958
INDUSTRIAL AND ENGINEERING CHEMISTRY
The optilllulil eondit,ionspvere chosen from this mark to tje those of experiment 115, and they proved t o be entirely satisfactory from the production angle. I t was significant, however, that, the reaction conditions could be varied over a fairly wide range with little effect on the product, This situation gav(? consi(]prah]c flesihility to tho operation of the process. LITERATURE
cxrm
Blair, J. S., and Braham, J. H., J . A m . Chr717. S o < . . 44, 3:348--5:! (1922). Blair, J. S., andBraham, J. H.. IKD. ESG.CHEM..16, 848 (19241. Burns, R., and Gay, P. F. (to Imperial Chemical Industries. Ltd.), Brit. Patent 507,498 (June 15, 1939). Davis, T. L., J . Am. Chem. SOC.,43, 2234-5 (19211. Davis, T. L., Org. Syntheses',Coll. T'ol. I, 295. Davis, T. L.. U. S.Patent 1,440,063 (Dee. 26, 1923). Erlenmeyer, E., Ann., 146, 258 (18fB). Evan, I., and Young, J. H., J . SOC.C'hem.I d , 40, 109 (19311. Garby, IND.ENC.CHEM.,17, 266 (1925). Gockel, H., Angem. Chem.,47, 555 (1934)
Vol. 39. No. 8
(11) Griesshach, R., and Iiosaley. A . . Geiman Patent 4 9 0 , 8 i 6 ( I l a ( , . 15, 1925). (12) Hill, W. H.. Swain, El. C.. and Paden, J. H. (to Am. Cyanainid C o . ) , U. 6. Patents 2.221.478 (Nov. 12. 1940) and 2,252,400 (Aug. 12, 1941). (13) Jones, K. Sf.,and Aldred, J. R. H., I ~ D EXG. . CHEM.,28, 272 4 (1936): .%Idred. U. S. Patent 2,114,280. (141 Kolthoff. I. SI.. and Furnian. 5 . H.. "Volumetric .%rial\ Vol. 11, p . 163, New York, John Wiley & Sons, 1929. (15) ltacktnann, Ann., 376, 163 (1910). ( 1 6 ) Schmidt. 1.2.. Arch. Pharm., 254, 630 (1916). (171 Smith. C:. B.. Salietta, V. J., and Steinbach, 0. F.,ISD. 1,;st;. CHEY.,23, 1124-9 (1931). (1s) Spurlin, H. ?J.(to Hercules Powder Co.),U. S.Patent 2,109,934 O f a r . 1, 1939). (19) Stickstoffwerke, Cernian Patent 222,552 (Oct. 30, 1908). ( 2 0 ) Traube, W,, and Gockel, H.. German Patent 600,86!1 ( A U K . 2 . 1934). (21) T'ozarick. Ai., %. u 7 ~ y e c L . ' h a . , 15, i o (1902). (22) Werner, E. A , . and Bell, ,J., (1.Chem. Soc., 117, 1133 (,1920!. PRESEXTED as part of t h e Syniposiiini o n Iligh Pressure Technology before the Diriaion of Industrial and Engineering Chemibtry :it the 110tll AlPPtinl: of the .A\rI:nrc.hs C t r l i v i c . ~S ~ o ( - r r v . ('liir:ixo, Ill.
Heat Transfer in a 3-1 HydrogenNitrogen Mixture at High Pressure iLLAN P. COLBURN', THOMAS B. DREW2, AND HOOD W-ORTHINGTOS E . I . d u Pont de Vemoctrs und Contpuny, Inc.. IP'ilrnington, Del. Experiments were conducted for flow iuside a &foot length of 6/s-inch i.d. steel tubing heated by steam, at gas pressures from 30 to 900 atmospheres, The Reynolds numbers extend from 40,000 to the unusually high value of 440,000. The results are in good agreement with the usual relations for heat transfer. In the correlations the effects of pressure on the relevant properties of the mixture are taken into account. RIethods of estimating these effects, which were not pronounced over the pressure range studied, are presented. Concurrence of the data Hith those for better known gases is shown by inclusion of e\perimental data for air at 5 to 8 atmospheres and at Reynolds numbers from 9000 to 50.000.
I
S DESIGNING equipnient for heating 01' cooling gases at high pressure, it is of great, importance to know rvhether formulas deduced from data for ordinary pressures can be applied or whether pressure exerts some specific influence on the transfer of heat not sensible at low pressures. S o experiniatal data have been found in the published literature for pressures higher than 14 atmospheres; Nusselt's data (18) on gases a t 1 to 14 atmospheres show no effect, of pressure. What indirect cvidvnce \vas available from the operation of plant equipment was conflicting. To resolve the conflict,, experiments were carried out \Tit h a mixture of hydrogen and nitrogen a t 900 atmospheres that is used in the synthesis of ammonia. An apparatus for heat transfer studies should be so deuigned that both the temperature rise of the material floxing and thc temperature differences b e t m e n that material and the heating medium may be adequately measured without elaborate instrumentation. Preliminary calculations on the basis of existing d a t a showed that about a 5-foot length of 5 ' 8 x 11/* inrh strrl tubing fulfilled these conditions. -4 double stcam jackrt was I 1
Present address. Cniversity of Delauare, S e w a r k , Del. Present addreai, Columbia University, S e a York. X . Y.
provided, as sholvn in Figure 1. Thus, the condensate from r t w test section could be collected without including that arising from heat. losses to the surroundings. The outer jacket \vas connected to a steam trap, and the inner jacket was connected t o a condensate chamber provided with a gage glass that prrniittt-tl the level of thc condensate to be determined. A line from t h i . bottom of the condensate chamber led to a cooler and a wllecting vessc~l. Vents on the steam line before and after the hcvtt exchanger permitted the line5 to be freed from condensate atid thp heat, exchanger to he purged of any air which might enter \vir11 thc steam. The gas mixture entered the heat exchanger through two higli prcssurci valves 1vhic.h were used in regulating the flow and pi--surr. From the heat exchanger thc gas passed through anothri, regulating valve by which the pwssure was reduced to 30 atnio-phercs, thc pressure for nhich the flowmeter was designed. Thc steani tcmperature was determined from thc pressui'v, using thtx corresponding temperatures for saturated steam. Thr, quality of the steam v a s estimated with an Ellison calorimetc%i.. The temperature of the gas was measured by thermocouples i i i nells which projected axially iii from the two ends of the exprr,inicntal tuhe. The test section was taken as the distance betn.cwt thts ~ ~ t i dofs ~vells(4.71 feet); the \vel1 a t the cold end projectt,cl 2.0 itirhc.? beynnd the inner eondensate jacket. The gas prcssrii.ts \vas measured by calibrated Bourdon gages. The gas flow \va\ read from a Bailey flowmeter equipped with a sharp-edged c'vcentric orifice; the readings were corrected for the differeriw betn-cwi thc- conditions for n-hieh the meter was calibrated :ttitl the pressure, tcmperature, and coniposition of the actual gas. The flox ratc \vas adjustrd until the pressure and rate were- i n the desired region, and the pressure at the flowmeter was 11c.al' the value for which it was calibrated. Then the flow was hctltl steady for 15 or 20 minutes until the temperatures became constant. .it this time the condensate chamber was drained until the level in the gage glass was at some predetermined point. Readings were then taken at 5-minute intervals for 30 minute% n-hilc, the lcwl in thc condensate chamher was kept nearly con-
August 1947
IN'DUSTRIAL
939
AND ENGINEERING CHEMISTRY TH E R MO M E TE R
OUTLET
Figure 1.
Experimental Heat Exchanger
.At the end of the 17111 the level in the condensate chambw brought carefully to the starting point, and the flow cut off. Thc. condensate was weighed as a basis for a heat balance. For the runs on air the apparatus was altered 'by the substit u t ion of diaphragm pressure regulators for the hand-operated v:tIves used n-ith the gas niixturc~.and a concentric orifice was 5turit. \vas
Il-.fYi.
DATA A N D CALCUL.4TIONS
Table I gives pertinent observed data and calculated results. T l i e readings of the thermocouples in the two wells are given, as * \v(l11 as corrected inlet anti outlet temperatures, as explained later.
'
The values of steam temperature are those corresponding to the oiiserved steam pressures. The observed values of flow rate arc. rt~portedas mass velocities. To obtain the correct average gas temperatures at the inlet :tiid exit of the test section from the thermocouple readings, corwctions ivere made for nonuniform temperature distribution :iud also, in the case of the air runs, for radiation t o the thermo1.13uplewells. Because of the high coefficients of heat transfer i l l thi, tcJsts with the process gas. the radiation was negligihle i n
those tests. A cdculation \vas also made of tliti cft'ect of l i t ' a t conduction along the thermocouple nells on the observed tempcsratures, and w e n in the air runs no correction wtts found necessary. The corrections for radiatioii from the hot tube wall to the thvrmocouple wells in the air runs nere made with a11 assumed value of 0.9 for emissivity and with a combined emissivity and arca factor of 0.87. Inasmuch as the net coefficients of heat transfer hy radiation are estimated to be 2.1 P.c.u./(hr.:l (sq. ft.) ( " C.) a t the air inlet and 2.9 at the exit, compared with coefficients of heat transfer of from 10 to 40 by convection, the corrections are small but appreciable. I n the process gas tests the coefficients of heat. transfer are from 100 t o 600, so that radiation can he ignored. The observed air temperatures, corrected for radiation are, for runs 24 to 27, respectively: inlet, 42.9", 40.6", 40.7",and 41.8" C.; exit, 138.0". 141.4', 148.2", and 1.55.9" C.
G Figure 2.
Determination of Combined Resistance of Condensate and Metal Wall
Figure 3.
Observed Gas-Side Coefficients of IIeat Transfer
. 960
INDUSTRIAL AND ENGINEERING CHEMISTRY 2 0001
I
I
i
I
'
l
Vol. 39, No. 8
rato of coudensation, computed ttieoretioally on the tlssuniptiori of a uniform over-all coefficient of hcat trsnsfcr. I t should l)e noted that the coefficients of heat transfer reported in Tablt. 1 ~ t ' not e b a d on the condensate collected. The values of over-all coefficient of hcat transfi,r. I:. \v('i'c wiiiputecl in thr usual manner:
r \r.here At,,,
= q 1-4Aim
(11
logarithmic mean temperature difference from steam to air A = inside surface area of test section of tube
I
2
I&
4
2
6 8
6 8
4
I o5
I o6
G Figure 4. Comparison of Gas and -4ir Data w i t h RlcAdams' Simplified Formula for Air (Equation 4)
=
Thc gas-side coefficient of heat translvr \vas found by utilizing [tie Lucke-Wilson method of plotting 1/ U against l/G0.3 (15'1. The method was modified to the cxtc.nt of including in the al)s k s a values of 1 ! C p p o . e ,lnasmuch as these values varied in ttic cxperiments. Figure 2 shows this plot, in which both U and D :%redivided by 1000 for convenience.. The intercept 011 the 1.asis is 0.0005 (hr.) (sq. f t . ) (' C . ) '(P.c.u.),and it should reprcsellt the combined thermal rcsistancc of tube wall and steam. For romparisori, the steam and wtlll rwintance, as calculated from Susselt's formula for film condensation arid a n assumed therninl cwnduct,ivitg of steel of 31 P,c.u.!(hr.) (sq. ft.) ( " C./ft.), is kipproximately 0.00082. h n average of the two values is O.O006(i, which is not so significantly different, from either of the predicted values t h a t i t cannot be accounted for by uncertainties in thr: vslue of thermal conductivity ascribed to the stecl and in tho location of the line in Figure 2. The values of gas roeffickiti II as listed in Table I were ohtaincd by the equation:
Corrections for nonuniform temperature distribution were applied t o both the p r o c e s gas and air data. The thermocouple 1 ' h = 1 ' C - 0.00066 (2) wells were located in the center of the tube and extended 0.219 0.625 or 0.35 of the diameter. Obviously the wells tend more Gab v k o r i t y p, (Table I ) ma.; evaluated a t an a v e ~ a g efilm to the center-line temperature than t o the "mixed-mean" or temperature dixfined as: average value. Boelter, Martinelli, and Jonassen (2) developed a relation between the mean and maximum temperature differt/ = t, - 1 / 2 ( L - t o ) ences as a function of Prandtl and Reynolds numbers. For .Vpr = 0.45 and S R=~100,000, Atmean ' Atm,,. is given by their = 1, - At,,, (1 - C"2h) 139 Figure 4 as 0.8. Sow, because of its width, the well i8 believed to have assumed a temperature bemeen t,he center-linc and averRESULTS age values, n'ith the likelihood of being nearer the center-line; therefore on the csit end a factor of 0.85 LTas employed to correct The gas coefficicAnti i ) i ' lieat transfer for the 3-1 hydr(igi.tithe observed temperature difference. On the inlet end the noriiitrogen misturc and for air are plotted in Figure 3 againat I I C / . mal temperature distribution .vias probably not established, SO mass velocity. It id evident th:it pressure lias no great effect 1111 only a slight correction was made-a factor of 0.95 \vas c~mploycd. t h r coeficierita of hcat transfer for the niiuture, even when t I t i s Table I gives the corrected inlet and outlet temperatures, 13-hich physical propertie.; are not inc1urdc.d. The data for air and for thc pro gas I ' : i l l be brought l l C X I ~ l > ~ were used in subsequent, calculations. Values of the heat capacity of the g a j (Table I ) n-eri~evnluatetl i t i r o agrtviiwrit by dividing thi>i~wfficientsof h u t traniiar by t t i ( , at the average of the inlet and outlet teniperaturrli and at thia otJilc.at capacitit,a and plotting :t. ii iunrlio11 of 1ii:iili velocity (Figui c served pressure. The rates of heat transfer ~ ~ c i ri l c uel : r t ~ d 1). T h derjree of w r r ~ l i ~ t i oot i i t liv gas d:tt:t among thc~nlrt~l\-c~i from the values of heat capacity, temperature rise OC gaq, ant1 i- no1 greatly diffeient irom that of Figurc. 3, since the v:~~.intii~ii weight rate of flow. The ratio of thp>e value+ t o t h lif,xt i i i \>(,;it rapwiry ovv1 rlir. p n - ~ ~ t ~ ti ~' n t g i)t' r ~ 30 t o (300at r n o \ p l I i , ~('5 given u p by the condensate is very close to u n i t r and, therebv lends support to .. the method of correcting the gas tcniperatures. In computing the quantity of lieat given u p hy the steam, due allowaucr~ as made for heat loss from steam inlet and exit lines as determined in blank runs and for the moisture in thc entering steam. The quality was approxiinately 0.95 in all runs. Furthermore the measured quantity of condensate was reduced in the ratio 1:0.935 to coinpensate for the fact that condensate I 0.301 was collected from a slightly greater 5 2 5 I o4 105 length of tube than that over n-hich the REYNO .PS NlJVB E P temperature rise was measured. This factor n'as deduced from a consideration Figure 5 . Compariqoii of Data with \ arious Fornlula3: Solid Line, Equatiotrs 5 and 6 ; Dashed Line. Eclnation 7 of the variation along the tube of the
4
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1947
is only around 10Fcfor this mixture. The line drawn on Figure 4 rqxesents McAdams' simplified formula for air ( 1 4 ) :
h = 0.0144CpGu*3/D"2
(4)
The air data are only slightly above the lint,, but the values for the process gas lie enough higher to suggest that sonic factor has been omitted in the correlation.
-9 , 6
0
200 4 0 0 600 800 1000 P R E S S U R E , Atm.
Figure 6. JIolal Heat Capacit? at Constant Pressure, MC,, of 3-1 Hydrogen-Nitrogen Mixture
Mure gc11cr~11correlations include the viscosity tu a power around 0.2, and the Prandtl number C,p]k, in various functions. -1s Table I sho\vst the viscosity of the mixture varies some 30% f i ~ o m30 to 900 atmospheres, but the values for air are essentially the same as for the mixture a t the highest pressure. The Prandtl iiunibcr is quite different for the trro gases, hon-ever, being 0.73 for air and around 0.45 for process gas. A general correlation is provided in Figure 5, where the "j-factor," h,!C,G+, is plotted against Reynolds number, DG lp,. I n this expression of j-factor, 4 is a function of Prandtl number and, to a slight degree, of Reynolds nunibrr. Although various pon-ers of Prandtl number such as ' 1 3 and 0.6 have been empl in the past, for values of A Y ~ r appreciably less than unity, t h iiple functions are inadequate. he correct function is that of One of the best development, Boelter, Martinelli, and Jonassen ( 2 ) , ~ h showed o that 6 depends not only on -\-I+,but also t o a slight extent upon .\-H~. Ftiliziiig the qua~ititativeexpressions of thcse authors for noii\-iscou,i fluids (as plotted for typical values in Figure l l ) , one finds, for a Reynolds nunibel, oi. ap ximatelj- 100,000, the following values of 4 at thc variouy p ures (for tlie 3 Iiydrogciii i i t rogc~nn i i r t u i ~:~ ) p,
96 1
The experimental data on both the hydrogt?ii-iiitrogeIiniisi UI'CI and air are in satisfactory agreement with the friction fact.or line and, therefore, support the conclusion that heat transfer at high pressure can be calculated correctly Titti equations derived from lo^ pressure data, provided the proper values of phy,4wI properties are utilized. It should be remembered that the pIiy>ical properties of the gases employed in the investigatioii do 1111vary to a great degree with pressure up to 900 atmosphews. .*o the degree of uncertainty in thc predictioiis is lo^. The prest'ii: results can hardly be extrapolated to the region of critical tc,inperature and pressure; experimental data on h a t tramsfw in t h i > region would be of special intercut. Consideration should be giveu to the effects of the r*orrc,c.tioii-. applied to the data. The adjustment for nonuniform velocity distribution has 1,aise.d the over-all coefficients of heat tritrisff.r about 1 5 5 for the process gas and 7 for the air over the ui~currected values. Figure 5 indicates that, if these corrections h ~ d riot been made so that the data w r e loiver by these amounts, the agreement with the curves would have been as satisfactory. If the corrections for radiation had not been made to the air data, they would lie around 10 to 1 5 7 higher than plotted; sur11 a change would mean poor agreement of the air and proces- HI data. Fortunately there is little question in the validity of the radiation correction. Since these high pressure experiments were carried out, heat transfer results on hydrogen-nitrogen mixtures a t atmospheriv pressure have been reported ( 6 ) . These results for a mixturc of 55% hydrogen (a composition having about the same value or' -I-P~ as the 75% mixture) are included in Figure 5. I n this ca>c, for -\-pr = 0.45 and NR?= 7000, + = 1.45. These results are slightly lorver than the solid curve baaed on Equation 6. It ahould be recalled that these data were obtained in an apparatu.5 with a long calming section whereas the apparatus for the high pressure data involved a slight expansion just a t the beginning oi the test length, inasmuch as the cross-sectional area of the thermucouple well was 1 2 5 of the cross-sectional : m a of the tube. This slight expansion T o d d be espccted to cause the heat t n i i i < fer rate to be raised a small amount. The daslied line on Figure 5 represents the equation:
h/C,G+ = 0.023 (DG,/p,) -".'
O'O'
* i
2
atiii.
CPM
1.
9
I;oi, ail,. w i t h ' k = 0.73 and at Ri~yrioldsnurillbeis around 20,000, = 1.12. These values \!-ere eniployed in calculating thc experimental data as j-factors. IT-ith this function + the j:factor is, furthcrniorc,. predicted t o be equal to one half the Ii,ictioii factor in the Fanning equation, or:
+
h;C&
= .7;2
(5)
Uoeltei, et al. showed support for this relation by reliable data 0x1 gases and water. The solid line on Figure 5 is obtained from the cori~elationof Drew, Koo, and 3Ic.\dams (9) for friction in smooth pipes, arid i* expressed as j / 2 = 0.00070
+ 0.0625 (DG/p)-C.3'
(6)
It is oi inteiest that this equation is substantially identical with that of Kikuradse ( I : ) over the range covered by the plot.
t
0.01 0
20
40
60
dC
100
P E R C E N T F2 B Y V O L ~ J M E Figure 7 . Viscosity of Hydrogen-Nitrogen Mixtures at 1 .4tmosphere ( I Y )
INDUSTRIAL AND ENGINEERING CHEMISTRY
962
TABLEI. ltun To.
&lass Pressure, Velocity, Atm. C
16 15 3 12 14 8 9 2 13 18 17 4 5
7 6 10 22 21 11 20 23 19
347 333 98 102 121 32.2 32 0 32 2 32 2 31 0 31 2
194,000 183,000 185,000 184,000 183,000 310,000 196,000 184,400 99,300 69,300 46,800
50,300 24 7 8 33,300 25 6.5 26 6.0 20,600 10,300 27 5.4 fl There is reason t o believe b This average exclude9 t h e
Temperature, C'bserved 11
37 7 40 1 42 2 46 4 45 0 35 5 38 8 44 2 48 0 41 9 43 0 28.0 (0.9 62.8 71.0 72.1 73.0 73 0 77.0 65.8 77 3 65 0
C. Steam.
corrected
fz
ti
l?
fa
SCJIMARY O F
Heat Capacity, C p
Vol. 39, NO. 8
DATA
t o Cas,
Heat Balance Ratio,
'io
qdqs
Heat
V15-
cosity, pi
Over-all Coeffi-. merit. 1
I'roress Gas (74% H?, 24 4 9 S2, 1.6% CHI, CO, etc., M o l . W t . = 8.69) 87 1 44 6 101 0 180 2 0 878 1 07 0 0549 101 4 47 1 181 1 0 878 113 3 0 0551 1.07 87 4 46 8 0 875 133 3 94 3 0 0559 0.92 115 5 53 1 125 I 181 7 0 875 0 0576 0.96 113 1 51 123 3 0 878 180 9 0 0573 ,... 117 0 49 8 132 7 187 0 0 877 0 0571 0 98 119 9 45 8 128 9 179 4 0 875 0 0569 1.01 111 2 51 182 0 0 875 121 8 0 0563 I 04 129 7 54 , 183 1 137 7 0 877 1 01 0 0575 118 2 181 6 127 7 48 9 0 877 0 0567 0 70a 131 8 180 3 49 9 0 675 139 1 0 0558 .... 101 2 71 3 106 0 133.1 0 858 22,500 0 96 0,0458 125.1 77.1 13i 0 183.9 0,855 35,800 0 0476 1.00 0.824 22,000 106.8 132 4 0 0415 0 99 6,9 1 99.3 127.8 (6 6 136 2 183 6 0 822 84,500 1.05 0,0438 131.5 77 5 138 8 180 0 0 826 :35.600 0 0441 1.09 116.2 78.4 125 9 180 6 0 811 45,800 0 0423 1 01 129.0 182 2 137 0 0 811 78.4 0 0429 35,600 0 89 135.4 142 7 18" 0 82.2 0 808 1 10 0 0431 34,600 140.0 146 4 183 1 71.8 0 0432 0 811 0 83 23.100 142,s 149.8 182 3 ' 0 . 8 1 1 82,s 0 0435 14,260 183 6 151.7 144.9 71.0 0 811 0 0435 11.600
Gab Coefficient, h
2
49.9 141.3 49.9 144.8 47.6 147.5 50.3 145.1 54.6 48.0 152.7 153.6 48.8 63 9 161.4 159 8 t h e apparatus was not fully heated w l u e 0.70 marked a.
183 1
182 2 183.8 182.9 u p in this
.iir 0.241 0.241 0.241 0.241 run
hr. = 0 995b 0 0556 0.0566 0 0568 0 0.568
~4,100
30,700 20.500 10.r1fio
379 354 380 839 381 434 363 364 24i 169 129
M
1000
437 511 606 479
-140 292 173 166 159 155 155 155 88 79 40 521 200 233" 219 216 382 138
516 295 190 141
0.00243 0.00258 0 00238 0 00282
223 119 8 s3 0 06 0
0 00316 0,00341 0 00376 0 00434
!7 1 .A1 2
0 0 0 0 0
608
43.0 30 6 21.0 12.1
4 1 ti 30.0 20.7 12 0
DG
CpG4
00169 00196 00199 00208 00199 0 00237 0 00252 0 00187 0 00237 0 00195 0 00240 0 00214 0 00208 0 00235 0 00204 0 00238 0 00170 0.00202
998 771 470 485 443 513 543 400 293 216 133 505 463
,
ir
6
7 1 0
5 9 0 7 8
18 9 8 90
ESTI>i.ATIOS O F T H ERMOPHY SICA L PROPERTI K S
HEATC.IPACITY. The molal heat capacities a t eonstaiit PN*Ssure, M C p , as derived by Deming and Shupe (8) for the pure constitncnts, werc select.ed at the prrssure and temperature of the misturc. These values n.ere combined linearly in accord with the mole fraction\: 0.75 hydrogen, 0.25 nitrogen. Tile results, shown i11 Figure 6, vary only slightly with small v:iriations of composition. The mrthod of combination used is not r:iiisistc,nt ivith the P-V-T data for hydrogen-nitrogen misturm, b u t the molal heat capacities of hydrogen and nitrogen are not' far different and, consequently, more clahorate methods of combination give only slightly different results. The specific heat, C p , is obtained by dividing the value of M C p read from Figure 6 b y the molccular weight of thci gas mixture used in t,he tests - - n : t ~ ~ l y , 8.69. (13) and T T ~ Kleint, ~ ~ ~ Trautz ~ ~ and ~Baumann ~ . (f9)titstermined the viscosities of hydrogen-nitrogen mixitures at' ortiinarg 0
200
400
600
800
I000
PRESSURE, A T M , Figure 8 . Effect of Pressure on Viscosity of 3-1 HydrogenNitrogen Mixtures Predicted from Graph of Comings and Egly (7) as Extended
This relation coincides with Equation 6 a t Reynolds numk)ijrs around 100,000, but is about 10% lower at 10,000. It is in (1srellent agreement with the low pressure hydrogen-nitrogen data. It is of interest to note that Equation 7 reduces to Equation 1of 1lcAdams for air by substituting + = 1.12 and p = 0.056 11). ' (hr.) (ft.). The Nusselt data (5, 18) on air a t pressures from 2 to 14 atmospheres and Reynolds numbers from 3000 to 200,000, however, are known to check with Equations 5 and 6, with the atmospheric pressure data dropping slightly lower at Rcynolds iiumbers less than 10,000; this suggcitv that the calming section niight affect low pressure data iii this manner. I n conclusion, l:quat,ions 5 and 6 and the solid line on Figure 5 would appear tci be suitable in general for heat trandtv for nonviscous fluids inside pipes without calming scctions, Ivirh I.:quation 7 being somewhat conservative in the loiv Reynolds riumher region.
0
20 PERCENT
40
H,
60
BY
80
100
VOLUME
Figure 9. Thermal Conductivity (12) and Heat Capacity at Constant Pressure of Hydrogen-Nitrogen RIixtures at 32" F. and 1 Atmosphere
August 1947
'
INDUSTRIAL AND ENGINEERING CHEMISTRY
pressures. Kleint's values for the mixture are somewhat higher than those of Trautz and Baumann, although his values for the constitutents agree quite well with theirs. The results of the latter workers have been accepted as the more reliable and are shown in Figure 7. The only dat,a found on the viscosity of the mixtures at, elevated pressures are those of Boyd ( 3 )which extend to 200 atmospheres, but they scatter too much to permit reliable conclusions; furthermore, his data on pure nitrogen are not in agreement with the very consistent data of Michels and Gibson (16) on nitrogen to 1000 atmospheres at 25", 50", and 75" C. These data form part of the basis of a generalized plot by Comings and Egl; (?), where p , ! p , is plotted against reduced pressure with reduced ternperature as parameter. The highest value of reduced temperature on this plot is 2.80. A curve for reduced temperature of 7.25 was added by employing the pure hydrogen data of Gibson ( I I ) , and then values were found for the 3 hydrogen-1 nitrogen mixtures by int,erpolating a t reduced conditions based on the pseudocritical temperature and pressure of the mixture; these values were calculated &s 62.3" IC. and 24 atmospheres, respectively. From a convenient cross plot, interpolated values were obtained arid plotted on Figure 8 in order to show the relative effects of temperature and pressure. The plot of generalized reduced viscosities of Uyehara and Watson ( 2 0 ) could have been utilized in a similar manner. While actual experimental values of the viscosity of the mixture a t high pressures would be desirable, this method of prediction is felt t o be reasonably good. Fortunately a considerable error in estimating the viscosity a t high pressures would have little effect on Figure 5 and no effect on the conclusions drawn from it. Figure Y shows Ibbs and Hirst's THERMAI. CONDUCTIVITY. data ( I d ) on the thermal ronductivity of hydrogen-nitrogen mixtures at 0" C. and 1 atmosphere. Weber's single point for 57.4'7 nitrogen a t 0 " C., as given in the International Critical Tables ( I Z A ) , is in agreement. S o data have been found on the effect of pressure, although estimation can he made from viscohity drttti as desc~ihedlater.
??kk&i 20
40
P E R C E N T H,
60
BY
80
100
VOLOME
Figure 10. Prandtl Number of HydrogenNitrogen Afiatures at 0 " C. and 1 Atmosphere
I'KANIXL NUMBER. Figure 10 shows the value of Cgp(:lk for 0'
