BOOKCOMP, Inc. — John Wiley & Sons / Page 755 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN SMOOTH TUBES 755 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [755], (37) Lines: 994 to 1042 ——— 0.48521pt PgVar ——— Normal Page PgEnds: T E X [755], (37) data analysis and physical guidance from analytical solutions. The final correlation separates the heat transfer by film condensation in the upper part of the horizontal tube from the forced-convective heat transfer in the bottom pool: Nu = 0.23Re 0.12 vo 1 + 1.11X 0.58 tt Ga · Pr l Ja l 0.25 + 1 − θ l π Nu f (10.56) where θ l is the angle subtended from the top of tube to the liquid level and Nu f = 0.0195Re 0.8 l · Pr 0.4 l 1.376 + C 1 X C 2 tt (10.57) For 0 < Fr l · 0.7, C 1 = 4.172 + 5.48Fr l − 1.564Fr 2 l (10.58a) C 2 = 1.773 − 0.169Fr l (10.58b) For Fr l > 0.7, C 1 = 7.242 (10.59a) C 2 = 1.655 (10.59b) where Fr l is the liquid Froude number. Due to the 1.376 inside the radical of eq. (10.57), the correlation above matches the Dittus–Boelter single-phase correlation when x = 0. If the area occupied by the thin condensate film is neglected, θ l is geometrically related to the void fraction by α = θ l π − sin 2θ l 2π (10.60) If a void fraction model is assumed, this transcendental equation must be solved to obtain the desired quantity, θ l . Jaster and Kosky (1976) deduced an approximate relationship which is much easier to use. In the context of the present topic, their simplification can be stated as 1 − θ l π arccos(2α − 1) π (10.61) The simplicity achieved by this assumption is well worth the modest errors as- sociated with it. These errors are themselves mitigated by the fact that the forced- convective Nusselt number, by which the quantity in eq. (10.61) is multiplied, is normally considerably smaller than the filmwise Nusselt number. The void frac- tion correlation of Zivi (1964), eq. (10.50), was used with this correlation. Equation (10.56) is to be used when G<500 kg/s · m 2 and Fr so < 20. Even though the Dob- son correlations yield reasonable results, available data suggest the need for further BOOKCOMP, Inc. — John Wiley & Sons / Page 756 / 2nd Proofs / Heat Transfer Handbook / Bejan 756 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [756], (38) Lines: 1042 to 1066 ——— -1.0039pt PgVar ——— Normal Page PgEnds: T E X [756], (38) development of heat transfer models in the wavy or wavy-annular regions at higher mass fluxes. Shear-Driven Annular Flow Condensation The annular flow regime repre- sents the situation where the interfacial shear stresses dominate and create a nearly symmetric annular film with a high-speed vapor core. A variety of approaches for predicting heat transfer during annular flow condensation have been developed. Al- though these approaches can be divided into many different categories, they can be reduced to three for the purposes of this review: two-phase multiplier approaches, shear-based approaches, and boundary layer approaches. Two-Phase Multiplier Correlations The simplest method of heat transfer predic- tion in the annular flow regime is the two-phase multiplier approach. This approach was pioneered for predicting convective evaporation data by Denglor and Addoms (1956) and was adapted for condensation by Shah (1979). The theoretical hypothesis is that the heat transfer process in annular two-phase flow is similar to that in single- phase flow of the liquid (through which all the heat is transferred), and thus their ratio may be characterized by a two-phase multiplier. This reasoning is in fact very similar to that of Lockhart and Martinelli (1947), who pioneered the two-phase multiplier approach for predicting two-phase pressure drop. The single-phase heat transfer co- efficients are typically predicted by modifications of the Dittus and Boelter (1930) correlation, which results in the form Nu = 0.023Re 0.8 l · Pr m l · F x, ρ l ρ g , µ l µ g , Fr l (10.62) where m is a constant between0.3and0.4and F is the two-phase multiplier. Although the two-phase multiplier can depend on more dimensionless groups than those indi- cated in eq. (10.62), the groups shown are the most relevant. The type of single-phase correlation shown is valid for turbulent flow and is based primarily on an analogy between heat and momentum transfer. One of the most widely cited correlations of the two-phase multiplier type is that of Shah (1979). It was developed from his observation that the mechanisms of condensation and evaporation were very similar in the absence of nucleate boiling. With this idea, he set out to modify the convective component of his flow boiling correlation for use during condensation. The form of his correlation is Nu = 0.023Re 0.8 l · Pr 0.4 l 1 + 3.8 p 0.38 r x 1 − x 0.76 (10.63) The bracketed term is the two-phase multiplier. It properly approaches unity as x ap- proaches 0, indicating that it predicts the single-phase liquid heat transfer coefficient when only liquid is present. As the reduced pressure is increased, the properties of the liquid and vapor become more alike and the two-phase multiplier decreases, as expected. BOOKCOMP, Inc. — John Wiley & Sons / Page 757 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN SMOOTH TUBES 757 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [757], (39) Lines: 1066 to 1094 ——— 0.63914pt PgVar ——— Normal Page * PgEnds: Eject [757], (39) Cavallini and Zecchin (1974) used the results of a theoretical annular flow analysis to deduce the dimensionless groups that should be present in an annular flow correla- tion. They then used regression analysis to justify neglecting many of the groups that did not appear in their empirically developed correlation, which can be shown to be of the two-phase multiplier form by writing it in the following way: Nu = 0.023Re 0.8 l · Pr 0.33 l 2.64 1 + ρ l ρ g 0.5 x 1 − x 0.8 (10.64) Here the bracketed term represents the two-phase multiplier. The two-phase multiplier approach was selected for correlating the annular flow heat transfer data by Dobson (1994), Dobson et al. (1994a,b), and Dobson and Chato (1998). To make sure that the correlation was not biased by data outside the annular flow regime, only data with Fr so > 20 were used to develop the correlation. This value was reported by Dobson (1994) to provide a good indicator of the transition from wavy-annular to annular flow and agreed well with the data from his study. The correlation developed was Nu = 0.023Re 0.8 l · Pr 0.4 l 1 + 2.22 X 0.89 tt (10.65) This form utilizes the single-phase heat transfer correlation of Dittus–Boelter (1930) with a Prandtl exponent of 0.4. At a quality of zero, the Lockhart–Martinelli parameter approaches infinity and eq. (10.65) becomes the single-phase liquid Nus- selt number. This correlation is to be used for G ≥ 500 kg/s·m 2 or for all mass fluxes if Fr so > 20. Shear-Based Correlations The use of shear-based correlations for annular flow condensation dates back to the early work of Carpenter and Colburn (1951). They argued that the resistance to heat transfer in the turbulent liquid flow was entirely inside the laminar sublayer and that the wall shear stress was composed of additive components due to friction, acceleration, and gravity. Although it was later pointed out by Soliman et al. (1968) that their equation for the accelerational shear component was incorrect, the framework that they established at a relatively early point in the history of forced-convective condensation remains useful. Soliman et al. (1968) utilized the framework established by Carpenter and Col- burn to develop their own semiempirical heat transfer correlation for annular flow. Neglecting the gravitational term (which is appropriate for horizontal flow), the Soli- man correlation can be written as Nu = 0.036Re lo · Pr 0.65 l ρ l ρ g 0.5 2(0.046)x 2 Re 0.2 g φ 2 g + Bo 5 n=1 a n ρ g ρ l n/3 (10.66a) where BOOKCOMP, Inc. — John Wiley & Sons / Page 758 / 2nd Proofs / Heat Transfer Handbook / Bejan 758 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [758], (40) Lines: 1094 to 1124 ——— -0.39786pt PgVar ——— Normal Page PgEnds: T E X [758], (40) a 1 = x(2 − γ) − 1 (10.66b) a 2 = 2(1 − x) (10.66c) a 3 = 2(γ − 1)(x − 1) (10.66d) a 4 = 1 x − 3 + 2x (10.66e) a 5 = γ 2 − 1 x − x (10.66f) γ = interface velocity mean film velocity = 1.25 for turbulent liquid (10.66g) Soliman et al. (1968) compared the predictions of their correlation to data for steam, R-113, R-22, ethanol, methanol, toluene, and tricholoroethylene. The agree- ment was correct in trend, although even on log-log axes the deviations appear quite large. No statistical information regarding deviations was given. Chen et al. (1987) developed a generalized correlation for vertical flow condensa- tion, which included several effects combined with an asymptotic model. They stated, as did Carey (1992), that their correlation for the shear-dominated regime was also appropriate for horizontal flow but made no comparison with horizontal flow data. Their correlation use the general form of Soliman et al. (1968), but the acceleration terms were neglected and the pressure drop model was replaced by one from Dukler (1960). The final result for the average modified Nusselt number is given in what follows in the discussion of flows in vertical channels, eq. (10.79). Boundary Layer Correlation The most theoretical correlation, based on boundary layer considerations, is that of Traviss et al. (1973). Under its rather stringent assump- tions, this method provides an analytical prediction of the Nusselt number. Before a pressure drop model is assumed, the correlation can be written as Nu = D + · Pr l F 2 (Re l , Pr l ) (10.67) The term D + is the tube diameter scaled by the turbulent length scale, µ l / √ τ w ρ l . A simple force balance indicates the proportionality between the wall shear and the pressure drop, establishing the fact that the annular flow Nusselt number is propor- tional to the square root of the pressure drop per unit length. The denominator of eq. (10.67), F 2 , can be thought of as a dimensionless heat transfer resistance. Guidance as to its evaluation is given in eq. (10.69). Physically, this resistance increases as the dimensionless film thickness increases, as would be expected from conduction arguments. A plot of F 2 versus Re l for various values of Pr l shows that as Re l increases from 0 to 1125 (the value where the fully turbulent region begins), F 2 increases very rapidly. As Re l is increased further, F 2 increases much more slowly. Physically, this occurs because the primary resistance to heat transfer is contained in the laminar sublayer and buffer regions. BOOKCOMP, Inc. — John Wiley & Sons / Page 759 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN SMOOTH TUBES 759 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [759], (41) Lines: 1124 to 1153 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [759], (41) Although the Traviss et al. (1973) analysis was performed after the advent of the simple shear-based correlations, it provides a useful method for understanding them. For relatively small changes in Re l when Re l > 1125, one could reasonably assume a constant value of F 2 at a fixed Prandtl number. If the Prandtl number dependence could be expressed as a power law function, the Nusselt number could then be expressed as Nu = aD + · Pr m l (10.68) where a is a constant. This is exactly the form of the original shear-based correlation of Carpenter and Colburn (1951). Thus, these correlations are justified for a narrow range of conditions by the more theoretically sound analysis of Traviss et al. (1973). Only a few manipulations are required to show the equivalence between the Traviss analysis and the two-phase-multiplier approach. The first important observation is that annular flow is seldom encountered for liquid Reynolds numbers less than 1125. Using the criterion for annular flow that Fr so = 18 [eqs. (10.40a,b)], the correspond- ing equation was solved for the quality above which annular flow could exist with Re l = 1125. The results indicated that the liquid film is seldom so thin that the fully turbulent region is not reached; thus the piecewise definition of F 2 is seldom necessary and its value can be well approximated by the function F 2 10.25Re 0.0605 l · Pr 0.592 l (10.69) If this approximation is used in eq. (10.68) and D + is evaluated with a pres- sure drop correlation using Lockhart and Martinelli’s two-phase liquid multiplier approach, the following equation is obtained for the Nusselt number: Nu = 0.0194Re 0.815 l · Pr 0.408 l φ 2 l (X tt ) (10.70) This is identical in form, and close in value, to the commonly used two-phase multi- plier correlations, such as eq. (10.63). Comparison of Heat Transfer Correlations The following comparisons were developed by Dobson (1994), Dobson et al. (1994a,b), and Dobson and Chato (1998). Details may be obtained from these publications. Gravity-Dominated Correlations Chato’s correlation was developed for stratified flow and was recommended for use at vapor Reynolds numbers of less than 35,000, that is, at low mass fluxes in the stratified flow regime. It was compared with 210 experimental data points that met this criterion and had a mean deviation of 12.8%. The range of applicability of the Jaster and Kosky (1976) correlation is specified by an upper limit of a dimensionless wall shear. The mean deviation between the 213 experimental points that met this criterion and the values predicted was 14.5%, slightly higher than for the simpler Chato (1962) correlation. Although the deviations between the Jaster and Kosky correlation and the present data were sometimes large, BOOKCOMP, Inc. — John Wiley & Sons / Page 760 / 2nd Proofs / Heat Transfer Handbook / Bejan 760 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [760], (42) Lines: 1153 to 1168 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [760], (42) the mean deviation of 14.5% was substantially better than the 37% standard deviation of their own data. The correlations of Chato and Jaster and Kosky were both able to predict most of the experimental data for the wavy flow regime within a range of ±25%. Chato’s analysis implies an essentially constant void fraction which is independent of quality. Jaster and Kosky’s correlation does not predict the variation with quality accurately. Neither accounted for heat transfer in the bottom of the liquid pool. For low mass fluxes, this approach is reasonable. Because no guidelines were given for use of the Rosson and Myers (1965) cor- relation, it was compared against the full database of points that were later used to develop the wavy flow correlation. Although Rosson and Myers attempted to account for forced-convective condensation in the liquid pool at the bottom of the tube, their correlation was actually a poor predictor of the experimental data. The correlation had a mean deviation of 21.3% from the experimental data, almost 10% worse than the simpler Chato or Jaster and Kosky correlations. The most problematic part of the cor- relation seemed to be the prediction of the parameter β, which represents the fraction of the tube circumference occupied by filmwise condensation. At low mass fluxes, this parameter should clearly be related to the void fraction and approach unity as the quality approaches unity. However, the empirical expressions developed by Rosson and Myers do not behave in this manner. The trends were very erratic, particularly for mass fluxes over 25 kg/s · m 2 , where the relationship was not even monotonic. Annular Flow Correlations The annular flow correlations that were selected for comparison with the experimental data encompass at least one member of each of the three broad classes: two-phase multiplier correlations (Shah, 1979; Cavallini and Zecchin, 1974; Dobson, 1994), shear-based correlations (Chen et al., 1987) and boundary layer analyses (Traviss et al., 1973). Of the five correlations, Shah’s and Dobson’s came with specific guidelines for a lower limit of applicability. The Shah correlation should not be used at mass fluxes where the vapor velocity with x = 1 was less than 3 m/s. In all cases this represents a vapor velocity well above the wavy-to-annular transition line on the Taitel–Dukler map. This criterion was selected for each of the correlations, so that they would be compared on an equal basis. The predictions of the Shah correlation agree fairly well with the data, with a mean deviation of 9.1%. Nearly all the data were predicted within ±25%. The most significant deviations occurred for some low Nusselt number data that were in the wavy-annular flow regime, and for some very high-mass-flux, high-quality data. In general, the Shah correlation underpredicted the experimental data. The mean deviation of the Cavallini and Zecchin correlation from the experimental data was 11.6%, slightly higher than that of the Shah correlation. Despite the slightly higher mean deviation, though, the predictions of the Cavallini and Zecchin correla- tion were more correct in trend than those of the Shah correlation. When the Cavallini and Zecchin correlation was in error, it tended to overpredict the experimental data. The largest errors occurred at low qualities because this correlation approaches a value of 2.18 times the single-phase Nusselt number at a quality of zero. BOOKCOMP, Inc. — John Wiley & Sons / Page 761 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN SMOOTH TUBES 761 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [761], (43) Lines: 1168 to 1201 ——— 3.49329pt PgVar ——— Normal Page PgEnds: T E X [761], (43) The mean deviation of the Traviss correlation was 11.8%, slightly higher than the Cavallini and Zecchin correlation. The Traviss correlation tended to overpredict the experimental data, particularly at high qualities, where their empirical correction was used. Without this correction, their correlation would have underpredicted the high- quality data. The Chen correlation was the worst predictor of the annular flow data, with a mean deviation of 23.3%. This correlation significantly underpredicted nearly all the data. The correlation of Soliman (1968) generally predicts lower Nusselt numbers than the Chen correlation. Thus, it would have performed even worse against the data of Dobson. The mean deviation of Dobson’s wavy flow correlation, eq. (10.56), from his experimental data was 6.6%. The mean deviation of his annular flow correlation, eq. (10.65), was 4.5%. The maximum mean deviation of both of these correlations from other experimental data in the literature was 13.7%. One problem with the annular flow correlations that is not apparent in a plot of experimental versus predicted Nusselt numbers concerns their range of applicability. The Nusselt numbers were well above the annular flow predictions at low qualities. As the quality reached about 70% and the flow pattern became fully annular, the predic- tions of the Cavallini and Zecchin correlation agreed very well with the experimental data. These data suggest the need for further development of heat transfer models in the wavy or wavy-annular regions at higher mass fluxes. Recently, Cavallini et al. (2002) suggested a set of correlations for annular, stratified, and slug flow which provide better results for high pressure refrigerants. 10.6.4 Pressure Drop The discussion of pressure drop could take up a chapter of its own. Here only one representative method is given. The pressure drop ∆P in a tube is caused by friction and by the acceleration due to phase change. Souza et al. (1992, 1993) developed an expression for the total pressure drop in a short section ∆z in which the quality can be considered constant at a mean value: − ∆P = 2f lo G 2 ρ l D φ 2 lo ∆z + G 2 x 2 o ρ g α o + (1 − x o ) 2 ρ l (1 − α o ) − x 2 l ρ g α i + (1 − x i ) 2 ρ l (1 − α i ) (10.71) where f lo = 0.0791Re −0.25 lo (10.72) φ 2 lo = 1.376 + C 1 X C 2 tt (1 − x) 1.75 (10.73a) C 1 and C 2 are given in eqs. (10.58) and (10.59) BOOKCOMP, Inc. — John Wiley & Sons / Page 762 / 2nd Proofs / Heat Transfer Handbook / Bejan 762 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [762], (44) Lines: 1201 to 1242 ——— 3.9141pt PgVar ——— Normal Page * PgEnds: Eject [762], (44) Souza and Pimenta (1995) developed another correlation: φ 2 lo = 1 + (Γ − 1)x 1.75 1 + 0.952ΓX 0.4126 tt (10.73b) Γ = ρ l ρ g 0.5 µ g µ l 0.125 (10.73c) Other pressure drop correlations were suggested by Friedel (1979) and Jung and Rademacher (1989), but neither one produced more accurate predictions than Souza’s. Cavallini et al. (2002) proposed a correlation that better predicted the pressure drops for high pressure refrigerants. 10.6.5 Effects of Oil Oil in the refrigerant decreases the heat transfer and increases the pressure drop. Gaibel et al. (1994) discussed these effects. He found that for oil mass fractions ω o < 0.05, the correction factor developed by Schlager et al. (1990) gave acceptable values for the Nusselt number with oil (Nu o ) when applied to the Dobson correlations (Nu) [eqs. (10.56) and (10.65)]: Nu o = Nu · e −3.2ω o (10.74) For the pressure drop with oil (∆P o ), the Souza et al. (1992, 1993) correction factor applied to the pure refrigerant pressure drop (∆P p ) was found acceptable in the same oil concentration range: ∆P o = ∆P p 1 + 12.4ω o − 110.8ω 2 o (10.75) 10.6.6 Condensation of Zeotropes Sweeney (1996) and Sweeney and Chato (1996) correlated the data of Kenney et al. (1994) obtained with Refrigerant 407c, a zeotropic mixture of R-32, R-125, and R-134a (23, 25, and 52% by mass), in a smooth tube. They found that the Nusselt numbers for zeotropic mixtures (Nu m ) could be predicted by the following simple modification of the Dobson correlation (Nu) [eq. (10.65)] for the annular flow regime: Nu m = 0.7 G 300 0.3 · Nu (10.76) For the wavy regime, the mixture Nusselt number is obtained by a similar modifica- tion of the Dobson correlation (Nu) [eq. (10.56)]: Nu m = G 300 0.3 · Nu (10.77) BOOKCOMP, Inc. — John Wiley & Sons / Page 763 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION IN SMOOTH TUBES 763 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [763], (45) Lines: 1242 to 1284 ——— 4.89925pt PgVar ——— Normal Page PgEnds: T E X [763], (45) where the mass flux G is in kg/s · m 2 . These correlations cannot be assumed to be generally applicable to zeotropes without additional data on other zeotropes, but they do indicate that the equations represent the underlying physical phenomena well. 10.6.7 Inclined and Vertical Tubes Inclining the tube from the horizontal will affect only the gravity-dominated flows, (i.e., stratified and wavy patterns) significantly. For the shear-dominated annular flows, the correlations are essentially independent of tube orientation. Chato (1960) studied both analytically and experimentally the effects of a downward inclination of a condenser tube with stratified flows. He found improvement in the heat transfer up to about a 15° inclination, caused by the reduction in depth of the bottom conden- sate pool. However, this improvement decreases at increasing angles as the vertical orientation is approached because of the thickening of the condensate layer on the wall as it traverses longer distances before reaching the bottom pool. It can be shown from eqs. (10.43) and (10.48) that if the L/D ratio of the tube is greater than 8.3, the horizontal tube will have better heat transfer. It is obvious that an upward inclination of the tube is counterproductive because gravity will retard the liquid flow, reducing the heat transfer. Chen et al. (1987) analyzed annular film condensation in a vertical tube and proposed the following approximate correlation for the average Nusselt number for complete condensation in the tube: Nu d = Re −0.44 T + Re 0.8 T · Pr 1.3 l 1.718 × 10 5 + C ·Pr 1.3 l · Re 1.8 T 2075.3 0.5 (10.78) where Nu d = h T k l ν 2 l g 1/3 Re T = 4m µ l πD C = 0.252µ 1.177 l µ 0.156 g D 2 g 0.667 ρ 0.553 l ρ 0.78 g (dimensionless) Chen et al., contended that similar derivations can be applied to horizontal annular flows with the following result: Nu d = 0.022 √ C ·Pr 0.65 l · Re 0.9 T (10.79) However, they did not verify this correlation with comparisons to experimental data. By the same argument, it can be suggested that the Dobson (1994) correlation of eq. (10.65) can be used for vertical, downward flow tubes at high mass fluxes. Although condensation in upward flow is worse than in horizontal or downward flow, it does occur in reflux condensers. Chen et al. (1987) treated this case in some detail. BOOKCOMP, Inc. — John Wiley & Sons / Page 764 / 2nd Proofs / Heat Transfer Handbook / Bejan 764 CONDENSATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [764], (46) Lines: 1284 to 1291 ——— 0.726pt PgVar ——— Normal Page PgEnds: T E X [764], (46) 10.7 ENHANCED IN-TUBE CONDENSATION 10.7.1 Microfin Tubes Most evaporators and condensers of new unitary refrigeration and air-conditioning equipment are manufactured with microfin tubes. The microfin tube dominates uni- tary equipment design because it provides the highest heat transfer with the lowest pressure drop of the commercially available internal enhancements (Webb, 1994). Cavallini et al. (2000) quotes an 80 to 180% heat transfer enhancement over an equiv- alent smooth tube with a relatively modest 20 to 80% increase in pressure drop. To- gether, R-134a, R-22, and replacements for R-22 replacements constitute by mass nearly all the refrigerants used in unitary products (Muir, 1989). As a result, much of the predictive development for convective condensation in microfin tubes has been focused on R-134a, R-22, and replacements for R-22 replacements. Figure 10.14 shows the cross section and characteristic dimensions of a microfin tube. The outside diameter (D o ) of commercially available microfin tubes ranges from 4 to 15 mm. The root diameter (D r ) is depicted in Fig. 10.14. Microfin tubes Figure 10.14 Cross section of microfin tube. . solutions. The final correlation separates the heat transfer by film condensation in the upper part of the horizontal tube from the forced-convective heat transfer in the bottom pool: Nu = 0.23Re 0.12 vo 1. primary resistance to heat transfer is contained in the laminar sublayer and buffer regions. BOOKCOMP, Inc. — John Wiley & Sons / Page 759 / 2nd Proofs / Heat Transfer Handbook / Bejan CONDENSATION. theoretical hypothesis is that the heat transfer process in annular two-phase flow is similar to that in single- phase flow of the liquid (through which all the heat is transferred), and thus their ratio may