General correlation for heat transfer during condensation in plain tubes: further development and verification.
Over three decades ago, the author had presented a general correlation for heat transfer during film condensation inside plain tubes (Shah 1979). While this correlation found wide acceptance, it is limited to higher flow rates and moderate pressures. The author presented an improved version that extended its applicability to low flow rates and pressures near critical pressure. It was shown to be in good agreement with data for 22 fluids in horizontal, vertical, and inclined tubes over a very wide range of flow rates and pressures (Shah 2009). Its further development and verification for horizontal tubes is presented in this paper.
The 2009 correlation has three heat transfer regimes (turbulent, mixed, and laminar) called Regimes I, II, and III. Different formulas apply in each regime. While the boundaries between the three regimes were clearly demarcated for vertical tubes in the 2009 correlation, the boundary between Regimes II and III for horizontal tubes was not demarcated due to lack of sufficient data. This boundary was determined during the present research using newly published data.
The boundaries between the regimes have been determined exclusively on an empirical basis. It is of interest to see the relation between these heat transfer regimes and flow pattern regimes. This was done during the present research, as reported in this paper.
Presently, there is a great deal of interest in using carbon dioxide as a refrigerant as it does not deplete the ozone layer and has zero global warming potential (GWP). Comparison with carbon dioxide data was not included in the 2009 paper. Several studies for this fluid have recently been published and comparison with their data is presented here. Comparison with other recently published data was also done for further verification. These data include dimethyl ether (DME), a fluid not included in the verification data in the 2009 paper.
In Shah (2009), data analyzed included tubes of diameter 2 mm (0.079 in.) and larger. The present work has also been confined to diameters larger than 2 mm (0.079 in.). There are wide variations in published data for smaller channels and many views about the physical phenomena in them. The author has published a comparison of this correlation with such data (Shah 2010).
THE PUBLISHED SHAH CORRELATION 2009
Heat Transfer Equations
The correlation uses the following two heat transfer equations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The second equation is:
[h.sub.Nu] = 1.32 [Re.sup.-1/3.sub.LS] [[[[rho].sub.l] ([[rho].sub.l] - [[rho].sub.g]) g[k.sup.3.sub.f]/[[mu].sup.2.sub.f]].sup.1/3] (2)
Equation 1 is the same as that in the Shah (1979) correlation except that the previous version did not have the viscosity ratio factor. Equation 2 is the Nusselt equation for laminar film condensation in vertical tubes; the constant has been increased by 20% as recommended by McAdams (1954) on the basis of comparison with test data. This equation can also be expressed in terms of heat flux or temperature difference instead of Reynolds number. This form has been preferred, as it is more convenient for this correlation and often it is also more convenient for design calculations.
These heat transfer equations are used as follows: For all tube orientations (except upward flow), in Regime I,
[h.sub.TP] = [h.sub.I] (3)
in Regime II,
[h.sub.TP] = [h.sub.I] + [h.sub.Nu] (4)
in Regime III,
[h.sub.TP] = [h.sub.Nu] (5)
[h.sub.LS] in Equation 1 is the heat transfer coefficient of the liquid phase flowing alone in the tube. It is calculated by the following equation:
[h.sub.LS] = 0.023 [Re.sup.0.8.sub.LS] [Pr.sup.0.4.sub.f] [k.sub.f]/D (6)
Heat Transfer Regimes for Horizontal Tubes
The boundary between Regimes I and II was deter mined through data analysis described in Shah (2009). The data that agreed with Equation 3 were considered to be in Regime I and those that agreed with Equation 4 were considered to be in Regime II. The data points were than plotted on a Z versus [J.sub.g] graph. A curve was drawn through the boundary between the data for the two regimes and an equation fitted to it. According to this curve, Regime I occurs when
[J.sub.g] [greater than or equal to] 0.98[(Z + 0.263).sup.-0.62] (7)
Otherwise, it is Regime II. A third regime was expected at very low flow rates. Analyzable data were not available for such conditions. Hence, its boundary had to be left un defined. This boundary has been determined during the present research as described later.
In Equation 7, [J.sub.g] is the dimensionless vapor velocity defined as:
[J.sub.g] = xG/[(gD[[rho].sub.g]([[rho].sub.l] - [[rho].sub.g])).sup.0.5] (8)
Z is the correlating parameter introduced by Shah (1979), defined as
Z = [([1/x] - 1).sup.0.8] [p.sup.0.4.sub.r] (9)
EFFORTS FOR FURTHER DEVELOPMENT
The Boundary Between Regimes II and III
By analyzing newly available data for low flow rates together with previously analyzed data, the boundary between Regimes II and III was determined as follows. Regime III occurs when:
[J.sub.g] [less than or equal to] 0.95[(1.254 + 2.27[Z.sup.1.249]).sup.-1] (10)
Otherwise it is Regime I or II as determined by Equation 7. This boundary was determined by comparing the predictions of the correlation for Regimes II and III with the measured data. The data points were assigned to the regimes which gave better agreement with measurements. There was some scatter across this boundary but 85% of data agreed with it. Scatter indicates that while the boundary criterion indicates a data point to be in Regime II, the heat transfer coefficient is in agreement with the equation for Regime III or vice versa; 15% of the data showed such scatter
Figure 1 shows the boundaries of the three heat transfer regimes. The curves have been limited to the range of data analyzed.
Relation with Flow Pattern Regimes
The heat transfer regimes defined in this correlation are purely empirical. Many predictive techniques for heat transfer and pressure drop, theoretical and empirical, are based on flow patterns. It was therefore investigated whether these heat transfer regimes can be defined on the basis of flow patterns. Many flow pattern maps are avail able. The flow pattern map of El Hajal et al. (2003) was shown by these authors to agree with a very wide range of data, including many fluids for condensation. It was there fore chosen. This correlation has five flow patterns, namely stratified, stratified wavy, intermittent, annular, and mist. Comparison of the predicted flow patterns with the predicted heat transfer regimes by Equations 7 and 10 gave the results shown in Table 1.
[FIGURE 1 OMITTED]
As seen in Table 1, the mist, annular, and intermittent regimes always correspond to Regime I, as predicted by the present correlation. However, the relationship with the stratified-wavy and stratified regimes is not so clear. While the majority of data in the stratified-wavy regime are in the predicted heat transfer Regime II, many others are in Regime III and a few are even in Regime I. The stratified regime includes data points in both Regimes II and III.
Thus, distinction between Regime II and III cannot be made using the El Hajal et al. map (2003). Many other flow pattern maps are available, for example Breber et al. (1980). It will be interesting to see whether any of them can be used to distinguish between Regimes II and III, but that study was outside the present scope.
COMPARISON WITH TEST DATA
A literature search was done to identify data published since the preparation of the Shah (2009) paper. Special emphasis was on finding data at low flow rates that may help developing the boundary between Regimes II and III. Special efforts were also made to locate data for carbon dioxide as its data were not analyzed in the 2009 paper and it is currently of great interest as a refrigerant. These efforts resulted in the collection of data whose range is given in Table 2.
The data collected were compared with the present correlation described in the foregoing. The single-phase heat transfer coefficient was calculated with Equation 6 for all data except for the data of Son and Lee (2009) for which the following equation was used:
[h.sub.LS] = 0.034 [Re.sup.0.8.sub.LS][Pr.sup.0.3.sub.f] [k.sub.f]/D (11)
The reason is that these authors' single-phase measurements were higher than Equation 7 and they fitted Equation 11 to their data.
All fluid properties were calculated at the saturation temperature using REFPROP 9.0 (Lemmon et al. 2010).
Results of Comparison of Data with the Present Correlation
The salient features of the new data that were analyzed are listed in Table 2.Some of the data were for mean heat transfer coefficients over the length of the tubes. Such data were analyzed by using the arithmetic average quality in calculations. It would be more correct to calculate local heat transfer coefficients along the length and then integrate them to get the predicted mean heat transfer coefficient, but it is not possible as distribution of quality along the length is not given in the papers. As discussed in Shah (1979), use of arithmetic mean quality gives a reasonable approximation to the more rigorous method.
Table 2 lists the average and mean deviations of the present correlation. Mean deviation [[delta].sub.m] is defined as:
[[delta].sub.m] = [1/N] [1.summation over (N)] ABS [([h.sub.predicted] - [h.sub.measured])/[h.sub.measured]] (12)
Average deviation is defined as:
[[delta].sub.avg] = [1/N] [1.summation over (N)] [([h.sup.predicted] - [h.sub.measured])/[h.sub.measured]] (13)
New Boundary for Regime III
The present research has provided Equation 10 as the boundary between Regime II and III. Figures 2 and 3 show test runs for which all data were predicted by Equation 10 to be in Regime III. It is seen that the agreement with the predictions of the present correlation is good. Without the boundary developed during the present research, all these data would have been grossly overpredicted as they would have been considered to be in Regime II.
The data analyzed in Shah (2009) were also examined to see the impact of the new boundary. Among the data of Akers et al. (1959) for propane, three were predicted to be in Regime III while they were in Regime II in the previous analysis. The mean deviation of these data was reduced from 43% to 23%. One data point of Akers et al. (1959) for R-12 was also found to be in Regime III; its deviation increased. None of the other data analyzed in Shah (2009) were found to be in Regime III.
Thus, overall the new boundary for Regime III was found to work reasonably well as deviations of most data were reduced by its introduction. It will be re-evaluated as more data become available.
Data for C[O.sub.2] and DME (dimethyl ether) were not analyzed in Shah (2009). Data for these fluids have been analyzed in the present study, as is discussed below.
As seen in Table 2, the data for DME cover a wide range of flow rates and show excellent agreement with the present correlation. Figure 4 shows comparison of some of these data with the present correlation.
As seen in Table 2, carbon dioxide data from four sources have been analyzed. All data show reasonable agreement except the data of Son and Oh (2012) at reduced pressure of 0.869 and 0.931, which are grossly overpredicted by the present correlation. Figure 5 compares their data at [p.sub.r] = 0.931 with the present correlation as well as the correlation of Cavallini et al. (2006), which has been reported to agree with other data at very high reduced pressures. The data are seen to be much lower than the predictions of these correlations. Figure 6 shows a comparison with the data of Kondou and Hrnjak (2011) for carbon dioxide at [p.sub.r] of 0.94. Excellent agreement with the present correlation is seen. Considering all the evidence, it appears that the high pressure data of Son and Oh (2012) are very unusual. In general, the present correlation can be considered reliable for C[O.sub.2]. This is a significant result, as C[O.sub.2] is being used more and more because of its zero environmental impact.
Results Considering All Data
In Shah (2009), the new correlation was compared to 1189 data points from 39 studies with a mean deviation of 14.4%. These data included 22 fluids in horizontal, vertical and inclined tubes. In the present study, 547 data points from 12 studies have been compared with the present correlation with a mean deviation of 20%. Thus, overall, 1736 data points for 24 fluids from 51 studies have been correlated with a mean deviation of 16.1%. The complete range of data is listed in Table 3.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
1. The boundary between Regimes II and III for horizontal tubes in the author's correlation (Shah 2009) was undetermined and hence all data not in Regime I were considered to be in Regime II. This boundary has been determined in the present research. It has improved the accuracy of the correlation at low flow rates.
2. Comparison with the flow pattern map of El Hajal et al. (2003) showed that heat transfer Regime I corresponds to the mist, annular, and intermittent flow patterns of their map. Regimes II and III could not be clearly classified in terms of their flow regimes.
3. Data for two fluids not analyzed earlier, carbon dioxide and DME, were compared to the present correlation. All these data show adequate agreement with the present correlation, except for very high pressure data for C[O.sub.2] from one source. However, even higher pressure data from another source shows good agreement.
4. Considering all data analyzed earlier and in the present study, the present correlation has been compared to 1736 data points for 24 fluids from 51 sources with a mean deviation of 16.1%.
5. The results of the data analysis have been presented in the foregoing. The reader may draw his own conclusions regarding the applicability of this correlation. The author recommends it in the range of dimensional and dimensionless parameters covered by the data analyzed.
All equations are dimensionless. Any consistent system may be used.
D = inside diameter of tube
G = total mass flux (liquid + vapor)
g = acceleration due to gravity
h = heat transfer coefficient
[h.sub.I] = heat transfer coefficient given by Equation 1
[h.sub.LS] = heat transfer coefficient assuming liquid phase flowing alone in the tube
[h.sub.LT] = heat transfer coefficient assuming all mass flowing as liquid
[h.sub.Nu] = heat transfer coefficient given by Equation 2, the Nusselt equation
[h.sub.TP] = two-phase heat transfer coefficient
[J.sub.g] = dimension less vapor velocity defined by Equation 8
k = thermal conductivity
N = number of data points
[p.sub.r] = reduced pressure
Pr = Prandtl number
[Re.sub.LS] = Reynolds number assuming liquid phase flowing alone, = G(1 - x)D/[[mu].sub.f]
[Re.sub.LT] = Reynolds number assuming total mass flowing as liquid, = GD/[[mu].sub.f]
[T.sub.SAT] = saturation temperature
x = vapor quality
Z = Shah's correlating parameter defined by Equation 9 Greek
[mu] = dynamic viscosity
[rho] = density
f = of liquid
g = of vapor
Afroz, H.M.M., A. Miyara, and K. Tsubaki 2008. Heat transfer coefficients and pressure drops during in-tube condensation of C[O.sub.2]/DME mixture refrigerant. International Journal of Refrigeration 31:1458-66.
Akers, W.W., H.A. Deans, and O.K. Crosser. 1959. Condensing heat transfer within horizontal tubes. Chemical Engineering Progress Symposium Series, 59(29):171-6.
Breber, G., J.W. Palen, and J. Taborek. 1980. Prediction of horizontal tubeside condensation of pure components using flow regime criteria. Journal of Heat Transfer 102(3):471-6.
Cavallini, A., D.D. Col, L. Doretti, M. Matkovic, L. Rossetto, and C. Zilio. 2006. Condensation in horizontal smooth tubes: a new heat transfer model for heat exchanger design. Heat Transfer Engineering 27(8):31-8.
Dalkilic, A.S. and O. Agra. 2009. Experimental apparatus for the determination of condensation heat transfer coefficients for R-134a and R-600a flowing inside vertical and horizontal tubes respectively. Proceedings of the 2009 ASME Summer Heat Transfer Conference CA: San Francisco.
El Hajal, J., J. R. Thome, and A. Cavallini. 2003. Condensation in horizontal tubes, part I: two-phase flow pattern map. International Journal of Heat and Mass Transfer 46:3349-63.
Iqbal, O., and P. Bansal. 2012. In-tube condensation of C[O.sub.2] heat transfer in a horizontal smooth tube. International Journal of Refrigeration 35(2): 270-7.
Kondou, C., and P. Hrnjak. 2011. Heat rejection from R744 flow under uniform temperature cooling in a horizontal smooth tube around the critical point. International Journal of Refrigeration 34:719-31.
Lee, H., and C. Son. 2010. Condensation heat transfer and pressure drop characteristics of R-290, R-600a, R-134a, and R-22 in horizontal tubes. Heat and Mass Transfer 46:571-84.
Lemmon, E. W., M. L. Huber, M. O. McLinden. 2010. NJST Reference Fluid Thermodynamic and Transport Properties, REFPROP Version 9.0, NIST, Gaithersburg, MD.
McAdams, W.H. 1954. Heat Transmission, 3rd edition. New York: McGraw-Hill.
Shah, M.M. 1979. A general correlation for heat transfer during film condensation in pipes. International Journal of Heat and Mass Transfer 22:547-56.
Shah, M.M. 2009. An improved and extended general correlation for heat transfer during condensation in plain tubes. HVAC&R Research 15(5):889-913.
Shah, M.M. 2010. Heat Transfer during condensation inside small channels: applicability of general correlation for macrochannels. Proceedings of the 14th International Heat Transfer Conference. DC: Washington.
Son, C. and H. Lee. 2009. Condensation heat transfer characteristics of R-22, R-134a and R-410A in small diameter tubes. Heat and Mass Transfer 45:1153-66.
Son, C. and H. Oh. 2012. Condensation heat transfer characteristics of C[O.sub.2] in a horizontal smooth- and microfintube at high saturation temperatures. Applied Thermal Engineering 36:51-62.
Wen, M., C. Ho, and J. Hsieh. 2006. Condensation heat transfer and pressure drop characteristics of R-290 (propane), R-600 (butane), and a mixture of R-290/R-600 in the serpentine small-tube bank. Applied Thermal Engineering. 26:2045-53.
Zilly, J., J. Jang, and P. Hrnjak. 2003. Condensation of C[O.sub.2] at low temperature inside horizontal micro-finned tube. ACRC Report CR-49. University of Illinois at Urbana Champaign.
Wilson, M.J., T. A. Newell, J. C. Chato, and C.A. Infante Ferreira. 2003. Refrigerant charge, pressure drop, and condensation heat transfer in flattened tubes. International Journal of Refrigeration 26:443-51.
Mirza Mohammed Shah, PhD, PE
Mirza Mohammed Shah is a consultant in Redding, CT.
Table 1. Flow Patterns Predicted by the Correlation of El Hajal et al. (2003) Compared with the Heat Transfer Regimes According to the Present Correlation. Predicted Flow Pattern Predicted Heat Transfer Regime Mist I (always) Annular I (always) Intermittent I (always) Stratified-wavy 70% II, 20% III, 10% I Stratified II or III Table 2. Range of Data Analyzed in the Present Work and Their Deviations with the Present Correlation. Source D mm Fluid [P.sub.r] (in.) Kondou and Hrnjak (2011) 6.1 C[O.sub.2] 0.81 (0.24) 0.946 Zilly et al. (2003) 6.1 C[O.sub.2] 0.227 (0.24) 0.309 0.774 Son and Oh (2012) 4.6 C[O.sub.2] 0.869 (0.18) 0.931 Iqbal and Bansal (2012) 6.52 C[O.sub.2] 0.309 (0.26) 0.470 Zilly et al. (2003) 6.1 R-22 0.049 (0.24) 0.136 Li and Ji-Tian (2007) 9.4 R-134a 0.249 (0.37) Butane 0.1 Wenetal. (2006) 2.46 R-134a 0.25 (0.10) Propane 0.32 Afroz et al. (2008) 4.35 DME 0.13 (0.17) 3.36 R-22 0.308 Son and Lee (2009) (0.13) R-134a 0.25 5.35 (0.21) R-410A 0.49 5.8 Propane 0.32 Lee and Son (0.23) Isobutane 0.146 (2010) 6.54 (0.26) 7.73 R-22 0.306 (0.30) 10.07 (0.40) R-134a 0.249 R-134a 0.22 Wilson et al. (2003) 3.7 * R-410A 0.44 (0.14) R-410A 0.44 Dalkilic and Agra (2009) 4.0 Isobutane 0.127 (0.16) All sources 2.46 0.127 (0.10) 10.07 0.946 (0.40) Source D mm G (in.) Kg/[m.sup.2]s G Lb/s.[ft.sup.2] Kondou and Hrnjak (2011) 6.1 100 20.5 (0.24) 200 41.0 150 30.7 Zilly et al. (2003) 6.1 200 41.0 (0.24) 400 82.0 400 82.0 800 164.0 Son and Oh (2012) 4.6 800 164.0 (0.18) 800 164.0 Iqbal and Bansal (2012) 6.52 50 10.2 (0.26) 200 41.0 Zilly et al. (2003) 6.1 400 82.0 (0.24) Li and Ji-Tian (2007) 9.4 100 20.5 (0.37) 400 82.0 205 42.0 510 104.5 Wenetal. (2006) 2.46 205 510 42.0 (0.10) 104.5 205 510 42.0 510.0 Afroz et al. (2008) 4.35 200 41.0 (0.17) 500 102.5 3.36 300 61.5 400 82.0 Son and Lee (2009) (0.13) 200 41.0 5.35 400 82.0 (0.21) 200 41.0 400 82.0 5.8 47 9.6 170 34.8 Lee and Son (0.23) 49 10.0 (2010) 6.54 170 34.8 (0.26) 7.73 50 10.2 (0.30) 155 10.07 (0.40) 52 10.7 165 33.8 75 15.3 400 82.0 Wilson et al. (2003) 3.7 * 75 15.3 (0.14) 400 82.0 75 15.3 400 82.0 Dalkilic and Agra (2009) 4.0 57 11.7 (0.16) 92 18.9 All sources 2.46 47 9.6 (0.10) 10.07 800 164.0 (0.40) Source D mm x [Re.sub.LT] [Re.sub.GT] (in.) Kondou and Hrnjak (2011) 6.1 0.10 9687 32472 (0.24) 0.95 19374 64945 0.10 18729 40083 0.95 Zilly et al. (2003) 6.1 0.10 8046 95529 (0.24) 0.80 18973 191058 0.10 27710 101417 0.88 55419 202834 Son and Oh (2012) 4.6 0.11 64171 183285 (0.18) 0.90 0.10 72597 173062 0.90 Iqbal and Bansal (2012) 6.52 0.02 2535 22071 (0.26) 0.90 13085 94145 Zilly et al. (2003) 6.1 0.20 9031 206932 (0.24) 0.78 12575 231669 Li and Ji-Tian (2007) 9.4 0.10 5811 76018 (0.37) 0.80 23245 304071 0.12 3665 64820 0.84 9118 161260 Wenetal. (2006) 2.46 0.12 2551 40072 (0.10) 0.8 6346 99692 0.12 6099 53719 0.80 15174 133642 Afroz et al. (2008) 4.35 .02 7131 92850 (0.17) .94 17828 232124 3.36 0.08 4917 70360 0.88 7830 170048 Son and Lee (2009) (0.13) 0.08 3399 53398 5.35 0.9 10834 106796 (0.21) 0.05 7117 45801 0.92 22663 145855 5.8 0.05 3453 32248 0.85 11882 110976 Lee and Son (0.23) 0.05 2211 36231 (2010) 6.54 0.87 7609 124681 (0.26) 7.73 0.06 6346 66041 (0.30) 0.89 10873 113152 10.07 (0.40) 0.05 1510 19747 0.86 7885 103146 0.1 1386 22701 0.79 7390 121073 Wilson et al. (2003) 3.7 * 0.1 2733 19687 (0.14) 0.8 14577 10499 0.1 2733 19687 0.8 14577 10499 Dalkilic and Agra (2009) 4.0 0.50 1671 29362 (0.16) 0.85 47392 All sources 2.46 0.02 1671 22071 (0.10) 10.07 0.95 55419 304071 (0.40) Source D mm Number of Deviation (in.) Data Points Mean Average Kondou and Hrnjak (2011) 6.1 23 14.7 (0.24) -12.1 8 10.0 +0.4 Zilly et al. (2003) 6.1 16 28.7 (0.24) +28.7 26 23.9 +16.3 Son and Oh (2012) 4.6 9 36.7 (0.18) +36.7 9 106 +106 Iqbal and Bansal (2012) 6.52 83 27.6 (0.26) 5.1 Zilly et al. (2003) 6.1 7 15.1 (0.24) +14.1 Li and Ji-Tian (2007) 9.4 20 6.4 (0.37) -3.0 18 15.1 -14.4 Wenetal. (2006) 2.46 18 9.9 (0.10) 2.6 18 10.8 -8.5 Afroz et al. (2008) 4.35 29 12.2 (0.17) -10.9 3.36 18 12.3 -10.9 Son and Lee (2009) (0.13) 20 10.8 5.35 -7.5 (0.21) 28 9.6 -5.5 5.8 46 15.5 -4.5 Lee and Son (0.23) 47 20.1 (2010) 6.54 -4.1 (0.26) 7.73 46 23.0 (0.30) +12.0 10.07 (0.40) 43 25.2 28.0 13 14.9 -3.9 Wilson et al. (2003) 3.7 * 12 15.8 (0.14) 15.5 12 15.8 15.5 Dalkilic and Agra (2009) 4.0 15 18.7 (0.16) -18.7 All sources 2.46 547 20.0 (0.10) 10.07 1.8 (0.40) * Equivalent hydraulic diameter of rectangular channel 12.5 mm x 2.6 mm Table 3. Complete Range of Parameters in the Data Showing Satisfactory Agreement with the Present Correlation Parameter Fluids Water, R-11, R-12, R-22, R-32, R-113, R-123, R-125, R-134a, R-142b, R-404A, R-410A, R-502, R-507, isobutane, propylene, propane, benzene, ethanol, methanol, toluene, Dowtherm 209, DME, C[O.sub.2] Tube diameter, mm (in.) 2 to 49 (0.079 to 1.93) Tube orientations Horizontal, vertical downwards, 15 degrees downwards Reduced pressure 0.0008 to 0.946 G, kg/[m.sup.2]s 4 to 820 (0.82 to 168.1) (lb/[ft.sup.2]s) [Pr.sub.f] 1to18 [Re.sub.LT] 68 to 84827 [Re.sub.GT] 9534 to 523317 x 0.01 to 0.99 Z 0.005 to 20 Jg 0.06 to 20 Number of data points 1736 Number of data sources 51
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|Author:||Shah, Mirza Mohammed|
|Date:||Jul 1, 2013|
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