes was within 9% o the total heat lux q when the emissivity o the polycarbonate wall an the tubes covere with the conensate were assume as 1. As an accurate estimation o the raiation heat transer is iicult, it was neglecte in the ollowing analysis. he total heat lux q consists o the convection heat lux q V an the conensation heat lux q C as q = q V + q C (8) In the experiments, q was obtaine rom the temperature ierence an low rate o the cooling water. he convection heat lux is expresse as q V = h V ( w ) (9) he conensation heat lux q C can be expresse as, q C = h C L W ( C C w ) (1) where C w is the mass concentration o saturate steam at the wall temperature w. Base on the previous stuies, the Nusselt number Nu or the average convective heat transer coeicient is m Nu = c Re 6. Pr (Pr / Pr w ) 5. (11) he moiie Nusselt number K is m K = Nu Pr (Pr / Pr w ) 5. = c Re 6. (1) Zukauskas(197) propose c=.6, m=.37 or the irst row tubes o an in-line bank with p/=1.6, which is approximately the same as that in the present stuy. Shown in Fig. 4 is the experimental ata o the moiie Nusselt number uner 4
non-conensation conition in the low an high velocity experiments along with previous ata by Zukauskas(197). he non-conensation heat transer ata agrees airly well with the previous ata an correlation (1). hese results show that the heat lux an the lue gas velocity were measure with eicient accuracy in the present stuy. For an analogous mass transer process, the Nusselt number an Prantl number in the heat transer relation Eq.(11) are simply replace by the Sherwoo number an the Schmit number, respectively. his proceure gives m Sh = c Re 6. Sc ( Sc / Sc w ) 5. (13) he rule gives a correct relation or the limiting situation in which the ierences in temperature an concentration are vanishingly small, an it is vali or inepenent analogous heat an mass transer situations as well as or a combine heat an mass transer process. Flue gas was treate as a mixture o N, CO, O, CO an H O an its property was estimate with special combinations o each gas property propose by the previous stuies(jsme, 1983). For example, the heat conuctivity an the viscosity were estimate with the methos by Linsay&Bromley(195), an Wilke(195), respectively. It is consiere that a strong correlation exists between the thermal an mass iusivities. As an irst attempt, the mass iusivity o steam in lue gas was estimate with the well-known mass iusivity o steam in air as κ D = D air (14) κ air where κ an κ air are the thermal iusivities o lue gas an air, respectively. he iusivity o steam in air can be expresse as (Fujii et. al., 1977), + D air = 765 1 5 7315 11 / (. ) 6. (15) P Shown in Fig.5 is the relation between the heat lux an average wall temperature at the air ratio o 1.33. he key (Ο) is the total heat lux an the key ( ) is the conensation heat lux obtaine rom the amount o conensate. he soli line shows the total heat lux preicte by the simple analogy correlations Eqs.(11) an (13). he ashe line is the preiction o the conensation heat lux by the Eq.(13). he preicte heat lux begins to increase at the ew point o 54.4 C ue to the initiation o conensation. he tube surace was covere with small roplets near the ew point. Conensation initiate at the ew point corresponing to the partial pressure o steam in the lue gas. Decreasing the wall temperature urthermore, the surace area covere with a thin ilm increase but a partially ry region covere with roplets coul be recognize. he experimental ata or the conensation heat lux agree well with the preictions. he total heat lux also can be preicte well with the correlation except or the low temperature region where the heat lux is slightly higher than the preiction. he same heat transer behaviors were observe in the experiments o the ierent air ratio. q w (kw/m ) 1 otal Con. otal Conensation 5 1 ( w ) ave. Fig. 5 Relation between heat lux an average wall temperature at air ratio o 1.33 ph 1 5 5 1 ( w ) ave. Fig. 6 ph value o conensate µ =1.9 µ =1. µ =1.33 Shown in Fig.6 is relation between the ph value o the conensate an the average wall temperature in the experiments 5
o the ierent air ratio. he ph value oes not epen on the wall temperature an it ecreases slightly with the air ratio. It is possible that the concentration o NO X in the lue gas increases with an increase in the air ratio. he increase o NO X is expecte to ecrease the ph value o conensate. he simple analogy correlation unerpreicte the convective an conensation heat transer in the experiment by aniguchi et. al.(1987) using a wet air. In their experiment, the wall temperature was between 18.8 C an 3.4 C. he unerpreiction o the total heat lux is also observe at a low average wall temperature less than approximately 3 C in the present experiment. High velocity experiment he maximum inner wall temperature o the polycarbonate test section was 85 C. he maximum contribution ratio o the raiation heat lux rom the inner wall to the test tubes was within 5% o the total heat lux q when the emissivity o the polycarbonate wall an the tubes covere with the conensate were assume as 1. Shown in Fig.7 is the relation between the average tube wall temperature an the heat lux at Re 135, µ 1.9 an 14 C. he experimental results or the total an conensation heat lux agree well with the preiction by the simple analogy correlations Eqs.(11) an (13). he ph value o the conensate in the high velocity experiment was approximately 4 which was slightly lower than that in the low velocity experiment. It is consiere that the concentration o NO X increases with the increase o lame temperature ue to the increase o uel low rate in the burner. he uel consumption rate in the high velocity experiment was approximately 5 times that in the low velocity experiment. he increase o NO X is expecte to ecrease the ph value o the conensate in the high velocity experiment. Shown in able.4 is the ion concentration o the conensate in the high velocity experiments. he conensate was sample at ierent subcoolings o the tube rom the ew point. he NO X an SO X ions are consiere to reuce the ph o conensate an promote the corrosion. he high concentration o these ions can be recognize near the ew point. o stuy the eect o steam concentration in the lue gas, experiments were conucte with steam injection into the lue gas upstream o the test tubes. he injecte steam low rate m S was between 31 an 53 kg/h. he steam concentration w in the lue gas varie between.16 an.79kg/kg an the corresponing ew point varie between 7.4 an 75.6 C. Shown in Fig.8 is the enlarge photograph o tube wall at 9 rom the tube top. he ew point was 71 C an the tube wall subcooling was 1.3 K. he tube surace was almost completely covere with a thin conensate ilm partially accompanie by roplets. he partial ry region coul be recognize near the roplets even in the steam injection experiment. he above simple analogy correlations Eqs.(11) an (13) preict well the experimental heat lux at a relatively small concentration o steam in the lue gas. When the steam concentration is large, the eect o mass absorption at the wall shoul be consiere(rose, 198 an Shiozaki et. al., 1998). q w (kw/m ) 4 otal Con. otal Conensation 5 1 ( w ) ave. Fig. 7 Relation between heat lux an average wall temperature in high velocity experiment able4. Ion concentration in conensate sub K 1 1 Cl - mg/l 1. <.5 <.5 SO 4 - mg/l 8.6 3..3 NO 3 - mg/l 4 8.8 7.1 NO - mg/l 17 11 11 CO 3 - mg/l < 1 < 1 < 1 1 mm Fig. 8 Photograph o tube wall at 9 rom tube top, sub =1.3 K an m S = 34 kg/h As an irst approximation, the eect is consiere only in the mass transer equation, not in the heat transer equation similar to the Hijikata s metho(1989a, b) or a binary mixture. he 6
integral equations or the mass an energy conservation are ρ uw wy i v i w w i i D w ( ) ( ) = x y i (16) ρu y ρκ ( ) = i x y i (17) where v i is the normal velocity to the wall generate by conensation. From the equation o continuity or the non-conensing components, D w v i = 1 w i y i (18) Non-imensional concentration an temperature are eine as w = w w i (19) w w i = i i () By using Eqs.(18), (19) an (), Eqs. (16) an (17) can be transorme to the ollowing: 1 w u w y i D ρ ( 1 ) = ρ w x 1 w i y (1) ρu( 1 y ρκ ) = i x y () he bounary conitions or the non-imensional concentration an temperature are same an are w*=*= at y= an w*=*=1 at y=. So the relation o 1 w κ = D (3) 1 w i is presume in Eqs.(1) an (), non-imensional concentration proile coincies with that o the temperature. In the other wors, the non-imensional concentration proile can be estimate rom that o the temperature by using Eq.(3). he empirical correlation or the heat transer gives Nu 1 6 m 5 = = c Re. Pr (Pr / Pr w ). (4) y he graient o concentration can be estimate by using Eq.(3) in Eq.(4) as m w 1 6 m 5 w i = c Re. Sc ( Sc / Sc w ). 1 (5) y 1 w By using Eq.(18), the conensation rate m C is expresse as, m c i v ρ i D w w w i i i D w = ρ = = ρ (6) 1 w i y i 1 w i y Equations (5) an (6) give the moiie Sherwoo number taking account o the mass absorption eect at the wall. he moiie Sherwoo number becomes m m c 1 1 w i 6 m Sh = = c Re. 5 i Dw Sc ( Sc / Sc w ). ρ ( w i ) 1 w i 1 w (7) Shown in Figs.9 an 1 is the relation between the total heat lux an the average tube wall temperature with an without steam injection. he steam mass concentration w was.13 without steam injection an increase to.16.79 with injection. he corresponing ew point increase rom 55.5 C to 7.4 75.6 C. he ashe line preicte by the simple analogy correlation agrees well with the experimental heat lux without steam injection but is smaller than that with steam injection. he soli line calculate with the moiie Sherwoo number agrees well with the measure results with steam injection. he ot-ashe line is the preiction with the semi-empirical correlation or a single tube by Rose(198). he Rose s preiction is slightly lower than the present ata an the present moiie correlation at the high wall temperature region near the ew point. q w (kw/m ) 1 5 Simple analogy Moiie analogy Rose(198) = kg/h =31 kg/h =53 kg/h 5 1 ( w ) ave. Fig. 9 Relation between heat lux an average wall temperature with an without steam injection 7
q w (kw/m ) 1 5 Simple analogy Moiie analogy Rose(198) = kg/h =43 kg/h =46 kg/h 5 1 ( w ) ave. Fig. 1 Relation between heat lux an average wall temperature with an without steam injection CONCLUSION Conensation heat transer o an actual lue gas rom a natural gas boiler on horizontal stainless steel tubes was investigate experimentally. he experiments were conucte at ierent air ratios an steam mass concentrations o the lue gas in a wie range o tube wall temperature. 1. he bounary between the ry an conensation regions was given by the ew point eine as the saturation temperature corresponing to the partial pressure o steam in the lue gas. he ph value o the conensate was approximately 4 5 an slightly ecreases with the air ratio an the uel low rate.. he conensation pattern was similar to ropwise conensation near the ew point. Decreasing the wall temperature, the wall region covere with a thin liqui ilm increase. 3. he conensation heat transer was well preicte with the simple analogy correlation in the high wall temperature region. In the low wall temperature region less than 3 C, the total heat transer was higher than that preicte by the analogy correlation. 4. At a high steam mass concentration artiicially generate with steam injection, the total heat transer was higher than the preiction by the simple analogy correlation. he analogy correlation using the moiie Sherwoo number taking account o the mass absorption eect was propose. he moiie correlation gave goo preiction on the heat lux at the high steam mass concentration. ACKNOWLEDGMEN he authors appreciate the inancial support by New Energy an Inustrial echnology Development Organization o Japan an he Japan Society o Inustrial Machinery Manuacturers. REFERENCES Fujii,., Kato, Y an Mihara, K., 1977, Expressions o transport an thermoynamic properties o air, steam an water, Univ. Kyushu Research Institute o Inustrial Science Rep.66, 81-95 Hijikata, K., Himeno, N. an Nakabeppu, O., 1989a, Conensation o a binary mixture o vapors in a vertical tube, (in Japanese), rans. o JSME, 55-518, B, 3183-3189 Hijikata, K., Himeno, N. an Goto, S., 1989b, Force convective conensation o a binary mixture o vapors(n report, conensation on vertical an horizontal tubes), (in Japanese), rans. o JSME, 55-518, B, 319-3198 JSME, 1983, Data Book: Heat ranser 3r Eition, (in Japanese) Kawamoto, K., Nagane, K. an Ohashi, Y., 1995, Investigation on the latent heat recovery rom lue gas, (in Japanese), Proc. o 3n Heat ranser Symposium o Japan, G14 Kanzaka, M., Soa, M., Yokoo, K., Iwabuchi, M. an Osaa, I., 199, Recovery o water rom lue gas(heat an mass transer on the spirally inne tube), (in Japanese), rans. o JSME, 58-545, B, 48-53 Linsay, A.L. an Bromley L.A., 195, hermal conuctivity o gas mixtures, Inust. Engng. Chem., 4, 158-151 Rose, J.W., 198, Approximate equations or orce-convection conensation in the presence o a non-conensing gas on a lat plate an horizontal tube, Int. J. Heat Mass ranser, 3, 539-546 Shiozaki, H., Namie S. an Osakabe, M., 1998, Stuy or conensation o steam with high contents o non-conensing gas, (in Japanese), Proc. o MESJ Annual Meeting, aniguchi, H., Kuo, K., Huang, Qi-Ri an Fujii, A., 1987, Heat mass transer rom air with high water content(latent heat recovery rom lue gas), (in Japanese) rans. o JSME, 53-495, B, 3377-338 Wilke, C.R., 195, A viscosity equation or gas mixture, J. Chem. Phys., 18, 517-519 Zukauskas, A., 197, Avances in Heat ranser, 8, Acaemic press, New York, 93-16 8