NAO
International Journal of Thermophysics,Vol.25,No.1,January2004(?2004) Viscosity and Thermal Conductivity Equations for
Nitrogen,Oxygen,Argon,and Air
E.W.Lemmon1,2and R.T Jacobsen3
Received October16,2003
New formulations for the viscosity and thermal conductivity for nitrogen,
oxygen,argon,and air are given.Air is treated as a pseudo-pure fluid using an
approach adopted from previous research on the equation of state for air.The
equations are valid over all liquid and vapor states,and a simplified cross-over
equation was used to model the behavior of the critical enhancement for
thermal conductivity.The extrapolation behavior of the equations for nitrogen
and argon well below their triple points was monitored so that both could be
used as reference equations for extended corresponding states applications.The
uncertainties of calculated values from the equations are generally within2%for
nitrogen and argon and within5%for oxygen and air,except in the critical
region where the uncertainties are https://www.360docs.net/doc/8e12903894.html,parisons with the available
experimental data are given.
KEY WORDS:air;argon;nitrogen;oxygen;thermal conductivity;viscosity.
1.INTRODUCTION
The work presented here on the transport properties of air and its constit-uent fluids is the result of more than a decade of research on the properties of air at the University of Idaho and the National Institute of Standards and Technology(NIST).Publications resulting from this work include measurements on the PVT,isochoric heat capacity,and speed of sound of dry air(Howley et al.[1];Magee[2];Younglove and Frederick[3]),the viscosity of air(Diller et al.[4]),and the thermal conductivity of nitrogen 1Physical and Chemical Properties Division,National Institute of Standards and Technology, 325Broadway,Boulder,Colorado80305,U.S.A.
2To whom correspondence should be addressed.E-mail:ericl@https://www.360docs.net/doc/8e12903894.html,
3Idaho National Engineering and Environmental Laboratory,P.O.Box1625,Idaho Falls,
22Lemmon and Jacobsen (Perkins et al.[5,6];Roder et al.[7]),argon(Perkins et al.[5,8];Roder et al.[7,9]),and air(Perkins and Cieszkiewicz[10]).From these mea-surements,equations of state representing the thermodynamic properties of air have been published(Jacobsen et al.[11,12];Panasiti et al.[13]; Lemmon et al.[14]),with the final paper reporting a mixture model for the nitrogen/argon/oxygen system in addition to an equation of state for air as a pseudo-pure fluid.Surface tension equations were given in Lemmon and Penoncello[15].Preliminary equations for the transport properties were available in the REFPROP7.0database(Lemmon et al.[16]).The improved equations for the viscosity and thermal conductivity for nitrogen, argon,and oxygen along with air treated as a pseudo-pure fluid are reported here and will be available in Version7.1of the REFPROP data-base.
The transport property equations developed in this work are a com-bination of theoretical models for the dilute gas and the thermal conduc-tivity critical enhancement,and empirical equations for the residual con-tribution resulting from the interaction between molecules.The equation for the dilute gas uses Chapman–Enskog theory with a collision integral fitted in this work to experimental data.The critical enhancement uses the simplified crossover model of Olchowy and Sengers[17].The empirical equations for the residual contributions are similar to the terms used in typical Helmholtz energy equations of state(Lemmon et al.[14]).The number of terms was kept to a minimum to aid in the extrapolation of the equations to low and high temperatures and to high pressures and densi-ties.Nonlinear fitting techniques similar to those employed in the devel-opment of the air and R-143a equations of state(Lemmon and Jacobsen [18])were used here to derive the final equations.
The extrapolation of the equations for argon and nitrogen at very low temperatures was monitored carefully so that the resulting equations could be used in corresponding states applications for fluids with reduced triple point temperatures below those of nitrogen or argon.Graphs are included in Section4to illustrate the extrapolation behavior of the equations.
The transport properties of fluids at extremely low pressures may be quite different from those measured at‘‘dilute’’states.The dilute states of the gas are generally taken to be at a pressure of about one atmosphere, and most measurements of dilute gas transport properties are taken at this pressure.In this work,properties of the ideal gas at zero pressure are taken to be nearly identical to those of the dilute gas(minus any pressure depen-dence),and other literature should be consulted if actual gas properties are required at very low pressures.The thermal conductivity and viscosity equations presented here are not valid when the mean free path of the gas
2.VISCOSITY AND THERMAL CONDUCTIVITY EQUATIONS Several correlations are currently available that calculate the transport properties of nitrogen,argon,and oxygen.Viscosity and thermal conduc-tivity equations are available in the work of Stephan and Krauss [19]for nitrogen,Laesecke et al.[20]for oxygen,Younglove and Hanley [21]for argon,and Younglove [22]for all three fluids.An equation for the thermal conductivity of air was reported by Stephan and Laesecke [23].
The transport property equations presented here use the independent properties temperature and density as input conditions.In most practical applications,including measured properties reported in the literature,the input conditions are temperature and pressure.Accurate equations of state for the pure fluids must be used to obtain the required density.The equa-tions of state of Span et al.[24]for nitrogen,Tegeler et al.[25]for argon,Schmidt and Wagner [26]for oxygen,and Lemmon et al.[14]for air were used here for this purpose.
The viscosities of nitrogen,argon,oxygen,and air are expressed in this work using the equation,
g =g 0(T)+g r (y ,d ),
(1)
where g is the viscosity in m Pa ·s,g 0is the dilute gas viscosity,g r is the residual fluid viscosity,y =T c /T ,and d =r /r c .The critical parameters T c and r c (taken from the thermodynamic equations of state referenced above)are given in Table I.Since the effects of the critical region behavior on viscosity are negligible for most practical states,no enhancement for the critical region viscosity was used in this work.The dilute gas contribution is given by
g 0(T)=0.0266958`MT
s 2W (T g )
,
(2)
where s is the Lennard-Jones size parameter and W is the collision integral,given by
W (T g
)=exp
1C 4
i=0
b i
[ln (T g
)]i
2,
where T*=T/(e /k)and e /k is the Lennard-Jones energy parameter.The Lennard-Jones parameters are given in Table I,and the coefficients b i (fitted in this work to the experimental data)are given in Table II.The residual fluid contribution to the viscosity is given (in m Pa ·s)by
g r
(y ,d )=C n
N i y t i d d i exp (?c i d l i ),
(3)
Viscosity and Thermal Conductivity Equations 23
Table I.Parameters of the Viscosity and Thermal Conductivity Equations Parameter Nitrogen Argon Oxygen Air
T c(K)126.192150.687154.581132.6312a
r c(mol·dm?3)11.183913.4074313.6310.4477a
p c(MPa) 3.3958 4.863 5.043 3.78502a
M(g·mol?1)28.0134839.94831.998828.9586
e/k(K)98.94143.2b118.5103.3
s(nm)0.36560.335b0.34280.360
t0(nm)0.170.130.240.11
C0.0550.0550.0550.055
q D(nm)0.400.320.510.31
T ref(K)252.384301.374309.162265.262
a The values given for air are the values at the maxcondentherm.
b Lennard-Jones parameters taken from Aziz[33].
where c i is zero when l i is zero and one when l i is not zero.The coefficients and exponents of this equation are given in Table III.
Similar to the model for viscosity,the thermal conductivities of nitrogen,argon,oxygen,and air are expressed as functions of temperature and density:
l=l0(T)+l r(y,d)+l c(y,d),(4) where l is the thermal conductivity in mW·m?1·K?1,l0is the dilute gas thermal conductivity,l r is the residual fluid thermal conductivity,l c is the thermal conductivity critical enhancement,y=T c/T,and d=r/r c.The critical parameters T c and r c are given in Table I.The dilute gas contribu-tion is given by
l0=N15g0(T)
1m Pa·s
6
+N2y t2+N3y t3,(5)
Table II.Coefficients of the
Collision Integral Equation
i b i
00.431
1?0.4623
20.08406
30.005341
4?0.00331
24Lemmon and Jacobsen
Viscosity and Thermal Conductivity Equations25 Table III.Coefficients and Exponents of the Residual
Fluid Viscosity Equations
i N i t i d i l i
Nitrogen
110.720.120
20.039890.25101
30.001208 3.2121
4?7.4020.922
5 4.6200.313
Argon
112.190.4210
213.990.020
30.0050270.95100
4?18.930.552
5?6.6980.914
6?3.8270.824
Oxygen
117.670.0510
20.40420.050
30.0001077 2.10120
40.35100.081
5?13.670.512
Air
110.720.210
2 1.1220.0540
30.002019 2.490
4?8.8760.611
5?0.02916 3.681
where g0is the dilute gas viscosity described previously.The coefficients and exponents are given in Table IV.The residual contribution to the thermal conductivity is given(in mW·m?1·K?1)by
n
l r=C
N i y t i d d i exp(?c i d l i),(6)
i=4
where c i is zero when l i is zero and one when l i is not zero.The coefficients
26Lemmon and Jacobsen Table IV.Coefficients and Exponents of the Residual
Fluid Thermal Conductivity Equations
i N i t i d i l i
Nitrogen
1 1.511
2 2.117?1.0
3?3.332?0.7
48.8620.010
531.110.0320
6?73.130.231
720.030.842
8?0.70960.682
90.2672 1.9102
Argon
10.8158
2?0.4320?0.77
30.0?1.0
413.730.010
510.070.020
60.73750.040
7?33.960.852
820.47 1.262
9?2.2740.892
10?3.9730.514
Oxygen
1 1.036
2 6.283?0.9
3?4.262?0.6
415.310.010
58.8980.030
6?0.73360.340
7 6.728 4.352
8?4.3740.572
9?0.4747 1.8102
Air
1 1.308
2 1.405?1.1
3?1.036?0.3
48.7430.110
514.760.020
6?16.620.532
7 3.793 2.772
8?6.1420.372
9?0.3778 1.3112
The thermal conductivity critical enhancement model of Olchowy and Sengers [17]was used to calculate the fluid properties in the critical region.The equations of Olchowy and Sengers are repeated here for completeness:
l c =r c p
kR 0T 6ptg (T,r )
(W ??W ?0),(7)
where
W ?=2p
51c p
?c v
c p
2tan ?1
(t /q D
)+c v
c p
(t /q D
)6and
(8)
W ?0
=2p 31?exp 5?1(t /q D
)?1
+13
(t /q D
)2
(r c
/r )
2
64.
(9)
The correlation length t is given by
t =t 0
5
q ?(T,r )?q ?(T ref ,r )T ref
T
C
6
n /c
,(10)
where
q ?(T,r )=p c r r 2
c 1“r
“p
2T
.
(11)
In these equations,k is Boltzmann’s constant (1.380658×10?23J ·K ?1),and R 0,n ,and c are theoretically based constants with values of R 0=1.01,n =0.63,and c =1.2415.The terms q D ,t 0,and C are fluid-specific (fitted)terms,and T ref is a reference temperature that is significantly above the cri-tical temperature (in this work,T ref was taken as twice the critical tempera-ture).The values of these terms are given in Table I.The value of l c should be set to zero when the bracketed term in Eq.(10)is negative (usually at high temperatures)or zero.The isochoric heat capacity (c v ),isobaric heat capacity (c p ),and the first derivative of density with respect to pressure are calculated from the equation of state at the specified temperature and density.
Calculated values of the viscosity and thermal conductivity are given in Table V for use in verifying computer programs developed using the equations given above.The additional digits do not reflect the accuracy of Viscosity and Thermal Conductivity Equations 27
28Lemmon and Jacobsen Table V.Viscosity and Thermal Conductivity Values Calculated from the Equations Temperature Density Viscosity Thermal conductivity (K)(mol·dm?3)(m Pa·s)(mW·m?1·K?1)
Nitrogen
100.00.0a 6.903499.27749
300.00.0a17.877125.9361
100.025.079.7418103.834
200.010.021.081036.0099
300.0 5.020.743032.7694
126.19511.1818.2978675.800
Argon
100.00.0a8.18940 6.36587
300.00.0a22.724117.8042
100.033.0184.232111.266
200.010.025.566226.1377
300.0 5.026.370623.2302
150.6913.427.6101856.793
Oxygen
100.00.0a7.702438.94334
300.00.0a20.630726.4403
100.035.0172.136146.044
200.010.022.444534.6124
300.0 5.023.757732.5491
154.613.624.7898377.476
Air
100.00.0a7.095599.35902
300.00.0a18.523026.3529
100.028.0107.923119.221
200.010.021.139235.3185
300.0 5.021.324132.6062
132.6410.417.762375.6231
a Dilute gas values at zero density.
3.EXPERIMENTAL DATA AND COMPARISONS TO THE
EQUATIONS
A comprehensive search was made to obtain the experimental data available in the open literature.Table VI gives the sources of experimental data,the temperature,pressure,and density ranges,the number of points, and the average absolute deviations(AAD)between the experimental data
Viscosity and Thermal Conductivity Equations29 Table VI.Summary of Experimental Data and Comparisons with the Equations
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%)
Nitrogen-viscosity
Baron et al.(1959)[36]40325–4080.68–55.20.20–14.5 1.38 Bonilla et al.(1951)[38]25200–25000.1Dilute Gas 4.60 Boon et al.(1967)[40]468.1–70.20.8330–30.310.3 Boyd(1930)[43]68303–3437.13–19.4 2.46–6.87 5.72 Chierici and Paratella(1969)[51]63230.6–30.50.22–9.830.54 Clarke and Smith(1968)[52]12114–3750.1Dilute Gas0.58 Clarke and Smith(1969)[53]13120–3600.001Dilute Gas0.22 Dawe and Smith(1970)[58]25293–15300.1Dilute Gas0.77 Diller(1983)[65]6590–3000.36–33.60.68–29.6 1.25 DiPippo and Kestin(1968)[66]30295–4560.03–0.17Dilute Gas0.15 DiPippo et al.(1966)[67]24296–7730.01–0.17Dilute Gas0.27 DiPippo et al.(1968)[68]53030.1–2.340.04–0.930.03 Ellis and Raw(1959)[70]7973–12700.1Dilute Gas 5.41 Evers et al.(2002)[71]76233–5230.09–29.70.03–10.70.08 Filippova and Ishkin(1962)[74]2790.2–273 3.5–15.1 3.58–28.28.71 Flynn et al.(1963)[76]34195–3730.68–17.90.27–12.80.28 Forster(1963)[77]1065.6–1210.01–2.6518.1–30.610.3 Gerf and Galkov(1940)[81]766.2–77.30.02–0.128.8–30.5 3.48 Goldman(1963)[83]16195–298 5.17–12.7 3.17–9.58 1.11 Golubev and Kurin(1974)[84]76273–4239.81–401 2.68–30.5 1.82 Golubev(1970)[89]94273–5230.1–81.10.02–18.8 1.38 Gough et al.(1976)[91]11120–3200.1Dilute Gas0.41 Gracki et al.(1969)[92]46183–2980.53–25.70.27–12.80.65 Grevendonk et al.(1970)[95]13466.5–1230.59–19.517.9–31.3 3.20 Guevara et al.(1969)[97]23283–21500.1Dilute Gas0.32 Hellemans et al.(1970)[106]4496.7–1250.61–9.8515.8–26.78.48 Hoogland et al.(1985)[110]15298–3330.2–11.70.07–4.670.12 Iwasaki and Kestin(1963)[116]32293–2980.1–9.980.04–4.010.13 Iwasaki(1954)[117]25298–423 2.09–190.59–7.210.55 Johnston and McCloskey(1940)[127]3790.2–3000.1Dilute Gas0.21 Johnston et al.(1951)[128]1678.6–3060.001–0.07Dilute Gas0.32 Kao and Kobayashi(1967)[132]35183–323 1.01–50.70.37–17.30.75 Kestin and Wang(1958)[135]132980.1–10.10.04–4.070.21 Kestin and Yata(1968)[136]63030.1–2.380.04–0.940.03 Kestin and Whitelaw(1963)[138]37344–5390.12–14.80.02–4.630.90 Kestin and Ro(1976)[139]9298–12700.1Dilute Gas0.19 Kestin and Leidenfrost(1959)[141]20293–2980.01–70.006–2.830.16 Kestin and Leidenfrost(1959)[142]14293–2960.1–15.50.04–6.20.17 Kestin et al.(1971)[144]332980.1–10.70.04–4.280.10 Kestin et al.(1977)[146]9298–6730.1Dilute Gas0.29 Kestin et al.(1982)[148]5298–4730.1Dilute Gas0.05 Kestin et al.(1972)[149]8298–9730.1Dilute Gas0.17 Kestin et al.(1972)[152]6298–9730.1Dilute Gas0.14
30Lemmon and Jacobsen
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Kobayashi and Kurase(1977)[161]62980.11–4.020.04–1.630.34 Lavushchev and Lyusternik(1978)[165]54375–19900.1Dilute Gas0.28 Lazarre and Vodar(1957)[167]21298–3480.09–3190.03–29.5 1.47 Lukin et al.(1983)[176]2376.5–2930.09–0.1Dilute Gas0.20 Maitland and Smith(1972)[177]28100–20000.1Dilute Gas0.17 Maitland and Smith(1974)[178]24394–15500.1Dilute Gas0.83 Maitland et al.(1983)[179]4301–3780.1Dilute Gas0.31 Makavetskas et al.(1963)[180]70285–933 1.53–60.70.23–16.7 2.49 Makita(1957)[181]54299–4730.1–78.50.02–18.5 1.62 Matthews et al.(1976)[185]15120–17000.1Dilute Gas0.72 Michels and Gibson(1932)[187]56298–348 1.11–97.90.44–20.30.25 Reynes and Thodos(1966)[211]30373–4737.14–69.4 1.76–14.8 1.99 Rigby and Smith(1966)[214]15293–9730.1Dilute Gas 1.97 Ross and Brown(1957)[219]41223–298 3.45–68.9 1.4–21.3 2.51 Rudenko and Schubnikow(1934)[221]863.9–77.30.01–0.128.8–30.8 1.19 Rudenko(1939)[222]677.4–1120.1–1.6221.7–28.819.1 Rutherford(1984)[223]152980.44–6.990.17–2.830.17 Schlumpf et al.(1975)[231]1132310–300 3.66–28.30.51 Shepeleva and Golubev(1968)[238]6480.5–2780.92–50.60.42–31.5 4.51 Timrot et al.(1969)[252]8300–6500.1Dilute Gas0.33 Timrot et al.(1974)[253]31295–5730.09–11.80.02–4.560.25 Trautz and Melster(1930)[256]4301–5500.1Dilute Gas 1.50 Trautz and Heberling(1931)[257]9293–5240.1Dilute Gas 1.54 Trautz and Zink(1930)[258]33482–11000.1Dilute Gas 4.13 van Itterbeek et al.(1966)[267]3370.1–90.20.09–2.426.6–30.1 1.35 van Itterbeek et al.(1966)[268]3870–90.10.05–9.9326.6–30.6 2.04 Vermesse(1969)[274]89273–37010.7–651 3.36–35.3 1.24 Vermesse et al.(1963)[275]24299–32254.9–48815.5–32.3 2.08 Vogel(1984)[277]10297–6400.1Dilute Gas0.26 Vogel et al.(1989)[278]44299–6890.03–0.16Dilute Gas0.27 Wobser and Muller(1941)[283]5293–3710.1Dilute Gas0.57 Yen(1919)[284]212960.1Dilute Gas0.35 Zozulya and Blagoi(1974)[291]122126–135 3.32–6.39 6.89–16.1 5.50
Nitrogen-thermal conductivity
Assael and Wakeham(1981)[31]18307–309 1.07–9.310.41–3.620.31 Borovik(1947)[41]2190.4–171 1.13–10 2.62–27 6.04 Borovik et al.(1940)[42]477.9–1120.1–1.6221.7–28.7 4.84 Brain(1967)[44]14420–5530.1Dilute Gas 1.71 Chen and Saxena(1973)[49]231373–24700.01–0.04Dilute Gas 1.24 Clifford et al.(1979)[54]34300–3030.58–35.60.23–11.90.40 Clifford et al.(1981)[55]41341–3880.52–26.50.17–7.870.38 Duan et al.(1997)[69]102970.43–2.060.17–0.830.76 Faubert and Springer(1972)[72]13800–20000.1Dilute Gas 3.61 Franck(1951)[78]1893–6760.009–0.04Dilute Gas 3.04
Viscosity and Thermal Conductivity Equations31
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Geier and Schafer(1961)[80]12273–13700.1Dilute Gas 4.59 Golubev and Kalzsina(1964)[85]32277.4–2730.1–50.70.04–31.8 3.64 Gray and Wright(1961)[93]4298–4220.1Dilute Gas0.31 Gregory and Marshall(1928)[94]152282–2990.005–0.11Dilute Gas 1.55 Haarman(1973)[98]8328–4680.1Dilute Gas0.49 Hammann(1938)[99]664.7–73.50.129.4–30.722.7 Haran et al.(1983)[102]45308–4290.45–10.10.17–3.910.82 Imaishi et al.(1984)[113]193000.76–12.10.30–4.790.29 Johannin and Vodar(1957)[121]50348–5730.1–1320.02–18.7 1.65 Johannin(1958)[122]71348–9740.1–1640.01–18.4 2.16 Johns et al.(1988)[123]12472–475 1.01–27.70.25–6.150.70 Johns et al.(1986)[124]14426–478 1.01–29.60.25–7.190.84 Keyes and Sandell(1950)[154]41274–6740.1–15.40.01–6.27 5.69 Keyes and Vines(1965)[155]21125–202 1.7–13.6 1.05–22.3 1.87 Keyes(1955)[157]492.1–2730.1–1.070.13–0.57 1.03 Keyes(1951)[158]13273–4230.1–14.50.02–5.68 1.65 Le Neindre(1972)[168]118298–8010.1–1000.01–20.5 1.14 Le Neindre et al.(1968)[169]50297–3050.1–1190.04–21.70.77 Lenoir and Comings(1951)[172]133140.1–20.80.03–7.440.65 Lenoir et al.(1953)[173]133260.1–220.03–7.460.87 Maitland et al.(1983)[179]4301–3780.1Dilute Gas0.31 Michels and Botzen(1953)[186]82298–3480.1–2520.03–26.2 5.90 Misic and Thodos(1965)[193]21295–324 6.2–31.9 2.54–11.2 1.17 Mostert et al.(1990)[194]20308 1.11–20.10.43–7.37 1.16 Moszynski and Singh(1973)[196]46323–3480.1–1500.03–22 1.25 Nuttall and Ginnings(1957)[203]60323–7800.07–10.10.01–3.7 3.75 Pereira and Raw(1963)[205]5305–4530.1Dilute Gas 1.25 Perkins et al.(1991)[5]72425–428 3.26–67.50.90–13.10.72 Perkins et al.(1991)[6]37781–3030.33–71.10.37–32.10.67 Powers et al.(1954)[207]1268.7–88.10.03–0.326.9–30.1 3.76 Richard and Shankland(1989)[213]6310–3520.0Dilute Gas0.37 Roder(1981)[215]93297–309 1.43–69.10.57–17.5 1.01 Rothman and Bromley(1955)[220]4639–9520.1Dilute Gas 1.29 Saxena and Chen(1975)[228]66338–25200.1Dilute Gas 2.27 Schafer and Reiter(1957)[229]12273–13700.0Dilute Gas 5.98 Schottky(1952)[232]9373–7730.1Dilute Gas 5.22 Schramm(1964)[233]10276–14000.1Dilute Gas 2.39 Slyusar et al.(1975)[240]3164.2–3000.01–2940.16–30.812.8 Stolyarov et al.(1950)[243]23286–5710.09–490.02–15.2 5.09 Tufeu and Le Neindre(1980)[261]132980.1–10000.04–390.88 Tufeu and Le Neindre(1979)[262]22481–7480.06–18.70.01–3.639.77 Uhlir(1952)[263]2276.4–1840.58–6.88 3.26–29.4 3.91 Vargaftik and Zimina(1964)[270]11304–11400.1Dilute Gas 1.21 Vines(1960)[276]4533–11700.1Dilute Gas0.97 Westenberg and deHaas(1962)[280]4300–10000.1Dilute Gas 1.51
32Lemmon and Jacobsen
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Yorizane et al.(1983)[285]28299–3230.1–150.03–5.90.74 Zheng et al.(1984)[287]182980.1–15.60.04–6.110.87 Ziebland and Burton(1958)[289]8680.7–2030.1–13.60.06–28.5 3.54 Ziebland and Marsh(1977)[290]4180–14000.1Dilute Gas0.85
Argon-viscosity
Abachi et al.(1980)[27]1883.8–900.06–0.1334.5–35.5 2.09 Baharudin et al.(1975)[34]685.7–1100.08–0.6431.2–35.2 5.43 Bonilla et al.(1951)[38]25200–25000.1Dilute Gas 4.84 Boon and Thomaes(1963)[39]684–890.07–0.1234.7–35.4 1.06 Boon et al.(1967)[40]684–890.07–0.1234.7–35.40.50 Clarke and Smith(1968)[52]12114–3750.1Dilute Gas0.52 Clifford et al.(1975)[56]9321–13000.1Dilute Gas0.51 Dawe and Smith(1970)[58]44292–15300.1Dilute Gas0.66 de Bock et al.(1967)[59]19900.13–13.534.5–35.5 2.39 de Bock et al.(1967)[60]7288.5–1400.39–19.624–36 4.71 De Rocco and Halford(1958)[63]20211–4710.1Dilute Gas0.65 DiPippo and Kestin(1968)[66]23297–5750.03–0.17Dilute Gas0.43 DiPippo et al.(1968)[68]10293–3030.1–2.340.04–0.960.13 Evers et al.(2002)[71]81233–5230.09–28.10.02–6.070.23 Filippova and Ishkin(1959)[73]3190.2–2730.09–14.70.04–35.5 6.30 Filippova and Ishkin(1962)[74]5290.2–273 3.6–15.3 1.78–35.510.2 Flynn et al.(1963)[76]27195–373 2.92–18.8 1.2–17.40.23 Forster(1963)[77]885.4–1140.08–0.8430.4–35.2 3.48 Golubev(1970)[89]49273–4730.1–48.10.02–17 3.15 Gough et al.(1976)[91]11120–3200.1Dilute Gas0.37 Gracki et al.(1969)[92]47173–2980.46–17.10.25–21 1.09 Guevara et al.(1969)[97]22283–21000.1Dilute Gas0.65 Haynes(1973)[103]16785–2980.07–34.50.06–35.30.92 Hellemans et al.(1970)[105]44105–1470.46–9.8120.1–33.18.38 Hellemans et al.(1974)[108]8298–9730.1Dilute Gas0.43 Hobley et al.(1989)[109]5301–5210.1Dilute Gas0.19 Iwasaki and Kestin(1963)[116]14293–3030.1–5.260.04–2.210.15 Iwasaki et al.(1964)[119]14293–3030.1–5.260.04–2.210.15 Johnston and Grilly(1942)[126]4290.3–2960.1Dilute Gas0.56 Kalelkar and Kestin(1970)[129]9298–11200.1Dilute Gas0.43 Kestin and Nagashima(1964)[134]20293–3030.1–5.180.04–2.180.23 Kestin and Wang(1958)[135]132980.1–10.10.04–4.290.21 Kestin and Whitelaw(1963)[138]47295–5380.12–14.20.02–5.13 1.64 Kestin and Ro(1976)[139]9298–12700.01Dilute Gas0.27 Kestin and Ro(1982)[140]5298–4730.1Dilute Gas0.59 Kestin and Leidenfrost(1959)[141]15293–2980.03–3.120.01–1.310.07 Kestin and Wakeham(1979)[143]5301–4730.1Dilute Gas0.58 Kestin et al.(1971)[144]402980.1–10.10.04–4.290.27 Kestin et al.(1978)[145]9298–7730.1Dilute Gas0.31
Viscosity and Thermal Conductivity Equations33
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Kestin et al.(1972)[150]7298–9730.1Dilute Gas0.29 Kestin et al.(1972)[151]8298–9730.1Dilute Gas0.50 Kestin et al.(1970)[153]8298–9730.1Dilute Gas0.26 Kiyama and Makita(1952)[159]40323–5730.1–9.970.02–3.76 1.81 Kurin and Golubev(1974)[163]104273–4239.81–380 2.76–34.9 1.44 Lowry et al.(1964)[175]20102–128 5.07–50.728.1–36.19.18 Lukin et al.(1983)[176]2193.2–2930.1Dilute Gas0.47 Maitland and Smith(1972)[177]28100–20000.1Dilute Gas0.18 Maitland and Smith(1974)[178]11295–15300.1Dilute Gas0.45 Makita(1957)[181]45298–4230.1–78.50.02–220.84 Makita(1955)[182]30323–5730.1–10.10.02–3.87 2.04 Malbrunot et al.(1983)[183]983.9–970.06–0.2533.4–35.5 2.66 Michels et al.(1954)[189]96273–3480.92–2020.41–28.90.25 Mostert et al.(1989)[195]2517416.1–47120.7–42 5.05 Naugle(1966)[200]484–1120.8130.7–35.5 1.07 Naugle et al.(1966)[201]5985–146 1.27–15.626.6–35.511.1 Rabinovich et al.(1976)[209]63298–523 2.56–58.90.58–19.10.64 Reynes and Thodos(1964)[212]35373–4737.14–83 1.79–18 4.28 Rigby and Smith(1966)[214]15293–9730.1Dilute Gas 2.15 Rudenko and Schubnikow(1934)[221]484.2–87.30.07–0.134.9–35.4 2.75 Saji and Okuda(1965)[224]584.1–86.90.07–0.0935–35.40.47 Timrot et al.(1969)[252]7300–6000.1Dilute Gas0.59 Timrot et al.(1975)[254]39292–5750.09–14.40.02–6.060.39 Trappeniers et al.(1980)[255]44223–32399.9–89723–44.5 5.08 Trautz and Zink(1930)[258]22567–11000.1Dilute Gas 3.87 van der Gulik and Trappeniers(1986)[264]2517416.1–47120.7–42 4.79 van Itterbeek et al.(1966)[268]1684.3–89.90.1–9.7934.5–35.50.90 Vermesse and Vidal(1973)[273]2530812–606 4.88–39.9 2.33 Vogel(1984)[277]10294–6680.1Dilute Gas0.21 Wilhelm and Vogel(2000)[282]160298–4230.09–20.10.02–8.490.12 Wobser and Muller(1941)[283]5293–3710.1Dilute Gas0.49 Zhdanova(1957)[286]1484.3–1490.07–4.5618.4–35.4 6.39
Argon-thermal conductivity
Amirkhanov et al.(1972)[29]140113–2539.81–98.1 5.21–37.1 2.62 Amirkhanov et al.(1970)[30]220282–6249.81–98.1 1.84–25 2.24 Assael et al.(1981)[32]273080.95–10.90.37–4.410.32 Bailey and Kellner(1968)[35]40588.6–2990.09–490.04–36.5 3.19 Brain(1967)[44]18419–5530.1Dilute Gas 1.68 Calado et al.(1987)[46]70107–1310.54–10.426.7–32.40.64 Chen and Saxena(1975)[50]88338–25200.02–0.09Dilute Gas0.70 Clifford et al.(1981)[55]73311–3770.65–17.40.24–5.90.37 Correia et al.(1968)[57]24276–12500.1Dilute Gas 1.36 de Castro and Roder(1981)[61]112297–309 1.46–68.70.58–20.70.97 de Groot et al.(1978)[62]120298–3020.59–32.10.23–12.8 1.40
34Lemmon and Jacobsen
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Faubert and Springer(1972)[72]13800–20000.1Dilute Gas0.94 Gambhir et al.(1967)[79]4309–3640.01Dilute Gas 2.76 Haarman(1973)[98]8328–4680.1Dilute Gas0.79 Hammerschmidt(1995)[100]5303–4630.1Dilute Gas0.83 Hansen et al.(1995)[101]14332–6460.1Dilute Gas 1.65 Haran et al.(1983)[102]49308–4290.8–10.20.22–3.930.53 Ikenberry and Rice(1963)[112]6291–2350.1–53.90.06–35.9 2.86 Irving et al.(1973)[114]4273–4480.1Dilute Gas0.20 Johns et al.(1986)[124]22427–473 1.04–24.80.29–6.620.87 Kestin et al.(1980)[147]323010.6–35.30.24–13.70.45 Kestin et al.(1972)[150]8298–9730.1Dilute Gas0.05 Keyes and Vines(1965)[155]8162–196 4.79–12.2 3.88–17.9 2.94 Keyes(1954)[156]10363–6230.1–1.980.02–0.65 1.08 Keyes(1955)[157]1686.9–2730.03–1.110.03–35.1 1.81 Le Neindre(1972)[168]177298–9770.1–1000.01–24.3 1.00 Le Neindre et al.(1969)[170]378294–9780.1–1280.01–26.20.91 Le Neindre et al.(1989)[171]112980.1–10000.04–44.9 1.86 Lenoir and Comings(1951)[172]93140.1–19.70.03–7.76 1.75 Lenoir et al.(1953)[173]163260.1–220.03–8.23 1.81 Mardolcar et al.(1986)[184]54107–4290.61–10.10.17–32.50.48 Michels et al.(1956)[188]82273–3480.1–2430.03–30.614.9 Michels et al.(1963)[190]110274–3480.1–2460.03–30.40.76 Millat et al.(1987)[191]77308–4280.58–10.90.22–3.70.65 Millat et al.(1989)[192]61174–3090.36–9.680.20–8.30.66 Moszynski and Singh(1973)[196]105323–4730.1–1620.02–26.9 1.24 Patek and Klomfar(2002)[204]170299–4260.15–15.70.04–6.45 1.11 Perkins et al.(1991)[5]144299–303 2.6–65.5 1.05–20.10.95 Perkins et al.(1991)[8]84103–3240.19–11.40.20–4.870.68 Roder et al.(1988)[7]1484102–3260.19–67.90.09–36 1.12 Roder et al.(2000)[9]718301–3440.16–8.330.05–3.210.80 Rosenbaum et al.(1966)[218]48279–322 2.65–71.3 1.11–21.9 1.90 Saxena and Saxena(1968)[227]12373–14700.1Dilute Gas0.47 Schafer and Reiter(1957)[229]12273–13700.1Dilute Gas 1.93 Schottky(1952)[232]9373–7730.1Dilute Gas 1.72 Schramm(1964)[233]19276–14000.1Dilute Gas0.73 Senftleben(1964)[236]8273–6730.1Dilute Gas 2.43 Shashkov et al.(1976)[237]1393.6–2710.1Dilute Gas0.94 Slyusar et al.(1977)[239]2490–1460.13–4.050.18–34.57.55 Smiley(1957)[241]121100–33000.1Dilute Gas 1.80 Springer and Wingeier(1973)[242]9900–25000.1Dilute Gas0.80 Sun et al.(2002)[244]236297–3280.81–62.30.29–19.80.71 Sun et al.(2002)[245]436296–4280.33–63.10.13–19.70.33 Tarzimanov and Arslanov(1971)[248]47298–6540.09–1960.02–30.3 1.61 Tiesinga et al.(1994)[251]142151–1750.08–18.80.06–24.3 5.34 Uhlir(1952)[263]6586.6–1940.09–9.740.06–35.2 4.13
Viscosity and Thermal Conductivity Equations35
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Vargaftik and Zimina(1964)[271]69273–12700.1Dilute Gas 1.49 Vines(1960)[276]4533–11700.1Dilute Gas 1.53 Yorizane et al.(1983)[285]42298–3240.1–19.70.03–7.71 1.06 Zheng et al.(1984)[287]202980.1–17.50.04–7.45 1.18 Ziebland and Burton(1958)[289]11993.3–1960.1–12.20.06–34.9 2.02 Ziebland and Marsh(1977)[290]53100–20000.1Dilute Gas0.33
Oxygen-viscosity
Bonilla et al.(1951)[38]25200–25000.1Dilute Gas 3.62 Boon and Thomaes(1963)[39]875.4–91.60.01–0.1135.4–37.9 1.27 Boon et al.(1967)[40]875.4–91.6 1.14–1.2135.5–37.9 4.29 Clifford et al.(1975)[56]9321–13000.1Dilute Gas0.39 de Bock et al.(1967)[59]17770.2–13.437.7–38.3 6.92 Golubev(1970)[89]36288–3730.1–70.90.03–21.7 1.21 Grevendonk et al.(1968)[96]9277.7–1500.78–19.223.1–38.5 4.34 Haynes(1977)[104]19775–3000.01–34.60.11–37.9 1.3 Hellemans et al.(1970)[106]4996–1520.18–9.8619.5–35.410.2 Hellemans et al.(1973)[107]12298–7700.1Dilute Gas0.97 Johnston and McCloskey(1940)[127]3590.3–3000.1Dilute Gas0.37 Kestin and Yata(1968)[136]12293–3030.1–2.510.04–1.040.19 Kestin and Leidenfrost(1959)[141]15293–2980.01–5.260.005–2.190.22 Kestin and Leidenfrost(1959)[142]11293–2960.1–9.280.04–3.990.23 Kiyama and Makita(1952)[159]35274–373 2.45–19.60.80–9.51 6.95 Kiyama and Makita(1956)[160]24298–3730.1–78.50.03–22.2 4.52 Lavushchev and Lyusternik(1976)[166]73400–19900.1Dilute Gas0.35 Maitland and Smith(1972)[177]2280–13000.03–0.1Dilute Gas0.65 Makita(1955)[182]30298–4730.1–10.10.02–4.3 3.63 Matthews et al.(1976)[185]15120–17000.1Dilute Gas0.48 Prosad(1952)[208]1591.2–93.60.11–0.1435.1–35.5 3.91 Raw and Ellis(1958)[210]11769–12900.1Dilute Gas 2.33 Rudenko and Schubnikow(1934)[221]1654.4–90.10–0.135.7–40.8 4.81 Rudenko(1939)[222]877.4–1540.02–4.9716.5–37.623.3 Saji and Okuda(1965)[224]580.1–87.50.03–0.0736.1–37.2 3.68 Timrot et al.(1974)[253]46296–5660.1–11.80.02–4.9712.9 Trautz and Melster(1930)[256]4292–5500.1Dilute Gas0.87 Trautz and Heberling(1931)[257]9294–5230.1Dilute Gas0.67 Trautz and Zink(1930)[258]12556–11000.1Dilute Gas 3.09 van Itterbeek and Claes(1936)[266]1272–2940.001–0.1Dilute Gas 3.16 van Itterbeek et al.(1966)[267]1477.3–90.20.03–2.4435.7–37.7 6.47 van Itterbeek et al.(1966)[268]3269.9–89.90.01–9.7535.7–39.1 4.52 Wobser and Muller(1941)[283]5293–3710.1Dilute Gas0.24 Yen(1919)[284]202960.1Dilute Gas0.08
Oxygen-thermal conductivity
Borovik(1947)[41]51560.1–9.810.07–23.6 6.42 Dickins(1934)[64]5277–2850.1Dilute Gas 1.21
36Lemmon and Jacobsen
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Franck(1951)[78]1493–6760.009–0.03Dilute Gas 2.56 Geier and Schafer(1961)[80]12273–13700.1Dilute Gas0.65 Gregory and Marshall(1928)[94]80286–2990.01–0.11Dilute Gas 1.91 Hammann(1938)[99]766–82.10.136.9–39.216.4 Ivanova et al.(1967)[115]8884.2–341 5.88–49 2.14–38.5 3.62 Jain and Saxena(1977)[120]13400–16000.1Dilute Gas 2.36 Johnston and Grilly(1946)[125]1886.5–3760.001–0.1Dilute Gas 2.38 Keyes(1955)[157]785.7–2730.1–1.060.04–36.4 1.22 Nothdurft(1937)[202]22275–3240.06–0.07Dilute Gas 1.21 Pereira and Raw(1963)[205]5305–4530.1Dilute Gas0.72 Prosad(1952)[208]1591.2–93.60.11–0.1435.1–35.529.2 Roder(1982)[216]113676.7–3130.02–68.40.03–40.30.95 Saxena and Gupta(1970)[226]13350–15000.1Dilute Gas 2.88 Tsederberg and Timrot(1957)[259]7873.2–3130.01–10.10.01–38.7 2.11 Vanicheva et al.(1985)[269]19303–9500.1Dilute Gas0.54 Weber(1982)[279]76153–174 4.72–8.7411.7–18.833.8 Westenberg and deHaas(1963)[281]10300–12000.1Dilute Gas0.93 Yorizane et al.(1983)[285]36299–3230.1–150.03–6.41 1.64 Zheng et al.(1984)[287]202980.1–17.80.04–7.59 1.18 Ziebland and Burton(1955)[288]6579.2–2000.1–13.80.06–37.7 2.27
Air-viscosity
Bearden(1939)[37]112930.1Dilute Gas0.07 Braune et al.(1928)[45]25292–9440.1Dilute Gas0.64 Carmichael and Sage(1966)[47]6294–3780.1Dilute Gas0.54 Diller et al.(1991)[4]6470–130 3.43–32.216.5–33.10.88 Filippova and Ishkin(1959)[73]3290.2–2730.09–14.70.04–29.87.54 Filippova and Ishkin(1962)[74]5390.2–273 1.99–14.80.88–29.614.1 Glassman and Bonilla(1953)[82]24200–25000.1Dilute Gas 4.50 Golubev(1938)[87]32273–3730.09–29.40.03–11.9 2.06 Golubev et al.(1971)[88]105293–776 2.03–50.70.31–15.6 2.00 Golubev(1970)[89]53273–3730.1–30.40.03–12.20.72 Goring and Eagan(1971)[90]12423 3.62–10.8 1.02–2.95 2.49 Hellemans et al.(1973)[107]19298–8730.1Dilute Gas0.33 Iwasaki and Kestin(1963)[116]272930.1Dilute Gas0.05 Iwasaki(1951)[118]28323–423 2.2–19.90.62–6.98 1.43 Johnston and McCloskey(1940)[127]4090.2–3000.1Dilute Gas0.25 Johnston et al.(1951)[128]1680.3–3060.001–0.09Dilute Gas0.60 Kellstroem(1941)[133]732930.77–3.090.31–1.280.12 Kestin and Wang(1958)[135]132980.1–10.10.04–4.120.39 Kestin and Whitelaw(1964)[137]42298–5240.1–14.40.02–5.690.47 Kestin and Leidenfrost(1959)[141]18293–2980.01–70.005–2.850.12 Kestin and Leidenfrost(1959)[142]9292–2950.1–10.40.04–4.320.23 Kompaneets(1953)[162]10285–10700.1Dilute Gas 2.65
Viscosity and Thermal Conductivity Equations37
Table VI.(Continued)
No.Temperature Pressure Density range AAD Author Points range(K)range(MPa)(mol·dm?3)(%) Kurin and Golubev(1974)[163]36293–3239.81–325 3.63–30.5 1.55 Latto and Saunders(1973)[164]26101–3980.11–14.50.03–13.5 1.14 Ling and Van Winkle(1958)[174]4273–4640.1Dilute Gas0.59 Maitland and Smith(1972)[177]1680–7000.0Dilute Gas0.38 Makita(1957)[181]102298–4730.1–81.10.02–19.5 2.54 Matthews et al.(1976)[185]15120–17000.1Dilute Gas0.41 Moulton and Beuschlein(1940)[197]453030.92–30.30.36–10.89.03 Nasini and Pastonesi(1933)[199]182870.1–20.30.04–8.31 3.89 Rudenko(1939)[222]590.1–1260.3–2.9219.1–28.433.5 Sutherland and Maass(1932)[246]779–2940.10.04–4.08 5.38 Timrot et al.(1974)[253]46296–5660.1–11.80.02–4.730.43 Timrot et al.(1975)[254]46296–5660.0Dilute Gas 2.96 Trautz and Zink(1930)[258]94346–11000.1Dilute Gas 5.52 Van Dyke(1923)[265]52960.09Dilute Gas0.70 Wobser and Muller(1941)[283]5293–3710.0Dilute Gas0.35
Air-thermal conductivity
Amirkhanov and Adamov(1963)[28]5293–3130.1Dilute Gas 1.39 Carmichael and Sage(1966)[47]6294–3780.1Dilute Gas0.40 Carroll et al.(1968)[48]378160–8000.1–1010.01–28.8 2.43 Fleeter et al.(1980)[75]33300–3010.81–36.20.32–12.40.25 Gambhir et al.(1967)[79]4308–3630.1Dilute Gas0.61 Geier and Schafer(1961)[80]12273–13700.1Dilute Gas 2.66 Glassman and Bonilla(1953)[82]24200–25000.1Dilute Gas 4.58 Golubev(1963)[86]72196–4260.1–50.70.02–22 2.98 Irving et al.(1973)[114]4273–4480.1Dilute Gas 2.58 Kannuluik and Carman(1951)[130]4690.2–4910.002–0.1Dilute Gas 1.85 Kannuluik and Martin(1934)[131]82760.001–0.1Dilute Gas0.64 Mustafaev(1972)[198]14423–6770.1Dilute Gas0.47 Perez Masia and Roig(1958)[206]7277–4060.0Dilute Gas 2.16 Perkins and Cieszkiewicz(1991)[10]106670–3040.15–70.20.20–34.10.45 Roder(1966)[217]2760–1100.001–0.50.002–0.69 1.28 Saksena and Saxena(1966)[225]6313–4130.1Dilute Gas 2.52 Schluender(1964)[230]6293–6990.1Dilute Gas 1.16 Scott et al.(1981)[234]43309–3750.87–23.80.27–8.70.24 Senftleben(1963)[235]8273–6730.1Dilute Gas 1.68 Senftleben(1964)[236]8273–6730.1Dilute Gas 1.69 Stolyarov et al.(1950)[243]16274–673 1.08–19.50.19–8.54 5.08 Tarzimanov and Salmanov(1977)[247]40406–12000.1–1000.01–13.4 1.69 Tarzimanov and Lozovoi(1968)[249]66299–7940.1–99.10.01–20.1 1.26 Taylor and Johnston(1946)[250]4387.5–3760.001–0.02Dilute Gas 2.26 Tsederberg and Ivanova(1971)[260]8582.6–3689.81–49 3.14–32.7 4.41 Vargaftik and Oleshchuk(1946)[272]12317–10700.1Dilute Gas 3.30 Vines(1960)[276]4513–11700.1Dilute Gas0.57
fewer data points were generally excluded from this list.The average absolute deviations are based on the percent deviation in any property,X, defined as
%D X=1001X data?X calc
X data
2
.(12)
Figures1through16compare calculated values from the equations to the experimental data.Smaller datasets were excluded from some of the com-parisons to eliminate crowding in both graphs and legends.In these figures, data are separated into temperature increments of10K or more;the tem-peratures listed at the top of each small plot are the lower bounds of the data in the plot.The discussion of deviations in the following text generally focuses on the average absolute deviation of calculated values from various datasets,and points with large apparent errors in a particular dataset are not considered when discussing deviation ranges and scatter.
Figures1through4and9through12compare the transport property formulations developed in this work to the dilute gas data.Only experi-mental data in the vapor phase at pressures less than1MPa were included in these figures.Thus,the calculations are a composite of the dilute gas equations given in Eqs.(2)and(5)and a small contribution from the resi-dual fluid behavior given in Eqs.(3)and(6).The major portion of each calculated property comes from the dilute gas equations.The ranges for deviations on the plots span from?5to5%,except those for the viscosity of nitrogen and argon(which span from?2to2%).
As shown in Figs.1through4,the dilute gas experimental data for viscosity are generally represented to within0.5%for nitrogen and argon, and within1%for oxygen and air.In Fig.3there are two datasets for oxygen,van Itterbeek and Claes[266]and Haynes[104],at temperatures below200K with deviations that exceed1%and that disagree with the data of Johnston and McCloskey[127],Maitland and Smith[177],and Matthews et al.[185].It is unclear which of these data give a better repre-sentation of the true properties of oxygen and uncertainty estimates must include all these data.At high temperatures for all four fluids there are two distinct groupings of data:one grouping was used to fit the equations;the second grouping of data shows systematic negative deviations from those selected for developing the equations reported here.For nitrogen,the trend starts at temperatures near300K,including the datasets of Bonilla et al.
[38],Ellis and Raw[70],Rigby and Smith[214],and Trautz and Zink [258],and reaches a maximum deviation of?14%at2500K as shown in 38Lemmon and Jacobsen
Temperature, K
P e r c e n t D e v i a t i o n i n V i s c o s i t y
Baron et al. (1959) [36]
Bonilla et al. (1951) [38]Clarke and Smith (1968) [52]Clarke and Smith (1969) [53]Dawe and Smith (1970) [58]DiPippo and Kestin (1968) [66]DiPippo et al. (1966) [67]Ellis and Raw (1959) [70]
Evers et al. (2002) [71]Golubev and Kurin (1974) [84]Golubev (1970) [89]Gough et al. (1976) [91]Gracki et al. (1969) [92]Guevara et al. (1969) [97]
Hoogland et al. (1985) [110]
Iwasaki and Kestin (1963) [116]Johnston and McCloskey (1940) [127]Johnston et al. (1951) [128]Kestin and Whitelaw (1963) [138]Kestin and Ro (1976) [139]Kestin and Leidenfrost (1959) [141]Kestin et al. (1971) [144]Kestin and Wang (1958) [135]Kestin et al. (1977) [146]Kestin et al. (1982) [148]Kestin et al. (1972) [149]
Kestin et al. (1972) [152]
Lavushchev and Lyusternik (1978) [165]Lazarre and Vodar (1957) [167]Lukin et al. (1983) [176]
Maitland and Smith (1972) [177]Maitland and Smith (1974) [178]Maitland et al. (1983) [179]Makavetskas et al. (1963) [180]Makita (1957) [181]
Matthews et al. (1976) [185]Rigby and Smith (1966) [214]Rutherford (1984) [223]Timrot et al. (1969) [252]
Timrot et al. (1974) [253]
Trautz and Melster (1930) [256]Trautz and Heberling (1931) [257]Trautz and Zink (1930) [258]Vogel (1984) [277]
Vogel et al. (1989) [278]Wobser and Muller (1941) [283]
Yen (1919) [284]
https://www.360docs.net/doc/8e12903894.html,parisons of calculated viscosities of nitrogen to experimental data in the dilute
gas.
Viscosity and Thermal Conductivity Equations 39
Temperature, K
P e r c e n t D e v i a t i o n i n V i s c o s i t y
Bonilla et al. (1951) [38]Clarke and Smith (1968) [52]Clifford et al. (1975) [56]
Dawe and Smith (1970) [58]De Rocco and Halford (1958) [63]DiPippo et al. (1968) [68]DiPippo and Kestin (1968) [66]Evers et al. (2002) [71]Filippova and Ishkin (1959) [73]Golubev (1970) [89]Gough et al. (1976) [91]Gracki et al. (1969) [92]Guevara et al. (1969) [97]Haynes (1973) [103]
Hellemans et al. (1974) [108]Hobley et al. (1989) [109]
Iwasaki et al. (1964) [119]
Iwasaki and Kestin (1963) [116]Johnston and Grilly (1942) [126]Kalelkar and Kestin (1970) [129]Kestin and Nagashima (1964) [134]Kestin and Wang (1958) [135]Kestin and Whitelaw (1963) [138]Kestin and Ro (1976) [139]
Kestin and Ro (1982) [140]
Kestin and Leidenfrost (1959) [141]Kestin and Wakeham (1979) [143]Kestin et al. (1971) [144]Kestin et al. (1978) [145]Kestin et al. (1972) [150]Kestin et al. (1972) [151]
Kestin et al. (1970) [153]
Kiyama and Makita (1952) [159]Kurin and Golubev (1974) [163]Lukin et al. (1983) [176]
Maitland and Smith (1972) [177]Maitland and Smith (1974) [178]Makita (1957) [181]
Makita (1955) [182]
Michels et al. (1954) [189]Rigby and Smith (1966) [214]Timrot et al. (1969) [252]Timrot et al. (1975) [254]Trautz and Zink (1930) [258]Vogel (1984) [277]
Wilhelm and Vogel (2000) [282]Wobser and Muller (1941) [283]
Hurly (2002) [111]
https://www.360docs.net/doc/8e12903894.html,parisons of calculated viscosities of argon to experimental data in the dilute gas.
40Lemmon and Jacobsen