A general correlation for heat transfer during saturated boiling with flow across tube bundles.INTRODUCTION Heat exchangers heat exchanger Any of several devices that transfer heat from a hot to a cold fluid. In many engineering applications, one fluid needs to be heated and another cooled, a requirement economically accomplished by a heat exchanger. consisting of bundles of horizontal tubes with boiling on the outer surface of the tubes are widely used in the industry. Examples are refrigerated re·frig·er·ate tr.v. re·frig·er·at·ed, re·frig·er·at·ing, re·frig·er·ates 1. To cool or chill (a substance). 2. To preserve (food) by chilling. liquid coolers and kettle kettle, oval depression found in glacial moraines, which are landforms made up of rock debris. When a glacier melts and draws away from an area, a block of ice may break off and be covered by earth and rock. reboilers. The boiling liquid may be flowing upwards or downwards. The outer surfaces of the tubes may be plain or enhanced. This paper is concerned only with upward flow across plain tubes. An evaporator/boiler involves one or more of the following modes of heat transfer: * subcooled boiling * saturated saturated /sat·u·rat·ed/ (sach´ah-rat?ed) 1. denoting a chemical compound that has only single bonds and no double or triple bonds between atoms. 2. unable to hold in solution any more of a given substance. boiling prior to dryout * post-dryout heat transfer The author has previously presented a general correlation for subcooled boiling heat transfer (Shah Shah is a Persian term for a monarch (ruler) that has been adopted in many other languages. This term is a Post Islamic Revolution term for monarchs in Iran which is replaced by valie faghih or Supreme Leader. 1984, 2005). This paper is concerned exclusively with saturated boiling at vapor qualities Steam Engines use water vapor to drive pistons which effects work through movement. The quality of steam can be quantitatively described. Vapor quality is a quantitative description of the usefulness of a vapor to do work. from zero upwards, prior to dryout. Because of the practical importance of such heat exchangers, many experimental studies have been conducted to observe and measure heat transfer on tube bundles and single tubes with cross flow. Further, many correlations for predicting heat transfer have been published. Many of these experimental studies and prediction methods have been reviewed fairly recently by Browne and Bansal (1999) and Cascario and Thome (2001). Study of this literature shows that no well-validated general method for predicting heat transfer in saturated boiling is available in the open literature. The study reported here was undertaken to fill this gap. It is agreed by most researchers that correlations for bundle mean heat transfer cannot be generally applicable. For reliable design, one has to use models such as that of Brisbane Brisbane (brĭz`bən), city (1991 pop. 1,145,537), capital of Queensland, E Australia, on the Brisbane River above its mouth on Moreton Bay. et al. (1980) that perform calculations of heat transfer coefficients The heat transfer coefficient is used in calculating the convection heat transfer between a moving fluid and a solid in thermodynamics. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). of each tube from bottom to top in terms of the local flow, quality, and heat flux flux In metallurgy, any substance introduced in the smelting of ores to promote fluidity and to remove objectionable impurities in the form of slag. Limestone is commonly used for this purpose in smelting iron ores. . Hence, the author's efforts were directed toward developing a correlation applicable to individual tubes in bundles. Presented here is a dimensionless correlation that shows good agreement with data for single tubes and tube bundles from many sources covering a wide range of parameters, including seven fluids (water, n-pentane, R-11, R-12, R-113, R-123, and R-134a), reduced pressures In thermodynamics, the reduced pressure of a fluid is defined as its actual pressure divided by its critical pressure. v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates v.tr. 1. To put or bring into causal, complementary, parallel, or reciprocal relation. 2. with a mean deviation mean deviation n. In a statistical distribution, the average of the absolute values of the differences between individual numbers and their mean. of 15.2%. The results of comparisons of the new correlation with test data are presented and discussed. TRENDS SHOWN BY EXPERIMENTAL DATA The reports on the effect of quality on heat transfer are apparently conflicting. A number of researchers have reported large increases in heat transfer coefficients on a slight increase of quality above zero. Examples are Bitter (1973), Polley et al. (1980), and Burnside and Shire Shire or Shiré (both: shē`rā), river, c.250 mi (400 km) long, flowing from the southern end of Lake Nyasa, Malawi, SE Africa, to the Zambezi River in central Mozambique. It is navigable to Nsanje. (2005). On the other hand, many researchers report that quality had no effect on heat transfer. Examples are Cotchin and Boyd Boyd may refer to any of the following: People See Boyd (surname) The name Boyd has Irish roots that originally meant "blondheaded". Fictional characters
Johannes Vilhelm Jensen et al. (1992) found no effect of quality except at very low qualities. Burnside and Shire (2005) reported a modest increase of heat transfer coefficient with quality. Chien and Wu (2004) found a significant increase in heat transfer with increasing quality at higher heat fluxes. Hwang Hwang can refer to:
Various Bantu-speaking peoples inhabiting southern Tanzania, northern Mozambique, and southern Malawi. In the colonial era the Yao were prominent as slave traders. They were never completely united but lived as small groups ruled by chiefs. (1986) found the heat transfer coefficient to increase with quality at low heat flux. Most of the studies show that at high heat fluxes, the heat transfer coefficient depends on heat flux only and is about the same as that during pool boiling on a single tube; mass flow rate and quality have no effect. Examples are Cotchin and Boyd (1992), Grant et al. (1983), Abbot and Comley (1938), and Webb and Chien (1994). However, methods for determining the heat flux beyond which this occurs are not available. Further, there is the question about which pool boiling correlation to use. The present research proposes answers to these questions. Many researchers report an increase in the heat transfer coefficient with increasing mass flow rates, for example Hwang and Yao (1986). On the other hand, no effect of mass flow rate is reported by many authors, as noted in the previous paragraph. From the above, it appears that the different trends reported by various researchers occur under different combinations of parameters. What is needed is to find under what combinations of parameters the various trends occur, i.e., to define the regimes in which particular trends occur. The next requirement is to find methods to predict heat transfer coefficients in the various regimes. This is what the research reported here attempts to do. THE NEW CORRELATION This author studied and analyzed an·a·lyze tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es 1. To examine methodically by separating into parts and studying their interrelations. 2. Chemistry To make a chemical analysis of. 3. test data from many sources. As a result, three regimes of heat transfer were identified and separate equations were developed for heat transfer in each regime, as is given in the following. Heat Transfer Regimes Three regimes of heat transfer were identified: 1. Regime I (Intense Boiling Regime). In this regime, heat transfer depends only on heat flux; mass velocity and vapor quality have a negligible  This article or section is written like a personal reflection or and may require .Please [ improve this article] by rewriting this article or section in an . effect. This regime occurs when [Y.sub.IB]>0.0008. (1) 2. Regime II (Convective Boiling Regime). In this regime, both heat flux and mass velocity have an effect on heat transfer; vapor quality has a negligible effect. Thus, both nucleate boiling This article or section is in need of attention from an expert on the subject.Please help recruit one or [ improve this article] yourself. See the talk page for details. and convection contribute to heat transfer. This regime occurs when 0.00021<[Y.sub.IB][less than or equal to]0.0008. (2) 3. Regime III (Convection Regime). In this regime, heat transfer is affected by mass velocity and vapor quality; heat flux has a negligible effect. This suggests that bubble A bit in bubble memory or a symbol in a bubble chart. nucleation nu·cle·a·tion n. 1. The beginning of chemical or physical changes at discrete points in a system, such as the formation of crystals in a liquid. 2. The formation of cell nuclei. is completely suppressed sup·press tr.v. sup·pressed, sup·press·ing, sup·press·es 1. To put an end to forcibly; subdue. 2. To curtail or prohibit the activities of. 3. . This regime occurs when [Y.sub.IB][less than or equal to]0.00021. (3) The boiling intensity parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind. [Y.sub.IB] is defined as [Y.sub.IB] = [F.sub.pb]Bo[Fr.sup.0.3] (4) where [F.sub.pb] = [h.sub.pb,actual]/[h.sub.cooper]. (5) The variable [h.sub.cooper] is the pool boiling heat transfer coefficient calculated by the simplified Cooper correlation, Equation 6: [h.sub.cooper] = 55.1[q.sup.0.67][p.sub.r.sup.0.12][( - log[p.sub.r]).sup.[ - 0.55]][M.sup.[ - 0.55]] (6) The variable [h.sub.pb,actual] is the same as [h.sub.cooper] unless pool boiling test data is available for the tubes to be used in the heat exchanger; in that case, [h.sub.pb,actual] is calculated from the test data. Thus, [F.sub.pb] = 1 unless test data for the actual tubes used or to be used are available. Figures 1-4 illustrate the data in the three regimes. [FIGURE 1 OMITTED] [FIGURE 2 OMITTED] [FIGURE 3 OMITTED] [FIGURE 4 OMITTED] Heat Transfer Equations In regime I, [h.sub.TP] = [F.sub.pb][h.sub.cooper]. (7) In regime II, [phi] = [[phi].sub.0]. (8) In regime III, [phi] = [2.3/[[Z.sup.0.08][Fr.sup.0.22]]]. (9) The parameter Z was introduced by this author to correlate heat transfer during film condensation in tubes (Shah 1979). As heat transfer during film condensation in tubes is due to convective effects only, it was felt that it may be applicable in this regime. It is defined as Z = [([1 - x]/x).sup.0.8][p.sub.r.sup.0.4]. (10) In the heat transfer equations above, [phi] = [h.sub.TP]/[h.sub.LT], (11) where [[phi].sub.0] is the value of [phi] when x = 0. It is the highest of that calculated by the following relations: [phi] = 443[Bo.sup.0.65][F.sub.pb] (12) [[phi].sub.0] = 31[Bo.sup.0.33][F.sub.pb] (13) [[phi].sub.0] = 1 (14) With [F.sub.pb] = 1, Equations 12 and 13 are the same as that developed by this author through analysis of varied data from many sources for flow across single tubes at zero vapor quality (Shah 2005). The variable [h.sub.LT] is the heat transfer coefficient for all mass flowing as a liquid. It is calculated by the following equation (Shah 1984): [h.sub.LT]D/k = 0.21[[Re].sub.L.sup.0.62][Pr.sup.0.4] (15) All fluid properties are calculated at the saturation saturation, of an organic compound saturation, of an organic compound, condition occurring when its molecules contain no double or triple bonds and thus cannot undergo addition reactions. temperature. It will be noted that Z cannot be calculated with Equation 10 at x = 0 and hence Equation 9 is inapplicable in·ap·pli·ca·ble adj. Not applicable: rules inapplicable to day students. in·ap at x = 0. This does not pose a problem, as there are no two-phase two-phase adj. Electricity Relating to two alternating currents with phases differing by 90°. convective effects at zero vapor quality; the heat transfer coefficient is calculated with Equations 12-14, which apply at x = 0. There may be a question about the continuity in regime III between x = 0 and qualities slightly higher than 0. The available data in this range showed adequate agreement with the present correlation. Further study is desirable when more data become available, though its practical interest will be limited, as only a very short length is involved. DEVELOPMENT OF THE CORRELATION The development of this correlation involved many trials and errors. A brief description of the process is given here. As noted previously, study of experimental data from many sources indicated the three regimes of boiling. In regime I, heat transfer depends only on heat flux and is the same as in pool boiling. In regime II, both heat flux and mass flux have an effect. As nucleate boiling is suppressed by convective effects of velocity, the author initially thought that the boundary between these regimes would depend on the boiling number, Bo, being the dimensionless ratio of heat flux to mass flux. Examination of data showed that the boundary between the regimes has additional dependence on the mass flux. The Froude number Froude number The dimensionless quantity U(gL)-1/2, where U is a characteristic velocity of flow, g is the acceleration of gravity, and L is a characteristic length. , Fr, was chosen as the dimensionless number dimensionless number A number representing a property of a physical system, but not measured on a scale of physical units (as of time, mass, or distance). Drag coefficients and stress, for example, are measured as dimensionless numbers. to represent the influence of mass flux. Data points showing dependence only on heat flux and those showing dependence on both heat flux and mass flux were plotted on a Bo vs. Fr graph. The boundary between the two regimes was found to be represented by the following equation: Bo[Fr.sup.0.3] = 0.0008 (16) The left-hand side left-hand side n → izquierda left-hand side left n → linke Seite f left-hand side n → lato or of this equation is the intensity of boiling parameter [Y.sub.IB] at [F.sub.pb] = 1. The factor [F.sub.pb] was added after considering all data, specially those of Robinson and Thome (2004). Thus, Equation 1 was established as the boundary between regimes I and II. In regime III, heat flux has no effect. Examination of data showed that the boundary between regimes II and III is at [Y.sub.IB] = 0.00021. Having established the boundaries between the three regimes, equations for heat transfer in these regimes were sought. The choice for regime I has been thoroughly discussed in the foregoing. In regime II, heat transfer depends on heat flux and mass flux while vapor quality has no effect. The author's correlation for boiling in tube bundles at zero vapor quality (Shah 2005), Equations 12-14, is therefore applicable. In regime III, heat transfer increases with increasing mass flux and vapor quality while heat flux has no effect. Thus, the increase of heat transfer above the single-phase sin·gle-phase adj. Producing, carrying, or powered by a single alternating voltage. heat transfer is purely due to convective effects. The author's first attempt was to calculate two-phase heat transfer using a single-phase heat transfer correlation with the velocity in the Reynolds number Reynolds number [for Osborne Reynolds], dimensionless quantity associated with the smoothness of flow of a fluid. It is an important quantity used in aerodynamics and hydraulics. of the two-phase mixture based on homogeneous The same. Contrast with heterogeneous. homogeneous - (Or "homogenous") Of uniform nature, similar in kind. 1. In the context of distributed systems, middleware makes heterogeneous systems appear as a homogeneous entity. For example see: interoperable network. flow. This attempt failed. The next attempt was to plot j against Z, the parameter used in the author's successful correlation for condensation in tubes (Shah 1979), the thinking being that condensation heat transfer is also purely convective. The plots showed that an additional parameter involving mass flux was needed. The Froude number was tried. This approach was successful. After several iterations, Equation 9 was obtained as the correlation for regime III. COLLECTION OF TEST DATA Efforts were made to collect data for as many fluids and as wide a range of parameters as possible for horizontal tube bundles as well as single tubes with upward flow of boiling fluid. While there are a large number of such studies, most of them do not provide analyzable an·a·lyze tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es 1. To examine methodically by separating into parts and studying their interrelations. 2. Chemistry To make a chemical analysis of. 3. data, as has been noted by Casciaro and Thome (2001). For the data to be analyzable, mass flow, heat flux, and quality at the tube location should be known. Most of the studies provide only the heat flux and heat transfer coefficient. The analyzable studies found and used here are listed in Tables 1 and 2 for single tubes and bundles, respectively. A couple of studies that provided analyzable data were not considered due to reasons discussed later in this paper.
Table 2. Summary of the Data for Tube Bundles and Results of Comparison
with the Present Correlation
Researcher D, mm Bundle Tube Fluid pr([dagger])
Geometry Material
(Data at) (P/D)
Roser et 19.05 Staggered Cu n-pentane 0.0089
al.
(1999)* 17 5 (1.33)
Cumo et 13.6 Staggered, SS R-12 0.189
al. 5 3
(middle
tube
heated)
(1980) (1.25)
Polley et 25.4 6 6 SS R-113 0.029
al. (middle
tube in top
row)
(1980) (1.244)
Hwang and 19.1 16 3 SS 304 R-113 0.041
Yao (1986) (middle (1.5)
tube of row
13)
Chien and 15.9 Staggered 5 (1.5) R-134a 0.102
Wu (2004) 3
(middle)
R-123 0.017
0.030
Jensen and 7.9 Inline 27 SS R-113 0.060
Hsu (1988) 5
(1.3)
Robinson 18.9 Staggered 8 Copper R-134a 0.084
and Thome 3
(2004)*
(1.17)
Cornwell 25.4 Inline 15 Brass R-113 0.029
and Scoones 6
(1988)
(1.25)
Webb and 16.8 Staggered Copper R-113 0.01
Chien
(1994)
(1.42) 0.021
R-123 0.019
0.038
Burnside 19.1 Inline 17 Cu-Ni R-113 0.03
and Shire 5
(2005)
(1.33)
Jensen et 19.1 Staggered Copper R-113 0.059
al. (1992) 15 5
(middle
column)
(1.17) 0.176
Copper R-113 0.059
7.9 1.17 0.005
25.4 1.5 0.189
Researcher G,([dagger]) q,([dagger]) X([dagger])
kg/[m.sup.2]s kW/[m.sup.2]
Roser et 30 20 0
al.
(1999)* 42 0.26
Cumo et 41 296 0.13
al.
(1980)
Polley et 450 17 0.002
al.
(1980) 0.017
Hwang and 132 3 0.014
Yao (1986)
80 0.062
Chien and 10 10 0.07
Wu (2004)
40 50 0.24
10 10 0.02
40 50 0.10
Jensen and 100 6.3 0.001
Hsu (1988)
675 37.8 0.184
Robinson 5 2 0.1
and Thome
(2004)*
39 35 0.81
Cornwell 150 6 0
and Scoones
(1988)
36 0.35
Webb and 7.9 13 0.07
Chien
(1994)
37.0 55 0.88
7.7 13 0.06
15.0 54 0.96
Burnside 211 10 0.004
and Shire
(2005)
622 65 0.25
Jensen et 51 10 0
al. (1992)
500 40 0.74
217 10 0
40 0.106
1.7 2 0
679 296 0.88
Researcher [Re.sub.L]([dagger]) 1/Z([dagger]) Bo
[10.sup.4]
([dagger])
Roser et 1276 0 16
al.
(1999)* 2.9 34
Cumo et 2297 0.42 534
al.
(1980)
Polley et 22165 .031 2.6
al.
(1980) .164
Hwang and 5497 0.014 0.12
Yao (1986)
0.016 0.41
Chien and 688 0.31 13.1
Wu (2004)
2752 0.99 261
482 0.18 14.7
1926 0.70 294.1
Jensen and 1980 0.01 0.67
Hsu (1988)
13326 0.93 7.6
Robinson 392 0.46 9
and Thome
(2004)*
3057 48.0 123
Cornwell 0 2.7
and Scoones
(1988)
7354 2.5 16.2
Webb and 184 0.28 24.0
Chien
(1994)
1077 23.7 430
348 0.41 51
819 47.0 408
Burnside 7800 0.06 1.0
and Shire
(2005)
23235 1.7 12.9
Jensen et 2452 0 3.3
al. (1992)
34930 7.2 32.8
10233 0 3.3
0.56 13.3
184 0 0.12
23235 48 534
Researcher [Y.sub.IB] Deviation,** No. of
104([dagger]) ([double Data
dagger]) % Points
Roser et 4 11.1 22
al.
(1999)* 9 -10.4
Cumo et 124 22.6 1
al.
(1980) 22.6
Polley et 1.9 37.3 4
al.
(1980) -37.3
Hwang and 0.6 18.8 28
Yao (1986)
6.8 -17.1
Chien and 5.6 20.8 30
Wu (2004)
30.5 -20.8
4.4 12.7 25
27.4 7.9
Jensen and 1.2 15.4 56
Hsu (1988)
6.9 9.6
Robinson 4.8 18.2 58
and Thome
(2004)*
21.1 -16.5
Cornwell 1.0 13.7 35
and Scoones
(1988)
6.1 10.5
Webb and 5.9 11.4 90
Chien
(1994)
34.8 0.2
6.6 10.3 63
36.5 1.4
Burnside 1.3 22.8 70
and Shire
(2005)
12.9 22.1
Jensen et 3.0 16.4 61
al. (1992)
8.8 -3.5
1.7 9.2 16
16.9 -9.2
0.5 15.6 559
124 -0.03
* Tubes heated by fluid; electrically heated tubes in all other tests.
([dagger]) In each cell, the upper line has the minimum value of the
parameter and the lower line has the maximum value.
** Mean absolute deviation
([double dagger]) Average deviation
COMPARISON OF CORRELATION WITH DATA The data listed in Tables 1 and 2 were compared to the present correlation. Where the researchers had also performed pool boiling measurements on the same tubes used for flow boiling tests, [F.sub.pb] was calculated based on these pool boiling data. The average values of [F.sub.pb] from such studies are included in Table 3. Where the researchers did not do pool boiling tests, [F.sub.pb] = 1 was used in analyzing their data. Vapor quality at the middle of the tube was used in calculations.
Table 3. Comparison of Data for Pool Boiling on Tubes with the
Simplified Cooper Correlation, Equation 6
Tube
Data Source Fluid Reduced Material Diameter, Rp,
Pressure mm [mu]m
Bitter R-11 0.021 Porcelain, 15.0 6
(1973) nickel
coated
Wallner R-11 0.023 Nickel 10.0 3
(1971) coated
ceramic
Singh et al. R-12 0.087 SS 9.5
(1985)
Jensen et R-113 .029 Cu 19.1
al. (1992)
Wege and R-113 0.05 SS 12.7
Jensen
(1984)
0.079
Hwang and R-113 0.029 SS 19.1
Yao (1986)
Marto and R-113 0.021 Cu 15.9
Anderson
(1992)
Webb and R-113 0.010 Cu 16.8
Chien
(1994)
0.021
Memory et R-114 0.031 Cu 15.9
al. (1995)
Webb and R-123 0.02 Cu 16.8
Chien
(1994)
0.038
Robinson and R-134a 0.084 Cu 18.9 <1 - >
Thome 7
(2004)
Gupta et al. Water 0.0046 SS 19.1
(1995)
Singh et al. Water 0.0046 SS 12.7
(1983)
Dieselhorst Water 0.0046 SS 6.0
(1978)
Cornwell and R-113 0.021 Brass 25.4
Scoones
(1988)
Chien and Wu R-123 0.017 Copper 19.05
(2004)
0.030
R-134a 0.102
Pool Boiling
Test Data
Data Source Data Average [F.sub.pb] =
Correlation* [h.sub.pb,actual]/[h.sub.cooper]
a n
Bitter 1.17
(1973)
Wallner 191 0.72 1.03
(1971)
Singh et al. 1.23
(1985)
Jensen et 1.0
al. (1992)
Wege and 1.14
Jensen
(1984)
Hwang and 224 0.67 1.1
Yao (1986)
Marto and 175 0.745 1.23
Anderson
(1992)
Webb and 1.1
Chien
(1994)
Memory et 1.19
al. (1995)
Webb and 1.17
Chien
(1994)
Robinson and 1008 0.66 2.7
Thome
(2004)
Gupta et al. 1.0
(1995)
Singh et al. 1.44
(1983)
Dieselhorst 1.0
(1978)
Cornwell and 1.0
Scoones
(1988)
Chien and Wu 453 0.48 1.25
(2004)
516 0.48
1010 0.49 1.37
* Correlated by h = [alpha] . [q.sub.n], with h in W/[m.sub.2] [degrees]C and q in kW/[m.sub.2].
Figures 1-7 show the comparison of some representative data with the present correlation. Figures 1 and 2 show some data of Webb and Chien (1994) in regime I ([Y.sub.IB] > 0.0008)--Figure 1 has data for R-113 while Figure 2 has data for R-123. It is seen that the heat transfer coefficient depends only on heat flux; neither vapor quality nor mass velocity affect heat transfer even though they vary over a considerable range. Figure 3 includes data from two test runs with R-113, one in regime II and one in regime III. Figure 4 has data for R-11 at low heat flux, showing the sharp increase in heat transfer coefficient with a small increase in quality characteristic of regime III. It is seen that the new correlation predicts the trends correctly and the quantitative agreement is also good. While Figures 1-4 have data only for halocarbon hal·o·car·bon n. A compound, such as a fluorocarbon, that consists of carbon and one or more halogens. halocarbon refrigerants Chemical refrigerants are assigned an R number(sometimes the label replaces it with the word Freon) which is determined systematically according to molecular structure. The following is a list of refrigerants with their R numbers, IUPAC chemical name, molecular formula, and CAS number. , Figure 5 has data for pentane pen·tane n. Any of three colorless, flammable isomeric hydrocarbons, C5H12, derived from petroleum and used as solvents. , an organic chemical. This gives confidence in the correlation's applicability to organics. Figure 6 shows comparison with data for R-12 from two sources. The good agreement here gives further confidence in the general applicability to all halocarbon refrigerants. Figure 7 is of special interest as it shows comparison of the present correlation with data for water. This good agreement and the fact that the properties of water differ vastly from those of refrigerants and organics encourages the hope that the correlation may be applicable to all Newtonian, non-metallic fluids. However, this optimism should be tempered with much caution, as all these water data are from tests on single tubes and at zero to slightly positive qualities. [FIGURE 5 OMITTED] [FIGURE 6 OMITTED] [FIGURE 7 OMITTED] Tables 1 and 2 summarize sum·ma·rize intr. & tr.v. sum·ma·rized, sum·ma·riz·ing, sum·ma·riz·es To make a summary or make a summary of. sum the results of comparison of the correlation with all data for single tubes and tube bundles, respectively. The definition of deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured. 2. is [delta] = [[predicted [h.sub.TP] - measured [h.sub.TP]]/[measured [h.sub.TP]]]. (17) The mean absolute deviation In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is the value of either the median or the mean of the data set. , [[delta].sub.mean], of a data set is defined as [[delta].sub.mean] = [[[summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) ](Absolute([delta]))]/N], (18) where N is the number of data points in the set. The average deviation of a data set is calculated using the actual deviations of the data points. It is seen that a very wide range of data from numerous sources is predicted with a mean absolute deviation of only 15.2%. These results and some aspects of the new correlation are discussed in the following section. DISCUSSION Choice of Single-Phase Correlation In the article on subcooled boiling during cross flow (Shah 2005), the author reported that several correlations for single-phase heat transfer were tried. Among these, the present Equation 15, the Holman Holman may refer to:
1 River, c.600 mi (970 km) long, issuing as the Ashuanipi River from Ashuanipi Lake, SW Labrador, N.L., Canada, and flowing in an arc north, then southeast through a series of lakes to Churchill Falls and McLean Canyon. and Bernstein Bern·stein , Leonard 1918-1990. American conductor and composer who wrote numerous choral and symphonic works, including Kaddish (1963), and musicals, notably On the Town (1944) and West Side Story (1957). (1977) gave comparable mean deviations considering all data sets. However, the results were best when using Equation 15 at a Reynolds number above 700 and the Holman correlation below 700. In the present study, it was found that the mean deviations are minimized by using Equation 15 throughout, including at Reynolds numbers lower than 700. The calculation of the single-phase heat transfer coefficient is required only when [Y.sub.IB] < 0.0008. The number of data points for [Re.sub.L] < 700 together with [Y.sub.IB] < 0.0008 is small. Therefore, the present recommendation to use Equation 15 at all Reynolds numbers needs to be verified ver·i·fy tr.v. ver·i·fied, ver·i·fy·ing, ver·i·fies 1. To prove the truth of by presentation of evidence or testimony; substantiate. 2. with more data. Calculation of Pool Boiling Heat Transfer Coefficient The new correlation for flow boiling presented here requires the calculation of the pool boiling heat transfer coefficient and uses the simplified Cooper correlation for this purpose. The reasons for this choice are discussed below. A very large number of correlations have been proposed for pool boiling heat transfer. Most of them are based on small amounts of data and have had little validation See validate. validation - The stage in the software life-cycle at the end of the development process where software is evaluated to ensure that it complies with the requirements. . However, those of Stephan Stephan is a male given name, a variant of Stephen. This page or section lists people with the given name Stephan. If an internal link for a specific person referred you to this page, you may wish to add the surname to that wikilink. and Abdelsalam (1980), Mostinski (1963), and Cooper (1984) have had considerable validation. Among these three, that of Cooper was developed from the largest database covering a very wide range of liquids and operating conditions. The full Cooper correlation is [h.sub.pb] = 55.1[C.sub.material][q.sup.0.67][p.sub.r.sup.(0.12 - 0.211log[R.sub.p])][( - log [p.sub.r]).sup.[ - 0.55]][M.sup.[ - 0.55]]. (19) The variable [C.sub.material] is 1.7 for copper cylinders and is equal to 1 for all other materials and shapes. Cooper stated that there was only indirect evidence supporting this factor of 1.7 and it was not conclusive Determinative; beyond dispute or question. That which is conclusive is manifest, clear, or obvious. It is a legal inference made so peremptorily that it cannot be overthrown or contradicted. . He further stated that this factor appears to be illogical and may be changed by new data. [R.sub.p] is the surface roughness in [mu]m; a value of 1 Am is recommended if the surface roughness is not known. With [C.sub.material] = 1 and [R.sub.p] = 1 [micro]m, Equation 19 becomes [h.sub.cooper] = 55.1[q.sup.0.67][p.sub.r.sup.0.12][( - log [p.sub.r]).sup.[ - 0.55]][M.sup.[ - 0.55]]. (6) In this paper, this is called the simplified Cooper correlation. This is the form in which the Cooper correlation is most commonly used. Many of the flow boiling studies whose data have been analyzed here also contain pool boiling data on the same tubes. These data were compared with Equation 6. Some readily available studies on bundles with recirculation Noun 1. recirculation - circulation again circulation - the spread or transmission of something (as news or money) to a wider group or area also included pool boiling data on the same tubes. These data were also analyzed. The results are shown in Table 3. It is noted that most of the data are in satisfactory agreement. The one notable exception is the data of Robinson and Thome (2004) for copper tubes, whose values are much higher. These data agree with Equation 18 when using the 1.7 factor for copper cylinders and assuming a surface roughness of 5.4 [thorn thorn, in botany thorn, sharp-pointed projection on some plants, usually protective in function. Botanically, thorns are distinguished as modified stems (as in the honey locust and hawthorn) from spines, which are modified leaves (as in the barberry), and ]m; the actual values measured varied from less than 1 to greater than 7. However, all other data sets for copper tubes shown in Table 3 are in reasonable agreement with the simplified Cooper correlation, Equation 6. Thus, it appears that the 1.7 factor for copper cylinders is applicable only rather rarely. It will also be noted in Table 3 that deviations from the Cooper correlation are not related to the tube material or the type of fluid. From the foregoing, it may be concluded that the simplified Cooper correlation, Equation 6, can be relied upon to make reasonable predictions of heat transfer for all materials with a high probability. There is a low probability that some commercial surfaces may have exceptionally favorable fa·vor·a·ble adj. 1. Advantageous; helpful: favorable winds. 2. Encouraging; propitious: a favorable diagnosis. 3. microstructure mi·cro·struc·ture n. The structure of an organism or object as revealed through microscopic examination. microstructure Noun a structure on a microscopic scale, such as that of a metal or a cell for nucleation and it may underpredict heat transfer for such cases. Designs should be based on the most probable case; hence, Equation 6 should be preferred to Equation 18. The use of Equation 18 would have resulted in gross overprediction of all data for copper tubes except those of Robinson and Thome (2004). While the results with the simplified Cooper correlation given in Table 3 are fairly good, further evaluation of this and other pool boiling correlations is desirable to find/develop the most reliable correlation. If a correlation better than Equation 6 is found or developed, it should be used in the present correlation instead of Equation 6. Consequence of Using [F.sub.pb] = 1 in Data Analysis If [F.sub.pb] is taken to be 1 for all data analyzed, instead of the values from pool boiling tests listed in Table 3, the mean deviations of all data sets will still be in acceptable range except for three data sets. The data of Robinson and Thome (2004) for R-134a will be greatly underpredicted. Indeed, it was the study of this data set that prompted this author to introduce [F.sub.pb] into the correlation. The other two not in acceptable range are the data of Chien and Wu (2004) for R-134a and Singh For the fictional global crime syndicate, see . Singh is a Sanskrit word meaning "lion". It is used as a common surname and middle name in North India by many communities, especially by the Sikhs and the Rajputs. et al. (1983) for water, which will be underpredicted by about 40%. Thus, only three of the many data sets analyzed here show large deviation from the present correlation using [F.sub.pb] = 1. This is very satisfying, as heat exchanger manufacturers are unlikely to be able to perform pool boiling tests on the tubes to be used in the heat exchanger. These results show that reliable designs can be done in most cases by using the Cooper correlation, Equation 6. It is also to be noted that in Table 3, the predictions of Equation 6 are always equal to or lower than the test measurements. Hence, any errors resulting from its use are likely to be on the safe side. Analyzable Data Sets Not Considered Cornwell et al. (1980) performed tests on a 25 mm wide section of a 17-row tube bundle. These data have also been published in other papers and have been widely quoted. However, Andrews Noun 1. Andrews - United States naturalist who contributed to paleontology and geology (1884-1960) Roy Chapman Andrews and Cornwell (1987) concluded that these data and other data from such narrow test sections are not accurate, being too high. As the person who performed those tests considers the data unreliable, the data were not included in the present study. The other analyzable data not considered are those of Fujita Fujita (藤田) is a common family name in Japan. It may also refer to the following.
n. A deficiency; a flaw. shortcoming Noun a fault or weakness Noun 1. of the present correlation. However, it may be mentioned that there is some indication of measurement problems. Their single-phase measurements often show a large decrease in heat transfer coefficient along the height, those at the top tube being up to 70% lower than those at the bottom tube. This unusual trend suggests the possibility of instrumentation instrumentation, in music: see orchestra and orchestration. instrumentation In technology, the development and use of precise measuring, analysis, and control equipment. errors. Hence, these data were not included in the results given in Table 1.
Table 1. Summary of the Data Analyzed for Flow Boiling on Single Tubes
and Results of Comparison with the Present Correlation
Researcher D,* Tube Material Fluid pr* G,*
mm kg/[m.sup.2]s
Gupta et 19.05 SS water 0.005 8.9
al.
(1995)
Singh et 12.7 SS water 0.005 1.3
al.
(1983) 2.5
Dieselhorst 3.0 SS water 0.005 300
(1978)
Bitter 9.0 Porcelain, R-11 0.023 55
nickel-coated
(1972, 15.0 1391
1973)
Singh et 9.5 SS R-12 0.088 2
al.
(1985) 5
Hwang and 19.1 SS 304 R-113 0.041 5.9
Yao (1984)
242
Wege and 12.7 SS 321 R-113 0.050 138
Jensen
(1984)
312
All Data 3.0 0.005 1.3
19.1 0.088 1391
Researcher q,* x,* % [Re.sub.L]* 1/Z* Bo
kW/[m.sup.2] [10.sup.4]*
Gupta et 10 5E-5 559 0.003 5.4
al.
(1995) 40 22E-5 0.010 21.6
Singh et 11 4E-5 58 0 40
al.
(1983) 44 34E-5 115 153
Dieselhorst 150 0 3226 0 2.2
(1978) 1000 14.7
Bitter 1 0.00 1973 0 0.04
(1972, 26 0.10 49462 0.775 26.0
1973)
Singh et 20 0.005 67 0 276
al.
(1985) 85 0.052 160 2632
Hwang and 2 0.002 246 0.02 0.58
Yao (1984)
100 0.14 10079 0.86 710
Wege and 30 0.1 4103 0.57 1.7
Jensen
(1984)
0.2 36271 1.09 15.5
All Data 1 0.000 58 0 1.7
1000 0.2 49462 1.09 2632
Researcher [Y.sub.IB] Deviation,([dagger])([double No. of
[10.sup.4]* dagger]) % Data
Points
Gupta et 0.45 16.2 5
al.
(1995) 2.01 2.4
Singh et 1.5 15.2 17
al.
(1983) 7.7 -14.7
Dieselhorst 3.2 14.9 6
(1978) 21.2 14.0
Bitter 0.07 14.6 34
(1972, 5.7 4.3
1973)
Singh et 23 6.0 11
al.
(1985) 132 -1.6
Hwang and .3 13.6 55
Yao (1984)
41.9 -3.9
Wege and 3.1 15.0 3
Jensen
(1984)
7.5 -6.5
All Data 0.07 13.7 131
132 -3.5
* In each cell, the upper line has the minimum value of the parameter
and the lower line has the maximum value.
([dagger]) Mean absolute deviation
([double dagger]) Average deviation
Other Predictive Techniques A very large number of heat transfer correlations have been proposed. Most of these have been reviewed by Casciaro and Thome (2001) and Browne and Bansal (1999). Only a few are mentioned below. Various theories about mechanisms of heat transfer are not discussed. Many of the correlations attempt to predict the mean heat transfer coefficient for the bundle as a whole. An early example is that of Palen and Taborek (1962), which was based on data from many heat exchangers for chemical processing. According to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. it, mean bundle heat transfer is always lower than that during pool boiling on a single tube. There are numerous test data now that show bundle heat transfer coefficients to be higher than those of single tubes. This illustrates the futility Futility See also Despair, Frustration. American Scene, The portrays Americans as having secured necessities; now looking for amenities. [Am. Lit.: The American Scene] Babio performs the useless and supererogatory. [Fr. of attempting general correlations for mean bundle heat transfer coefficients. Many dimensional correlations have been proposed for particular fluids that include parameters like pressure and number of rows. Examples are the correlations of Danilova Da·ni·lo·va , Alexandra 1904-1997. Russian-born American ballerina who danced with the Ballet Russe de Monte Carlo from 1938 to 1958. et al. (1972) for ammonia ammonia, chemical compound, NH3, colorless gas that is about one half as dense as air at ordinary temperatures and pressures. It has a characteristic pungent, penetrating odor. and R-22. These correlations as well as other similar correlations have had very little validation. Many predictive techniques for local heat transfer based on the correlation of Chen for boiling inside tubes (Chen 1966) have been proposed. An example is the computer program developed by Webb et al. (1989), which was validated val·i·date tr.v. val·i·dat·ed, val·i·dat·ing, val·i·dates 1. To declare or make legally valid. 2. To mark with an indication of official sanction. 3. with performance data on three commercial chillers provided by the manufacturer. No other validation of this method has come to this author's notice. Chen-type correlations have also been presented by Polley et al. (1980), Hwang and Yao (1986), Webb and Chien (1994), Gupta Gupta (g  p`tə), Indian dynasty, A.D. c.320–c.550, whose empire at its height encompassed much of N India. Ancient Indian culture reached a high point during this period. et al. (1995), Fujita and Hidaka (1998),
and Wege For the radio station in Westerville, Ohio formerly known as WEGE, see .WEGE (formerly WUZZ) "104.9 The Eagle" is a small market radio station located in Lima, Ohio (pop. 40,000) and broadcasting on the 104.9 FM frequency. and Jensen (1984). These were validated with one or two data sets, each covering a small range of parameters. Their general applicability is unknown. Webb and Chien (1994) also developed an asymptotic model that agreed with their own data as well as R-113 data from two other sources; its general applicability is unknown. A two-dimensional recirculation model together with correlating equations has been given by Kumar Kumar (from Sanskrit meaning prince or an (unmarried) youth) is an Indian title, given name or family name. As a title it can mean son of a Rājā, prince, or heir apparent and enters in princely compound titles. et al. (2003) but has been validated with only one data set. Hence, its general applicability is unknown. Palen and Yang yang (yang) [Chinese] in Chinese philosophy, the active, positive, masculine principle that is complementary to yin; see yin, under principle. (1983) presented a correlation based on a wide range of proprietary data for reboilers used in chemical processing. While it seems to be a good rational correlation, it is not available for general use as the authors have not revealed the constants and exponents in their correlation. It is thus clear that no well-validated method for predicting heat transfer during saturated boiling in tube bundles is available in the open literature. On the Heat Transfer Regimes The three heat transfer regimes in the present correlation were arrived at empirically by the study of experimental data. While these have resulted in reasonably satisfactory correlation of data, there seems to be room for improvement. A number of data points identified in a particular regime show better agreement with the heat transfer correlation in another regime. It is also to be noted from Table 4 that the correlation shows significantly higher deviations in regimes II and III compared to regime I. Hence, further efforts are desirable for improving the correlations for these two regimes.
Table 4. Comparison of the Present Correlation with Data in the Three
Heat Transfer Regimes of This Correlation
No. of Data
Points with
Deviation
Regime No. of Data Mean Deviation > 30% > 40%
Points Percent
I 261 10.7 10 1
II 288 18.2 51 7
III 141 17.6 18 7
All 690 15.2 79 15
Regimes
Type of Fluid The data analyzed are for seven fluids. Five of the fluids are halocarbon refrigerants; their data show satisfactory agreement. The properties of these vary to some extent but are generally similar. Another fluid is n-pentane. Satisfactory agreement with these data suggests general applicability to organics. The seventh fluid is water. Its properties differ vastly from those of the other fluids. There are three data sets for water. All of these are at zero or near-zero vapor quality and are for single tubes. While these are reasonably well correlated, applicability to water at higher qualities and to tube bundles remains unverified. Hence, at present, the new correlation can be recommended only for halocarbon refrigerants and organics. Tube Arrangement and Pitch Data on inline and staggered tube bundles are included. No significant difference in deviations from the present correlation is apparent. This is in agreement with experimental studies in which the effect of tube arrangement was tested. An example is the study by Andrews and Cornwell (1987) in which an inline bundle with square pitch was rotated rotated turned around; pivoted. rotated tibia see rotated tibia. 90[degrees] to form a staggered bundle. The difference in heat transfer coefficients in the two cases was found to be negligible. Palen et al. (1972) also did not find any difference between the performance of inline and staggered bundles. The tube bundle data analyzed include pitch to diameter ratios from 1.17 to 1.5. Deviations do not appear to be related to P/D P/D Production and Development P/D Press Die P/D Production/Deployment P/D Payable Date (stock dividends) . Thus, in this range, P/D does not appear to have any effect. Application to smaller P/D ratios should be made with much caution, as tests by Liu and Qiu (2004) show that behavior changes Behavior change refers to any transformation or modification of human behavior. Such changes can occur intentionally, through behavior modification, without intention, or change rapidly in situations of mental illness. drastically dras·tic adj. 1. Severe or radical in nature; extreme: the drastic measure of amputating the entire leg; drastic social change brought about by the French Revolution. 2. as the gap between adjacent tubes approaches zero. They found that as the gap between tubes approaches zero, heat transfer coefficients at lower heat fluxes increase and dryout heat flux is lowered. Effect of Heating Mode Robinson and Thome (2004) measured pool boiling and flow boiling heat transfer on liquid- heated tubes. As seen in Table 3, their pool boiling heat transfer coefficient measurements are much higher than the simplified Cooper correlation, Equation 6. All other pool boiling studies listed in Table 3 were on electrically heated tubes and show reasonable agreement with Equation 6. It makes one wonder whether this difference is due to the difference in heating mode. However, there is a lot of evidence against such a view. First of all, the flow boiling measurements of Roser Ros´er n. 1. A rosier; a rosebush. et al. (1999) were also done on a bundle of liquid heated tubes. These data are in good agreement with the present correlation using Equation 6 to calculate the pool boiling heat transfer coefficient. The pioneering correlation of Chen (1966) for boiling inside tubes directly used a pool boiling correlation to account for the nucleate boiling component. Yet it was based on and verified with data that included electric heating Electric heating Methods of converting electric energy to heat energy by resisting the free flow of electric current. Electric heating has several advantages: it can be precisely controlled to allow a uniformity of temperature within very narrow limits; it is , heating by condensing con·dense v. con·densed, con·dens·ing, con·dens·es v.tr. 1. To reduce the volume or compass of. 2. To make more concise; abridge or shorten. 3. Physics a. steam, and heating by hot liquid. The same is the situation with the Gungor and Winterton In the United Kingdom Winterton is the name of several places:
Range of Various Parameters The complete range of dimensional and nondimensional parameters covered by the data analyzed is listed in Table 5. This range is very wide except that of reduced pressure, which is limited to a maximum of 0.18. However, the heat exchangers involving boiling outside tubes normally operate at low pressures. Hence, the range of reduced pressures covered is adequate for most practical purposes.
Table 5. Complete Range of Data Correlated
Fluids Water, n-pentane, R-11,
R-12, R-113,R-123, R-134a
Tube diameter 3-25.4 mm
Tube material Copper, brass,
cupro-nickel, stainless
steel, nickel-coated
porcelain
Tube arrangements Single tubes and tube
bundles.
Square inline and
equilateral triangular
staggered, P/D from 1.17
to 1.5.
Pressure 0.3-7.8 bar
Reduced pressure 0.005-0.189
Heat flux 1-1000 kW/[m.sup.2]
Mass flux 1.3-1391 kg/[m.sup.2]s
[Re.sub.L] 58-4949,462
1/Z 0-2.9
Bo [10.sup.4] 0.12-2632
[Y.SUB.IB] [10.sup.4] 0.07-132
SUMMARY AND CONCLUSIONS 1. A general correlation for heat transfer during saturated boiling during upflow Up`flow´ v. i. 1. To flow or stream up. across plain tubes has been presented. It agrees with most of the published data for single tubes as well as tube bundles. The data include seven fluids over a wide range of parameters. The new correlation is recommended for halocarbon refrigerants and organics. For other fluids, more validation is needed. 2. None of the presently available nonproprietary nonproprietary adjective Generic, see there predictive techniques has had much validation. Hence, the new correlation may be useful in the design of heat exchangers. 3. Further evaluation and development of the new correlation is desirable. Specially desirable is comparison with more data for water and other fluids whose properties differ widely from halocarbon refrigerants and organics--for example, ammonia. New experimental studies are needed for this purpose. NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc. binomial nomenclature All equations are dimensionless except the Cooper correlation, Equations 6 and 18. Any consistent system of units may be used in the dimensionless equations. A = total surface area of tube Bo = boiling number, q /(G [i.sub.fg]) D = outside diameter Outside diameter is the diameter of the addendum (tip) circle. In a bevel gear it is the diameter of the crown circle. In a throated wormgear it is the maximum diameter of the blank. The term applies to external gears.1 Notes 1. of tube [F.sub.pb] = parameter defined by Equation 5 Fr = Froude number, [G.sup.2]/[[rho].sub.L.sup.2]gD G = mass velocity, based on the narrowest gap between tubes of bundle h = heat transfer coefficient [h.sub.cooper] = pool boiling heat transfer by simplified Cooper correlation, Equation 6, W/[m.sup.2] K [h.sub.LT] = single-phase heat transfer coefficient assuming all mass flowing as liquid [h.sub.pb] = heat transfer coefficient during pool boiling [h.sub.pb,actual] = heat transfer coefficient from pool boiling tests on the actual tube used [h.sub.TP] = heat transfer coefficient with forced convection boiling [i.sub.fg] = latent heat latent heat, heat change associated with a change of state or phase (see states of matter). Latent heat, also called heat of transformation, is the heat given up or absorbed by a unit mass of a substance as it changes from a solid to a liquid, from a liquid to a gas, of vaporization vaporization, change of a liquid or solid substance to a gas or vapor. There is fundamentally no difference between the terms gas and vapor, but gas is used commonly to describe a substance that appears in the gaseous state under standard conditions of k = thermal conductivity thermal conductivity A measure of the ability of a material to transfer heat. Given two surfaces on either side of the material with a temperature difference between them, the thermal conductivity is the heat energy transferred per unit time and per unit of liquid M = molecular weight Nu = Nusselt number The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface that occurs in a 'real' situation, compared to the heat transferred if just conduction occurred. , hD/k p = absolute pressure [p.sub.c] = critical pressure [p.sub.r] = reduced pressure, p/[p.sub.c] P = pitch of tube bundle, i.e., center-to-center distance between adjacent tubes Pr = Prandtl number The Prandtl number is a dimensionless number approximating the ratio of momentum diffusivity (viscosity) and thermal diffusivity. It is named after Ludwig Prandtl. It is defined as: q = total heat flux on the tube, W/[m.sup.2] in Cooper correlation [R.sub,p] = roughness of surface, [mu]m [Re.sub.L] = Reynolds number assuming all mass flowing as liquid, GD/[mu] x = thermodynamic ther·mo·dy·nam·ic adj. 1. Characteristic of or resulting from the conversion of heat into other forms of energy. 2. Of or relating to thermodynamics. vapor quality [Y.SUB.IB] = boiling intensity parameter, defined by Equation 4 Z = parameter defined by Equation 10 Greek Letters Greek letters, n.pl symbols based on the Greek alphabet that are used to represent phenomena and objects in science. [phi] = parameter defined by Equation 11 [[phi].sub.0] = value of [phi] at x = 0 [mu] = dynamic viscosity dynamic viscosity n. Symbol  A measure of the molecular frictional resistance of a fluid as calculated using Newton's law. of liquid
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For example, water, when placed in a shallow open container exposed to air, gradually disappears, evaporating at a rate that depends on the amount of surface exposed, the humidity on plain tube and low-fin tube banks using R-123 and R-134a. ASHRAE Trans. 110(1):101-108. Churchill, S.W., and M.A. Bernstein. 1977. A correlating equation for forced convection from gases and liquids to a circular cylinder cylinder, in mathematics, surface generated by a line moving parallel to a given fixed line and continually intersecting a given fixed curve called the directrix; each line of the family of lines forming the cylinder is called a ruling, or generator. in crossflow Cross´flow` v. i. 1. To flow across, or in a contrary direction. . J. Heat Transfer 99:300-306. Cooper, M.G. 1984. Heat flow rates in saturated nucleate nu·cle·ate adj. Nucleated. v. 1. To form into a nucleus. 2. To serve or act as a nucleus for. 3. To provide a nucleus for. n. A salt of a nucleic acid. pool boiling--A wide ranging examination using reduced properties. Advances in Heat Transfer 16:157-239. Cornwell, K., N.W. Duffin, and R.B. Schuller. 1980. An experimental study of the effects of fluid flow on boiling within a kettle reboiler tube bundle. ASME Paper 80-HT-45, American Society of Mechanical Engineers, New York, NY. Cornwell, K., and D.S D.S Drainage Structure (flood protection) . Scoones. 1988. Analysis of low quality boiling on plain and low finned finned adj. Having a fin, fins, or finlike parts. Often used in combination: single-finned; multifinned. tube bundles. IMechE/IChemE, Proc. 2nd UK Heat Transfer Conf. 1:21-32. Cited in Webb and Gupte (1992). Cotchin, C., and E. Boyd. 1992. Boiling of refrigerant and refrigerant/oil mixture in a flooded evaporator evaporator Industrial apparatus for converting liquid into gas or vapour. The single-effect evaporator consists of a container or surface and a heating unit; the multiple-effect evaporator uses the vapour produced in one unit to heat a succeeding unit. . Heat Transfer: 3rd UK National Conference Incorporating 1st European European emanating from or pertaining to Europe. European bat lyssavirus see lyssavirus. European beech tree fagussylvaticus. European blastomycosis see cryptococcosis. Conference on Thermal Sciences Thermal science is the combined study of thermodynamics, fluid mechanics, and heat transfer. This umbrella-subject is typically designed for non-engineering students and functions to provide a general introduction to each of three core heat-related subjects. 1:131-37. Cumo, M., G.E. Farello, J. Gasiorowski, G. Iovino, and A. Naviglio. 1980. Quality influence on the departure from nucleate boiling in cross flows through bundles. Nuclear Technology 49:337-46. Danilova, G.N., V.A. Dyundin, and A.G. Soloviyov. 1972. Heat transfer in boiling of R-717 and R-22 in multirow tube bundles, Heat Transfer Research 24(7):889-93. Dieselhorst, T. 1978. Hydrodynamische und oberflachenspezifische Einflusse auf die Siedekrisis beim Behaltersieden. DrIng thesis, Technical University of Munich Munich University of Technology, or Technical University of Munich (TUM) (in German: Technische Universität München, TUM), is a major German university located in Munich (and the towns of Garching and Freising outside of Munich). , Munich, Germany. Fujita, Y., and S. Hidaka. 1998. Effect of tube bundles on nucleate boiling and critical heat flux Critical heat flux describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing localised overheating of the heating . Heat Transfer--Asian Research 27:312-24. Grant, I.D.R., C.D. Cotchin, and J.A.R. Henry. 1983. Tests on a small kettle reboiler. Heat Exchangers for Two-Phase Applications. ASME HTD HTD Heated HTD Heat Transfer Division HTD Haste the Day (band) HTD High Torque Drive (synchronous belt drives) HTD HEDS Technology Demonstration (NASA) HTD Hit The Deck 27:41-45. American Society of Mechanical Engineers, New York, NY. Gungor, K.E., and R.H.S h.s., n Latin phrase for “at bedtime”; used in writing prescriptions. . Winterton. 1986. A general correlation for flow boiling in tubes and annuli an·nu·li n. A plural of annulus. . Int. J. Heat Mass Transfer 29:351-58. Gupta, A., J.S. Saini, and H.K. Varma. 1995. Boiling heat transfer in small horizontal tube bundles at low cross-flow velocities. Int. J. Heat Mass Transfer 38(4):599-605. Holman, J.P. 1968. Heat Transfer, 2d ed. New York: McGraw-Hill. Hwang, T.H., and S.C. Yao. 1984. Boiling heat transfer of a horizontal cylinder at low quality crossflow. ASME HTD 38:9-17. American Society of Mechanical Engineers, New York, NY. Hwang, T.H., and S.C. Yao. 1986. Forced convection boiling in tube bundles. Int. J. Heat Mass Transfer 29(5):785-95. Jensen, M.K., R.R. Trewin, and A.E. Bergles. 1992. Cross-flow boiling in enhanced tubes. Proc. Engineering Foundation Conf. on Pool and External Flow Boiling, pp. 373-79. Jensen, M.K., and J.T. Hsu. 1988. A parametric See parametric modeling, parametric symbol and PTC. study of boiling heat transfer in a horizontal tube bundle. J. Heat Transfer 110:976-81. Kumar, S., A. Jain, B. Mohanty, and S.C. Gupta. 2003. Recirculation model of kettle reboiler. Int. J. Heat Mass Transfer 46:2899-2909. Liu, Z., and Y. Qiu. 2004. Boiling characteristics of R-11 in compact tube bundles with smooth and enhanced tubes. Experimental Heat Transfer 17:91-102. Marto, P.J., and C.L. Anderson Anderson, river, Canada Anderson, river, c.465 mi (750 km) long, rising in several lakes in N central Northwest Territories, Canada. It meanders north and west before receiving the Carnwath River and flowing north to Liverpool Bay, an arm of the Arctic . 1992. Nucleate boiling characteristics of R-113 in a small tube bundle. J. Heat Transfer 35(4):425-33. Memory, S.B., N. Akcasayar, H. Eraydin, and P.J. Marto. 1995. Nucleate pool boiling of R-114 and R-114-oil mixtures from smooth and enhanced surfaces, part II: Tube bundles. Int. J. Heat Mass Transfer 38:1363-76. Mostinski, I.K. 1963. Teploenergetica, vol. 66. English abstract in British Chemical Engng 8(8):580. Palen, J.W., and J.J. Taborek. 1962. Refinery kettle reboilers--Proposed method for design and optimization optimization Field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics. . Chemical Engineering Progress 58(7):37-46. Palen, W., and C.C. Yang. 1983. Circulation boiling model for the analysis of kettle and internal reboiler performance. ASME HTD 27:55-61. American Society of Mechanical Engineers, New York, NY. Palen, J.W., A. Yarden, and J. Taborek. 1972. Characteristics of boiling outside large-scale horizontal multitube bundles. AIChE Symp. Ser. 68(118):50-61. Polley, G.T., T. Ralston, and I.D.R. Grant. 1980. Forced crossflow boiling in an ideal in-line In-line Used in the context of general equities. (1) An order or market in a specific security within the inside market; 2) any announcement (earnings) that adheres closely to Wall Street analysts' expectations. tube bundle. ASME Paper 8-HT-46, American Society of Mechanical Engineers, New York, NY. Robinson, D.M., and J.R. Thome. 2004. Local bundle boiling heat transfer coefficients on a plain tube bundle (RP-1089). HVAC&R Research 10(1):33-51. Roser, R., B. Thonon, and P. Mercer mer·cer n. Chiefly British A dealer in textiles, especially silks. [Middle English, from Old French mercier, trader, from merz, merchandise, from Latin merx . 1999. Experimental investigations on boiling of n-pentane across a horizontal tube bundle: Two-phase flow In fluid mechanics, two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases. Historically, probably the most commonly-studied cases of two-phase flow are in large-scale power systems. and heat transfer characteristics. Int. J. Refrigeration 22:536-47. Shah, M.M. 1979. A general correlation for heat transfer during film condensation inside pipes. Int. J. Heat Mass Transfer 22:547-56. Shah, M.M. 1982. Chart correlation for saturated boiling heat transfer: Equations and further study. ASHRAE Trans. 88(1):185-96. Shah, M.M. 1984. A correlation for heat transfer during subcooled boiling on a single tube with forced crossflow. Int. J. Heat & Fluid Flow 5(1):13-20. Shah, M.M. 2005. Improved general correlation for subcooled boiling heat transfer during flow across tubes and tube bundles. HVAC&R Research 11(2):285-304. Shah, M.M. 2006. Evaluation of general correlations for heat transfer during boiling of saturated liquids in tubes and annuli. HVAC&R Research 12(4):1047-63. Singh, R.L., J.S. Saini, and H.K. Varma. 1983. Effect of crossflow in boiling heat transfer. Int. J. Heat Mass Transfer 26(12):1882-85. Singh, R.L., J.S. Saini, and H.K. Varma. 1985. Effect of cross-flow on boiling heat transfer of Refrigerant- 12. Int. J. Heat Mass Transfer 28(2):512-14. Stephan, K., and M. Abdelsalam. 1980. Heat transfer correlations for natural convection boiling. Int. J. Heat Mass Transfer 23:73-87. Wallner, R. 1971. Boiling heat transfer in flooded shell and tube evaporators. Proceedings of the 13th International Congress on Refrigeration, Paper No. 2.19, pp. 185. Webb, R.L., T.R. Apparao, and K.D. Choi. 1989. Prediction of the heat duty in flooded refrigerant evaporators. ASHRAE Trans. 95(1):339-48. Webb, R.L., and L.H. Chien. 1994. Correlation of convective boiling on banks of plain tubes using refrigerants. Heat Transfer Engineering 15(3):57-69. (Data tabulations kindly provided by the authors.) Webb, R.L., and N.S. Gupte. 1992. A critical review of correlations for convective vaporization in tubes and tube banks. Heat Transfer Engineering 13(3):58-81. Wege, M.E., and M.K. Jensen. 1984. Boiling heat transfer from a horizontal tube in an upward flowing two-phase crossflow. J. Heat Transfer 106:849-55. M. Mohammed Shah is the director of Engineering Research Consultation, Redding Redding, city (1990 pop. 66,462), seat of Shasta co., N central Calif., on the Sacramento River; inc. 1872. A principal tourist center for a mountain and lake region, it also has lumbering, food-processing, and diverse manufacturing. , CT. M. Mohammed Shah, PhD, PE Fellow ASHRAE Received June 8, 2006; accepted May 24, 2007 |
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