Evaluation of general correlations for heat transfer during boiling of saturated liquids in tubes and annuli.Six of the most 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. correlations for boiling heat transfer were compared to data for horizontal and vertical tubes and annuli an·nu·li n. A plural of annulus. . The correlations evaluated were: Chen (1966), 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. (1982), Gungor and Winterton In the United Kingdom Winterton is the name of several places:
Austrian social philosopher who investigated theosophy and founded anthroposophy. Noun 1. Steiner - Austrian philosopher who founded anthroposophy (1861-1925) Rudolf Steiner and Taborek (1992). The database used to evaluate these correlations included 30 fluids, consisting of water, 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. , cryogens, and organic and inorganic inorganic /in·or·gan·ic/ (in?or-gan´ik) 1. having no organs. 2. not of organic origin. in·or·gan·ic n. 1. chemicals. The data cover reduced pressures In thermodynamics, the reduced pressure of a fluid is defined as its actual pressure divided by its critical pressure. 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. from 28 to 11071 kg/[m.sup.2]s, vapor quality 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 0 to 0.95, and boiling numbers from 0.000026 to 0.00742. The correlations of Shah (1982) and Gungor and Winterton (1987) gave the best agreement with data 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 about 17.5%, with only a couple of data sets showing large deviations. This paper presents and discusses the results of this study. Included are tables giving the range of dimensional and nondimensional parameters covered by each experimental study. INTRODUCTION Hundreds of correlations were proposed for the calculation of heat transfer during the boiling of 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. liquids inside tubes and annuli. Most of them were compared to only a limited amount of data. However, some of them were shown to agree with a wide range of data with many fluids and are therefore considered general correlations. It is desirable to know their comparative accuracy and limitations so that the most reliable correlations may be used for practical calculations. This paper reports the results of such a study in which six of the best known general correlations were compared to a very wide range of data for 30 fluids. Included are tables giving the range of dimensional and nondimensional parameters covered by each experimental study. AVAILABLE CORRELATIONS A very large number of correlations were published. Most of them had very little verification. Only the ones that had extensive verification with a wide range of fluids and found wide acceptance are mentioned here. The first general correlation was published by Chen (1966). It was based entirely on data for vertical channels. The correlation is [h.sub.TP] = [F.sub.chen][h.sub.LO] + S[h.sub.pb]. (1) It showed excellent agreement with the data 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. by Chen. However, many later researchers compared it to large databases and reported that its agreement was satisfactory with neither horizontal nor vertical channels. Examples of such studies are Kandlikar (1990), Gungor and Winterton (1986, 1987), Liu and Winterton (1991), and Steiner and Taborek (1992). Hundreds of correlations in the form of Equation 1 were proposed, most based only on one data set. The present author (Shah 1976, 1982) presented a correlation with the functional form [h.sub.TP]/[h.sub.LO] = f(Co, Bo, [Fr.sub.L]). (2) 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.sub.L]) accounts for stratification stratification (Lat.,=made in layers), layered structure formed by the deposition of sedimentary rocks. Changes between strata are interpreted as the result of fluctuations in the intensity and persistence of the depositional agent, e.g. in horizontal channels Horizontal Channel Two parallel horizontal trendlines acting as very strong support and resistance. The upper trendline connects a stock's highs over a period of time, and each high is equal to the previous high. ; it is not used for vertical channels. This was the first correlation applicable to both horizontal and vertical tubes. It was tested with large databases with mostly satisfactory results by many researchers, such as Kandlikar (1990), Gungor and Winterton (1986, 1987), and Liu and Winterton (1991). Kandlikar (1990) gives a correlation applicable to both horizontal and vertical channels. It uses the same correlating parameters as the Shah correlation but also has a fluid specific multiplier multiplier In economics, a numerical coefficient showing the effect of a change in one economic variable on another. One macroeconomic multiplier, the autonomous expenditures multiplier, relates the impact of a change in total national investment on the nation's total for 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. . Values of this multiplier were given for only ten fluids; hence, it is applicable to only those ten fluids. Gungor and Winterton (1986) presented a correlation similar to Equation 1 but incorporated the Froude number for horizontal channels in the same way as in the Shah correlation. Liu and Winterton (1991) also presented a similar correlation and showed it to be more accurate than the Gungor and Winterton (1986) correlation. Gungor and Winterton (1987) presented a correlation similar to the Shah correlation and showed that it agreed with a wide range of data. Steiner and Taborek (1992) give a correlation that is based on a large and varied database for vertical channels. It has the form [h.sub.TP] =(([F.sub.st][h.sub.LT])[.sup.3] + [h.sub.pb.sup.3])[.sup.1/3]. (3) CORRELATIONS TESTED The following correlations were tested: * Chen (1966) with pool boiling component calculated by the Cooper correlation (1984) * Steiner and Taborek (1992) * Shah (1982) * Kandlikar (1990) * Liu and Winterton (1991) * Gungor and Winterton (1987) The reason for using the Cooper pool boiling correlation with the Chen correlation is that the Cooper correlation was verified with an extremely wide range of data, while the pool boiling correlation originally used by Chen had very little verification. It was felt that this change will improve the accuracy of the Chen correlation. Hence, the Chen correlation incorporating this change is called the Chen-Cooper correlation. Note that the Cooper correlation was used with roughness at 1 [micro]m and without the factor 1.7 for copper tubes. The Gungor and Winterton (1986) correlation was not tested as that of Liu and Winterton (1991) was tested in the present study, and they had shown that their correlation gave better agreement with the data. All of the above correlations require the calculation of a single-phase sin·gle-phase adj. Producing, carrying, or powered by a single alternating voltage. liquid heat transfer coefficient 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). . For use with the Steiner and Taborek correlation, the formula of Pethukov and Krillov (1958) was used in accordance Accordance is Bible Study Software for Macintosh developed by OakTree Software, Inc.[] As well as a standalone program, it is the base software packaged by Zondervan in their Bible Study suites for Macintosh. with their recommendation. For all other tested correlations, liquid convective heat transfer Convective heat transfer is a mechanism of heat transfer occurring because of bulk motion (observable movement) of fluids. This can be contrasted with conductive heat transfer, which is the transfer of energy molecule by molecule through a solid or fluid, and radiative heat was calculated by the McAdams (1954) equation: [h.sub.LT]D/k = 0.023(GD/[mu])[.sup.0.8][pr.sup.0.4] (4) Ogata and Sato Sa·to , Eisaku 1901-1975. Japanese politician who served as prime minister (1964-1972). He shared the 1974 Nobel Peace Prize for his efforts toward nuclear disarmament. (1974) compared their nonboiling helium helium (hē`lēəm), gaseous chemical element; symbol He; at. no. 2; at. wt. 4.0026; m.p. below −272°C; at 26 atmospheres pressure; b.p. −268.934°C; at 1 atmosphere pressure; density 0. data with Equation 4 and found that the constant should be changed to 0.015 to fit their data. Therefore, in analyzing their data, the constant in Equation 4 was changed to 0.015. For application to annuli, D was replaced by the equivalent diameter [D.sup.hp], defined as four times the flow area divided by the heated perimeter The boundary of a system or network, which defines the inside and outside. It is typically determined by firewalls and addresses. See DMZ. . DATA ANALYZED Efforts were made to collect data for as many fluids as possible, covering a wide range of parameters. Only single-component fluids and azeotropic mixtures were considered. For refrigerants, only those data were considered for which oil content was stated to be zero or 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 . . The salient features and range of data analyzed are listed in Tables 1 and 2. These include 30 fluids, namely, water, R-11, R-12, R-22, R-32, R-113, R-114, R-123, R-134a, R-152a, R-502, 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. , propane propane, CH3CH2CH3, colorless, gaseous alkane. It is readily liquefied by compression and cooling. It melts at −189.9°C; and boils at −42.2°C;. , isobutane isobutane (ī'səby  `tān): see butane. , carbon tetrachloride carbon tetrachloride (tĕ'trəklôr`īd) or tetrachloromethane (tĕ'trəklôr'əmĕth`ān), CCl4, colorless, poisonous, liquid organic compound that boils at 76. , isopropyl alcohol isopropyl alcohol: see isopropanol. , ethanol ethanol (ĕth`ənōl') or ethyl alcohol, CH3CH2OH, a colorless liquid with characteristic odor and taste; commonly called grain alcohol or simply alcohol. ,
methanol methanol, methyl alcohol, or wood alcohol, CH3OH, a colorless, flammable liquid that is miscible with water in all proportions. Methanol is a monohydric alcohol. It melts at −97. , n-butanol, cyclohexane cyclohexane (sī'kləhĕk`sān), C6H12, colorless liquid hydrocarbon. It is a cyclic alkane that melts at 6°C; and boils at 81°C;. It is nearly insoluble in water. , benzene benzene (bĕn`zēn, bĕnzēn`), colorless, flammable, toxic liquid with a pleasant aromatic odor. It boils at 80.1°C; and solidifies at 5.5°C;. Benzene is a hydrocarbon, with formula C6H6. , heptane hep·tane n. A volatile, colorless, highly flammable liquid hydrocarbon, C7H16, obtained in the fractional distillation of petroleum and used as a standard in determining octane ratings, as an anesthetic, and as a solvent. , ethylene glycol ethylene glycol: see glycol. ethylene glycol Simplest member of the glycol family, also called 1,2-ethanediol (HOCH2CH2OH). It is a colourless, oily liquid with a mild odour and sweet taste. , pentane pen·tane n. Any of three colorless, flammable isomeric hydrocarbons, C5H12, derived from petroleum and used as solvents. , nitrogen, argon argon (är`gŏn) [Gr.,=inert], gaseous chemical element; symbol Ar; at. no. 18; at. wt. 39.948; m.p. −189.2°C;; b.p. −185.7°C;; density 1.784 grams per liter at STP; valence 0. , neon neon (nē`ŏn) [Gr.,=new], gaseous chemical element; symbol Ne; at. no. 10; at. wt. 20.179; m.p. −248.67°C;; b.p. −246.048°C;; density 0.8999 grams per liter at STP; valence 0. Neon is a colorless, odorless, and tasteless gas. , hydrogen, nitrogen, and helium. The results for ethylene glycol are from Liu and Winterton (1991). Data for carbon dioxide carbon dioxide, chemical compound, CO2, a colorless, odorless, tasteless gas that is about one and one-half times as dense as air under ordinary conditions of temperature and pressure. (C[O.sub.2]) from several sources were also analyzed but none of them agreed with any of the tested correlations. It was concluded that C[O.sub.2] is a special fluid requiring separate treatment; hence, C[O.sub.2] data were not included in Tables 1 and 2. This is further discussed later in the paper. Most of the data analyzed are for local heat transfer coefficients. Some researchers reported only the average heat transfer coefficients and heat flux over the tube length as indicated in Tables 1 and 2. Comparison with such data was done by using the mean quality and the mean heat flux in the evaluated correlations. The data of Ogata and Sato (1974) for helium showed strong hysterisis. The mean of the heat transfer coefficients for ascending and descending Ascending and Descending is a lithograph print by the Dutch artist M. C. Escher which was first printed in March 1960. The original print measures 14" x 11 1/4”. The lithograph depicts a large building roofed by a never-ending staircase. heat fluxes was used for comparison with all correlations. FLUID PROPERTY DATA The main source of fluid property data was the University of Ottawa
This article is about reference works. For the subnotebook computer, see .
British photographer, diarist, and theatrical designer noted for his sets and costumes for My Fair Lady (stage, 1956; film, 1964). and Hewitt Hewitt may refer to:
RESULTS OF DATA ANALYSIS The mean and average deviations of data from correlations are listed in Tables 1 and 2 for horizontal and vertical channels, respectively. The deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured. 2. [delta] for a data point is defined as [delta] = ([h.sub.pred] - [h.sub.meas])/[h.sub.meas]. (5) The average deviation [[delta].sub.avg] of a data set is defined as [[delta].sub.avg]=([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) ]([delta])/N), (6) where N is the number of data points in the data sets. The mean deviation [[delta].sub.mean] of a data set is defined as [[delta].sub.mean] = ([summation]Abs,([delta])/N). (7) Table 3 gives the combined results for horizontal and vertical channels. In this table, the deviations for each correlation are given in two ways: 1. Giving equal weight to each data point. 2. Giving equal weight to each data set. The second way probably gives a better indication of the reliability of the correlation. DISCUSSION OF RESULTS Accuracy of Correlations It is apparent from the results in Tables 1-3 that the correlations of Shah (1982) and Gungor and Winterton (1987) are the most reliable, with a main deviation of about 17.5% for all 1960 data points. The Shah correlation is more consistent, as only 5 of the 69 data sets have a mean deviation of more than 30%, while the Gungor and Winterton correlation has 9 data sets exceeding 30% deviation. These two correlations show reasonable agreement with almost all data sets. One notable exception is the data of Mohr and Runge Runge may relate to the following: People
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 for neon could be found. However, Pappel and Hendricks Hendricks is a surname, and may refer to
The other notable exception is the data of Steiner and Schlunder (1977) for nitrogen; these are much higher than the Shah correlation. However, nitrogen data from four other sources (Klimenko and Sudarchikov 1983; Klimenko et al. 1987; Klein Klein , Melanie 1882-1960. Austrian-born British psychoanalyst who first introduced play therapy and was the first to use psychoanalysis to treat young children. 1976; Pappel and Hendricks 1978) agree well with this correlation. The Steiner and Schlunder data are also much higher than the Gungor and Winterton and Liu and Winterton correlations. Hence, these data are apparently unique. The Liu and Winterton correlation's performance is erratic er·rat·ic adj. 1. Having no fixed or regular course; wandering. 2. Lacking consistency, regularity, or uniformity: an erratic heartbeat. 3. . While it agrees well with many data sets, it also shows large deviations with many data sets, such as the data of Muller Mul·ler , Hermann Joseph 1890-1967. American geneticist. He won a 1946 Nobel Prize for the study of the hereditary effect of x-rays on genes. Mül·ler , Johannes Peter 1801-1858. et al. (1983) for argon, the cyclohexane data of Talty (1953), and the data of Piret and Isbin (1954) for water, C[Cl.sub.4], n-butanol, and isopropanol isopropanol, isopropyl alcohol, or 2-propanol (ī'səprō`pənōl, ī'səprō`pĭl), (CH3)2CHOH, a colorless liquid that is miscible with water. . The Steiner and Taborek correlation did not perform well in predicting horizontal tube data. Indeed, these authors recommended it only for vertical channels. Even with vertical channels, it shows large deviations with some data sets. The Chen and Cooper correlation works fairly well with both horizontal and vertical tubes, but its accuracy is significantly less than the Shah and the Gungor and Winterton correlations. The Kandlikar correlation could be compared with data for only those fluids for which he gave the nucleate boiling multiplying mul·ti·ply 1 v. mul·ti·plied, mul·ti·ply·ing, mul·ti·plies v.tr. 1. To increase the amount, number, or degree of. 2. Mathematics To perform multiplication on. factors. Even among those fluids, it performed poorly with data for R-22, nitrogen, and neon. Figures 1 and 2 show the comparison of some data for R-22 and nitrogen with the correlations of Shah and Kandlikar. The Shah correlation is seen to be in good agreement with data, while the Kandlikar correlation predicts too high. These figures are typical of the results for these fluids. [FIGURE 1 OMITTED] [FIGURE 2 OMITTED] Tube Material The data analyzed include many types of tube materials, including copper, stainless steel stainless steel: see steel. stainless steel Any of a family of alloy steels usually containing 10–30% chromium. The presence of chromium, together with low carbon content, gives remarkable resistance to corrosion and heat. , monel, brass, and nickel-coated glass. All the test sections were made from commercial grade tubes except the nickel-coated glass used by Gouse and Coumou (1965). There is no indication that the accuracy of the correlations is affected by the type of material. Tube Surface 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 It is generally agreed that the intensity of nucleate boiling depends on the shape and population densities of cavities in the surface. This was demonstrated by pool boiling tests on surfaces with artificially prepared cavities. Information on cavity cavity /cav·i·ty/ (kav´i-te) 1. a hollow place or space, or a potential space, within the body or one of its organs. 2. in dentistry, the lesion produced by caries. sizes and their population density is not available for any of the test data evaluated here. The fact that almost all data sets analyzed are in fair agreement with the Shah correlation (which does not have any factor for surface microstructure) indicates that the microstructures of most commercial tubes are normally similar. It may be noted that the most successful general correlations for pool boiling (those of Stephen and Abdelsalam [1980] and Cooper [1984]) do not have any factor for surface microstructure. It is statistically probable that some commercial tubes may have a microstructure very favorable fa·vor·a·ble adj. 1. Advantageous; helpful: favorable winds. 2. Encouraging; propitious: a favorable diagnosis. 3. to nucleate boiling. This may be the explanation for the data of Steiner and Schlunder and Mohr and Runge being much higher than the predictions of almost all tested correlations. However, it will be inadvisable to base designs on such unusually high data. The designer of a heat exchanger 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. does not have any way of knowing the microstructure of tubes that will be used during fabrication fabrication (fab´rikā´sh  n),n the construction or making of a restoration. . It is therefore fortunate that heat transfer coefficients can be predicted with a high probability of accuracy without the knowledge of microstructure. Heating Mode The data analyzed include 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 liquids. Data for all heating modes are satisfactorily correlated cor·re·late 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. by the Shah and the Gungor and Winterton correlations. Type of Fluid The Shah and the Gungor and Winterton correlations show good agreement with 29 of the 30 fluids included in Tables 1 and 2. The only available single data set for neon does not agree with any of the tested correlations but, as was pointed out earlier, the measurements of Pappel and Hendricks (1978) appear to be in agreement with the Shah correlation. C[O.sub.2] data from several sources were analyzed but none of the correlations tested here were found to agree with them. Among such data are those of Bredsen et al. (1997), Yoon et al. (2004), and Knudsen and Jensen (1997). These authors also compared their data with well-known general correlations with poor results. Thome and Hejal (2004) compared C[O.sub.2] data with their correlation that was based on data for several refrigerants but found poor agreement. They concluded that carbon dioxide is a unique fluid and developed a correlation specifically for C[O.sub.2]. However, Park and Hrnjak (2005) found that it did not agree with their data. Thus, the Shah and the Gungor and Winterton correlations appear to be suitable for all Newtonian, nonmetallic non·me·tal·lic adj. 1. Not metallic. 2. Chemistry Of, relating to, or being a nonmetal. Adj. 1. fluids except C[O.sub.2]. Annuli The present analysis included only 94 data points from two sources. The present author (Shah 1982) compared the Shah correlation with 736 data points from five sources, covering a wide range of parameters. The mean deviation for all data was 17.1%. Hence, the Shah correlation is well verified for annuli. SUMMARY AND CONCLUSION 1. Six of the best known general correlations were tested with data for 30 fluids, including water, refrigerants, organics, and cryogens boiling in horizontal and vertical tubes and annuli. The data covered a very wide range of parameters. 2. The correlations of Shah (1982) and Gungor and Winterton (1987) gave good agreement with data, with the mean deviation around 17.5%. The Shah correlation is more consistent. The range of data satisfactorily predicted is given in Table 4. The other four correlations had mean deviations from 22% to 55%. 3. The results indicate that the Shah and the Gungor and Winterton correlations can be used with confidence for all Newtonian nonmetallic fluids (except C[O.sub.2]). NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc. binomial nomenclature Bo = boiling number = q/(G[h.sub.fg]) D = ID of tube [D.sub.hp] = equivalent diameter of annulus annulus /an·nu·lus/ (an´u-lus) pl. an´nuli [L.] anulus. an·nu·lus or an·u·lus n. pl. an·nu·lus·es or an·nu·li A circular or ring-shaped structure. Co = convection number, (1/x - 1)[.sup.0.8]([[rho].sub.g]/[[rho].sub.L]0.5 [F.sub.chen] = convective enhancement factor in Chen correlation [F.sub.st] = convective enhancement factor in Steiner and Taborek correlation [Fr.sub.L] = Froude number, [G.sup.2]/([[rho].sub.L.sup.2]gD) G = total mass flux (liquid plus vapor vapor /va·por/ (va´por) pl. vapo´res, vapors [L.] 1. steam, gas, or exhalation. 2. an atmospheric dispersion of a substance that in its normal state is liquid or solid. ) g = acceleration due to gravity Acceleration due to gravity can refer to:
[h.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 [h.sub.LO] = heat transfer coefficient assuming liquid phase flowing alone [h.sub.LT] = heat transfer coefficient assuming all mass flowing as liquid [h.sub.meas] = measured heat transfer coefficient [h.sub.pb] = pool boiling heat transfer coefficient [h.sub.pred] = predicted heat transfer coefficient [h.sub.TP] = two-phase heat transfer coefficient 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 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: [p.sub.r] = reduced pressure q = heat flux S = nucleate boiling suppression suppression /sup·pres·sion/ (su-presh´un) 1. the act of holding back or checking. 2. sudden stoppage of a secretion, excretion, or normal discharge. 3. factor in Chen correlation [mu] = viscosity of liquid [[rho].sub.L] = density of liquid [[rho].sub.g] = density of vapor REFERENCES Adorni, N., et al. 1961. Results of wet steam cooling experiments pressure drop heat transfer and burnout Burnout Depletion of a tax shelter's benefits. In the context of mortgage backed securities it refers to the percentage of the pool that has prepaid their mortgage. measurements in annular annular /an·nu·lar/ (an´u-ler) ring-shaped. an·nu·lar adj. Shaped like or forming a ring. annular ring-shaped. tubes with internal and bilateral bilateral /bi·lat·er·al/ (-lat´er-al) having two sides, or pertaining to both sides. bi·lat·er·al adj. 1. Having or formed of two sides; two-sided. 2. heating. C.I.S.E. Report R 31, TID tid 3 times a day 12459. ASHRAE. 1997. 1997 ASHRAE Handbook--Fundamentals. Atlanta: American Society of Heating, Refrigerating 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. and Air-Conditioning Engineers, Inc. Beaton, C.F., and G.F. Hewitt (eds.) 1989. Physical Property Data for the Chemical and Mechanical Engineer. New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of : Hemisphere hemisphere /hemi·sphere/ (hem´i-sfer) half of a spherical or roughly spherical structure or organ. cerebellar hemisphere either of two lobes of the cerebellum lateral to the vermis. Publishing Corp. Bennet bennet excludes the devil; used on door frames. [Medieval Folklore: Boland, 56] See : Protection , D.L. 1976. PhD thesis, Lehigh University Lehigh University, at Bethlehem, Pa.; coeducational; chartered and opened 1866 by Asa Packer. It has undergraduate colleges of arts and science, business and economics, and engineering and applied science, as well as several graduate programs. , PA. Quoted in Liuand Winterton (1991). Bhatti, M.S., and R.K. Shah. 1987. Turbulent and transition flow convective heat transfer in ducts. In Kacak, S., R.K. Shah, and W. Aung (eds.). Handbook of Single Phase Heat Transfer. New York: John Wiley John Wiley may refer to:
Bredsen, A.M., A. Hafner, J. Petterson, P. Neksa, and K. Aflekt. 1997. Heat transfer and pressure drop for in-tube evaporation evaporation, change of a liquid into vapor at any temperature below its boiling point. 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 of C[O.sub.2]. Proceedings of the Conf. of Commission B1 with E1, Paris, International Institute of Refrigeration refrigeration, process for drawing heat from substances to lower their temperature, often for purposes of preservation. Refrigeration in its modern, portable form also depends on insulating materials that are thin yet effective. . Chaddock, J., and G. Buzzard buzzard, common name for hawks of the genus Buteo and the genus Pernis, or honey buzzard, of the Old World family Accipitridae. Honey buzzards feed on insects, wasp and bumblebee larvae, and small reptiles. . 1986. Film coefficients for in-tube evaporation with and without small percentages of mineral oil. ASHRAE Trans. 92(1A):22-40. Chaddock, J.B., and J.A. Noerager. 1966. Evaporation of refrigerant re·frig·er·ant adj. 1. Cooling or freezing; refrigerating. 2. Reducing fever. n. 1. A substance, such as air, ammonia, water, or carbon dioxide, used to provide cooling either as the working substance of 12 in horizontal tube with constant heat flux. ASHRAE Trans. 72(1):99-103. Chawla, J.M. 1967. Warmeubergang und Druckabfall in Wagrechten Rohren bei der Stromung von Verdampfenden Kaltmitteln. VDI (1) (Video Device Interface) An Intel standard for speeding up full-motion video performance. See DCI. (2) (Virtual Device Interface) An ANSI standard format for creating device drivers. VDI has been incorporated into CGI. Forschungsheft: 523. Chen, J.C. 1966. A correlation for boiling heat transfer to saturated fluids in convective flow. Ind IND Investigational new drug Therapeutics A status assigned by the FDA to a drug before allowing its use in humans, exempting it from premarketing approval requirements so that experimental clinical trials may be conducted. See Phase 1.2, 3 studies, Sponsorship. . Eng. Chem. Process Design and Development 5(3):322-29. 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. In Advances in Heat Transfer 16:157-239. New York: Academic Press. Dengler, C.E., and J.N. Addoms. 1956. Heat transfer mechanism for vaporization of water in vertical tubes. Chem. Eng. Prog. Symp. Ser. 52(18):95-103. Ebisu, T., and K. Torikoshi. 1998. Heat transfer characteristics and correlations for R-410A flowing inside a horizontal smooth tube. ASHRAE Trans. 104(2). Gouse, S.W., and K.G. Coumo. 1965. Heat transfer and fluid flow inside a horizontal tube 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. . ASHRAE Trans. 71(2): 152-60. 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. Int. J. Heat Mass Transfer 29:351-58. Gungor, K.E., and R.H.S. Winterton. 1987. Simplified general correlation for saturated flow boiling and comparisons of correlations with data. Chem. Eng. Res Des., 65:148-56. Hambreaus, K. 1995. Heat transfer of oil-contaminated HFC 1. (networking) HFC - Hybrid Fiber Coax. 2. (hardware) HFC - hydrofluorocarbon. 134a in a horizontal evaporator. Int. J. Refrig. 18(2):87-99. Haynes, B.S., and D.F. Fletcher Fletcher may refer to one of the following: Ideas and companies
Johannes C. 1972. Studies of forced convection heat transfer to Helium I helium I n. Liquid helium existing as a normal fluid between the superfluid transition point of approximately 2.2°K at 1 atmosphere pressure and its boiling point of 4.2°K. . Advances in Cryogenic cryogenic /cry·o·gen·ic/ (-jen´ik) producing low temperatures. cry·o·gen·ic adj. 1. Relating to or producing low temperatures. 2. Engng. 15:352-80. Johnston, R.C., and J.B. Chaddock. 1964. Heat transfer and pressure drop of refrigerants evaporating in horizontal tubes. ASHRAE Trans. 70:163-72. Jung Jung , Carl Gustav 1875-1961. Swiss psychiatrist who founded analytical psychology and came up with the concepts of extraversion and introversion and the notion of the collective unconscious. , D.S D.S Drainage Structure (flood protection) ., M. McLinden, R. Radermacher, and S. Didion. 1989a. Horizontal flow boiling heat transfer experiments with a mixture of R22/R114. Int. J. Heat Mass Transfer 32(1):131-45. Jung, D.S., M. McLinden, R. Radermacher, and S. Didion. 1989b. A study of flow boiling heat transfer with refrigerant mixtures. Int. J. Heat Mass Transfer 32(9):1751-64. Kandlikar, S.G. 1990. A general correlation for saturated 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. boiling heat transfer inside horizontal and vertical tubes. J. Heat Transfer 112:219-28. Kattan, N., J.R. Thome, and D. Favrat. 1998. Flow boiling in horizontal tubes: Part 2--New heat transfer data for five refrigerants. J. Heat Transfer 120:148-55. Keilin, V.E., I.A. Kovalev, and V.V. Likov. 1975. Forced convection heat transfer to liquid Helium Liquid helium in the nucleate boiling region. Cryogenics cryogenics: see low-temperature physics. cryogenics Study and use of low-temperature phenomena. The cryogenic temperature range is from −238°F (−150°C) to absolute zero. At low temperatures, matter has unusual properties. 15(3):141-45. Klein, G. 1976. Heat transfer for evaporating nitrogen streaming in a horizontal tube. Proc. Sixth Int. Cryogenic Engineering Conference. IPC (1) (InterProcess Communication) The exchange of data between one program and another either within the same computer or over a network. It implies a protocol that guarantees a response to a request. Science & Technology Press, pp. 314-18. Klimenko, V.V., Y.A. Fomichev, and A.V. Grigoriev. 1987. An experimental investigation of heat transfer with evaporation of liquid nitrogen Noun 1. liquid nitrogen - nitrogen in a liquid state atomic number 7, N, nitrogen - a common nonmetallic element that is normally a colorless odorless tasteless inert diatomic gas; constitutes 78 percent of the atmosphere by volume; a constituent of all living in a vertical channel. Thermal Engineering 34(9):493-97. Klimenko, V.V., and A.M. Sudarchikov. 1983. Investigation of forced flow boiling of nitrogen in a long vertical tube. Cryogenics 23:379-85. Knudsen, H.J.H., and P.H. Jensen. 1997. Heat transfer coefficients for boiling carbon dioxide. Workshop Proceedings--Carbon Dioxide Technology in Refrigeration, Heat Pump heat pump: see air conditioning. heat pump Device for transferring heat from a substance or space at one temperature to another at a higher temperature. and Air Conditioning air conditioning, mechanical process for controlling the humidity, temperature, cleanliness, and circulation of air in buildings and rooms. Indoor air is conditioned and regulated to maintain the temperature-humidity ratio that is most comfortable and healthful. Systems. Trondheim, Norway, pp. 319-28. Lahey, R.T. (ed.). 1992. Boiling Heat Transfer. Amsterdam: Elsevier Science. Lazarek, G.M., and S.H. Black. 1982 Evaporative evaporative pertaining to evaporation. evaporative loss loss of body water by evaporation of water from the body to the air; a heat control mechanism and a factor in water balance studies. heat transfer, pressure drop 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 in a small vertical tube with R-113. Int. J. Heat Mass Transfer 25:945-59. Liu, Z., and R.H.S. Winterton. 1991. A general correlation for saturated and subcooled flow boiling in tubes and annuli based on a nucleate pool boiling equation. Int. J. Heat Mass Transfer 34(11):2759-66. Mathur, A.P. 1976. Heat transfer to oil-refrigerant mixtures evaporating in tubes. PhD thesis, Department of Mechanical Engineering, Duke University, Durham, NC. McAdams, W.H. 1954. Heat Transmission. 3d ed. New York: McGraw-Hill. McCarty, R.D. 1972. Thermophysical properties of Helium-4 from 2 to 1500 K with pressures to 1000 atmospheres. Report NBS-TN-631. Mohr, V., and R. Runge 1977. Forced convection boiling of neon in horizontal tubes. In Heat Transfer in Boiling, E. Hahne and U. Grigull (eds.). Washington: Hemisphere. pp. 307-44. Morozov, V.G. 1969. Heat transfer during boiling of water in tubes. In Convective Heat Transfer in Two-Phase and One-Phase Flow, V.M. Borishanskii and I.I. Paleev (eds.). Israel Program for Scientific Translation Inc. Muller, H., W. Bonn, and D. Steiner 1983. Heat transfer and critical heat flux at flow boiling of nitrogen and argon within a horizontal tube. In Heat Exchangers Theory and Practice, J. Taborek, G.F. Hewitt, and N. Afgan (eds.). Washington: Hemisphere. pp. 230-50. Mumm, J.F. 1954. Heat transfer to boiling water forced through a uniformly heated tube. Argonne National Laboratory Argonne National Laboratory, research center, based in Argonne, Ill., 27 mi (43 km) SW of downtown Chicago, with other facilities at the Idaho National Engineering Laboratory, 50 mi (80 km) W of Idaho Falls, Idaho. Founded in 1946 by the U.S. Report ANL-5276. Murata, K., and K. Hashizume 1990. An investigation of forced convection boiling of non-azeotropic mixtures. Heat Transfer Japanese Research. 19(2):95-109. Muzzio, A., A. Niro, and S. Arosio. 1998. Heat transfer and pressure drop during evaporation and condensation of R22 inside 9.52-mm O.D. microfin tubes of different geometries. Enhanced Heat Transfer Heat exchangers were initially developed to use plain (or smooth) heat transfer surfaces. An Enhanced heat transfer surface has a special surface geometry that provides a higher thermal performance, per unit base surface area than a plain surface. 5:39-52. Naitoh, M. 1974. Dryout in helically coiled coil 1 n. 1. a. A series of connected spirals or concentric rings formed by gathering or winding: a coil of rope; long coils of hair. b. tube of sodium heated generator generator, in electricity, machine used to change mechanical energy into electrical energy. It operates on the principle of electromagnetic induction, discovered (1831) by Michael Faraday. . ASME ASME - American Society of Mechanical Engineers Paper 74-WA/HT-48, ASME, New York. Ogata, H., and S. Sato 1974. Forced convection heat transfer to boiling helium in a tube. Cryogenics. 14:375-80. Pappel, S.S., and R.C. Hendricks. 1978. Boiling incipience in·cip·i·ent adj. Beginning to exist or appear: detecting incipient tumors; an incipient personnel problem. [Latin incipi and convective boiling of neon and nitrogen. Advances in Cryogenic Engineering 23:284-94. Park, C.Y., and P.S. Hrnjak. 2005. Flow boiling heat transfer of C[O.sub.2] at low temperature in a horizontal smooth tube. J. Heat Transfer 127:1305-13. Pierre, B. 1957. Varmeovergongen vid Kokande Koldmedier I Horisontella Ror. Kylteknisk Tidskrift (3):129-37. Piret, E.L., and H.S. Isbin. 1954. Natural circulation evaporation two phase heat transfer. Chem. Eng. Prog. 50(6):305-11. Pethukov, B.S., and V.V. Krillov. 1958. The problem of heat exchange in the turbulent flow of liquids in tubes. Teploenergetica 4(4):63-68. Quoted in Bhatti and Shah (1987). Reid, R.S., M.B. Pate, and A.E. Bergles. 1987. ASME Paper no. 87-HT-51. ASME, New York. Quoted in Lahey (1992). Robertson, J.M., and V.V. Wadekar. 1988. Vertical upflow boiling of ethanol in a 10 mm tube. Trans. 2nd UK National Heat Transfer Conf. 1:67-77. Quoted in Steiner and Taborek (1992). Shah, M.M. 1976. A new correlation for heat transfer during boiling flow through pipes. ASHRAE Trans. 82(2):66-86. Shah, M.M. 1982. Chart correlation for saturated boiling heat transfer: equations and further study. ASHRAE Trans. 88(1):185-196. Shin shin (shin) the prominent anterior edge of the tibia or the leg. saber shin marked anterior convexity of the tibia, seen in congenital syphilis and in yaws. , J.Y., M.S. Kim, and S.T. Roe. 1997. Experimental study on forced convective boiling heat transfer of pure refrigerants and refrigerant mixtures in a horizontal tube. Int. J. Refrig. 20(4):267-75. Staub, F.W., and N. Zuber. 1966. Void fraction profiles flow mechanism and heat transfer coefficients in Refrigerant 22 evaporating in vertical tube. ASHRAE Trans. 66(1):130-46. Steiner, D., and E.U. Schlunder. 1977. Heat transfer and pressure drop for boiling nitrogen flowing in horizontal tube. In Hahne, E. and U. Grigull (eds.). Heat Transfer in Boiling. pp. 263-306, Washington: Hemisphere. Steiner, D., and J. Taborek. 1992. Flow boiling heat transfer in vertical tubes correlated by an asymptotic model. Heat Transfer Engineering 13(2):43-68. Stephen, K., and M. Abdelsalam. 1980. Heat transfer correlations for natural convection boiling. Int. J. Heat Mass Transfer 23:73-8. Talty, R.D. 1953. A study of heat transfer to organic liquids in a natural circulation vertical tube boiler boiler, device for generating steam. It consists of two principal parts: the furnace, which provides heat, usually by burning a fuel, and the boiler proper, a device in which the heat changes water into steam. . PhD thesis, University of Delaware [3] The student body at the University of Delaware is largely an undergraduate population. Delaware students have a great deal of access to work and internship opportunities. . Thome, J.R., and J.E. Hajal. 2004. Flow boiling heat transfer to carbon dioxide: general prediction method. Int. J. Refrigeration 27:294-301. Uchida, H., and S. Yamaguchi. 1966. Heat transfer in two-phase flow of Refrigerant 12 through horizontal tube. Proc. 3rd International Heat Transfer Conference, Chicago. Wattelet, J.P., J.C. Chato, A.L. Souza. and B.R. Christofferson. 1994. Evaporative characteristics of R-12, R-134a, and a mixture at low mass fluxes. ASHRAE Trans. 100:603-15. Wright, R.M. 1961. Downflow forced convection boiling of water in uniformly heated tube. Report UCRL UCRL University of California Radiation Laboratory (Berkeley, CA USA) 9744, University of California The University of California has a combined student body of more than 191,000 students, over 1,340,000 living alumni, and a combined systemwide and campus endowment of just over $7.3 billion (8th largest in the United States). , Berkley. Wright, C.C., and H.H. Walters. 1959. Single tube heat transfer tests gaseous gas·e·ous adj. 1. Of, relating to, or existing as a gas. 2. Full of or containing gas; gassy. and liquid hydrogen Liquid hydrogen is the liquid state of the element hydrogen. It is a common liquid rocket fuel for rocket applications. In the aerospace industry, its name is often abbreviated to LH2 or LH2. . WADC WADC Wright Air Development Center (USAF) WADC Washington District of Columbia Technical Report 59-423. Yoon, S.H., E.S. Cho, Y.W. Hwang, M.S. Kim, K. Min, and Y. Kim. 2004. Characteristics of evaporative heat transfer and pressure drop of carbon dioxide and correlation development, International J. Refrigeration, 27:111-19. Zurcher, O., J.R. Thome, and D. Farvat. 1998. Evaporation of ammonia in smooth horizontal tube: Heat transfer measurements and predictions. J. Heat Transfer 121:89-101. M. Mohammed Shah, PhD, PE Fellow/Life Member ASHRAE Received November 27, 2005; accepted June 7, 2006 M. Mohammed Shah is Director at Engineering Research & Consultation (ERC (database) ERC - An extended entity-relationship model. ), 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.
Table 1. Results of Comparison of Data for Horizontal Tubes with Various
Correlations
Dia., Material
Data of mm (Heating by) Fluid [p.sub.r]
Mumm (1954) 11.8 SS Water 0.014
(Elec.) 0.0624
Chawla 6.0 Copper R-11 0.0135
(1967) (Elec.)
14.0 0.0135
25.0 0.0089
0.0198
Haynes and 1.95 Copper R-11 0.0987
Fletcher (Elec.)
(2003)
Wattalet et 7.0 Copper R-12 0.088
al. (1994) (Elec.)
R-134a 0.086
Uchida and 6.4 SS R-12 0.097
Yamaguchi (Elec.)
(1966)
Chaddock 11.7 SS R-12 0.1098
and (Elec.)
Noerager
(1966)*
Ebisu, and 6.4 Copper R-22 0.11
Torikoshi (Liquid)
(1998)
Mathur 9.5 SS R-22 0.097
(1976) (Elec.) 0.16
Johnston 11.6 Copper R-22 0.0134
and (Elec.) 0.0581
Chaddock
(1964)*
Muzzio et 8.9 Copper R-22 0.117
al. (1998)* (Liquid)
Pierre 18.0 Copper R-22 0.071
(1957)* (Liquid)
12.0 0.049
Jung et al. 9.0 Copper R-22 0.080
(1989a, (Elec.)
1989b) R-114 0.081
R-152a 0.08
Reid et al. 8.7 (Elec.) R-113 0.117
(1987)
Shin et al. 7.7 SS R-22 0.145
(1997) (Elec.)
R-32 0.20
R-134a 0.109
Propane 0.158
Isobutane 0.065
Gouse and 10.9 Glass, nickel- R-113 0.031
Coumo coated 0.035
(1965) (Elec.)
Murata and 10.3 Copper R-114 0.061
Hashizume
(1990) R-123 0.0546
Hambreaus 12.0 Copper R-134a 0.049
(1995) (Elec.)
Chaddock 7.7 Copper R-502 0.0085
and (Elec.) 0.059
Buzzard
(1986)
Kattan 12.0 Copper R-502 0.15
et al. (liquid)
(1998)
Zurcher et 14.0 SS N[H.sub.3] 0.044
al. (1998) (liquid)
Steiner and 14.0 Copper Nitrogen 0.186
Schlunder (Elec.) 0.461
(1977)
Klein 12.0 Copper Nitrogen 0.0873
(1976) (Elec.)
Mohr and 4.0 Copper Neon 0.0564
Runge (Elec.)
(1977)
Wright and 6.3 Copper Para [H.sub.2] 0.0175
Walters (Elec.)
(1959)
Muller 14.0 Copper Argon 0.036
et al. (Elec.) 0.413
(1983)
All data 1.95 0.0134
25.0 0.413
Data of G, kg/[m.sup.2]s q, kW/[m.sup.2] x, % Bo x [10.sup.4]
Mumm 345 157 0.00 0.53
(1954) 1382 788 52.0 11.0
Chawla 40 2.3 10.0 2.0
(1967) 252 69.9 90.0 26.7
25 1.2 10.0 0.51
130 23.3 90.0 24.3
22 1.8 10 1.3
74 11.6 90 28.0
Haynes and 150 53.0 0.00 7.75
Fletcher 420 17.0 21.7
(2003)
Wattalet et 50 2.0 10.0 1.1
al. (1994) 300 20.0 92.0 6.7
300 50 5.0 0.85
300 90.0 5.1
Uchida and 345 14.4 0.00 1.9
Yamaguchi 518 27.9 95.0 5.7
(1966)
Chaddock 122 3.5 26.1 0.99
and 585 35.2 54.5 7.94
Noerager
(1966)*
Ebisu, and 300 7.5 20.0 1.2
Torikoshi 80.0
(1998)
Mathur 146 7.7 3.0 2.5
(1976) 877 40.5 80.0 6.8
Johnston 15 1.7 9.7 3.2
and 571 21.5 38.5 13.3
Chaddock
(1964)*
Muzzio et 90 5.2 0.45 2.9
al. (1998)* 400 24.0 3.0
Pierre 52 3.5 0.45 3.1
(1957)* 178 11.7
132 12.8 0.55 4.4
225 21.5 4.8
Jung et al. 362 17.0 10.0 2.2
(1989a, 516 44.0 70.0 4.1
1989b) 362 10.0 12.0 1.5
516 36.4 70.0 4.1
367 17.0 5.0 1.5
36.2 68.0 4.0
Reid et al. 248 18.4 3.0 5.8
(1987) 75.0
Shin et al. 424 18 10 0.69
(1997) 742 30 79 3.64
424 30.0 5.0 1.7
583 50.0 2.4
424 30.0 10.0 2.7
583 79.0 3.7
424 30.0 10.0 1.44
583 68.0 1.98
424 30.0 1.0 1.5
583 68.0 2.1
Gouse and 517 12.9 2.2 1.3
Coumo 699 22.1 36.6 2.9
(1965)
Murata and 300 30.0 20.0 4.1
Hashizume 80.0
(1990) 100 10.0 20.0 2.1
300 30.0 92.0 18.5
Hambreaus 137 6.0 30.0 2.1
(1995) 90.0
Chaddock 45 3.8 20 4.2
and 358 23.7 70 5.2
Buzzard
(1986)
Kattan 100 8.0 3.0 2.1
et al. 300 10.0 54.0 6.2
(1998)
Zurcher et 10 8.0 0.03 0.76
al. (1998) 140 71.6 0.90 6.5
Steiner and 44 0.5 5.0 1.0
Schlunder 460 34.6 75.0 9.2
(1977)
Klein 154 1.0 10 0.26
(1976) 209 50.0 90 17.4
Mohr and 78 1.0 13.0 6.0
Runge 125 20.0 70.0 34.7
(1977)
Wright and 412 10.0 2.6 0.42
Walters 1180 99.7 5.2 2.5
(1959)
Muller 120 1.8 0.1 0.36
et al. 460 97.0 0.9 74.2
(1983)
All data 10 1.0 0.0 0.26
1382 788 95.0 74.2
No. of Shah
Data of Co [Fr.sub.L] data 1982
Mumm (1954) 0.04 1.1 184 11.4
1000 20.0 -5.6
0.02 0.025 57 14.8
Chawla 0.28 0.46 -14.8
(1967) 0.01 0.002 29 11.7
0.28 0.045 8.2
0.01 8E-4 52 18.8
0.34 0.099 15.8
Haynes and 0.46 0.63 6 27.0
Fletcher 1000 4.93 -23.1
(2003)
Wattalet et 0.01 0.019 50 12.9
al. (1994) 0.72 0.62 -12.3
0.02 0.022 52 16.3
1.2 0.80 -8.5
Uchida and 0.01 0.25 40 21.8
Yamaguchi 1000 2.5 -21.5
(1966)
Chaddock 0.16 0.071 19 16.4
and 0.36 1.63 -13.6
Noerager
(1966)*
Ebisu, and 0.04 0.88 4 20.2
Torikoshi 0.41 -20.2
(1998)
Mathur 0.03 0.14 69 17.1
(1976) 2.7 5.8 -8.7
Johnston 0.09 0.0016 22 13.8
and 0.28 0.0147 -1.7
Chaddock
(1964)*
Muzzio et 0.16 0.058 4 26.7
al. (1998)* 1.14 -26.7
Pierre 0.13 0.009 6 8.2
(1957)* 0.103 -1.3
0.08 0.082 8 5.1
0.232 5.1
Jung et al. 0.06 0.87 12 13.4
(1989a, 0.66 1.8 -12.7
1989b) 0.05 0.69 20 7.8
0.56 1.4 3.4
0.06 2.1 19 9.7
0.44 -9.7
Reid et al. 0.06 0.362 9 19.9
(1987) 2.24 -19.5
Shin et al. 0.05 1.54 35 8.5
(1997) 0.91 4.74 -4.7
0.18 2.3 12 9.6
1.9 4.4 -9.4
0.05 1.52 16 8.5
0.6 2.9 1.2
0.09 9.1 12 5.9
0.98 17.1 3.8
0.06 7.4 13 16.8
4.1 14.0 16.8
Gouse and 2.2 1.05 10 8.4
Coumo 36.6 1.91 7.6
(1965)
Murata and 0.08 0.39 3 13.0
Hashizume 0.66 -13.0
(1990) 0.01 0.05 26 13.0
0.28 0.45 -12.3
Hambreaus 0.02 0.09 21 18.9
(1995) 0.17 11.5
Chaddock 0.04 0.008 26 12.3
and 0.36 0.567 5.4
Buzzard
(1986)
Kattan 0.14 0.049 15 19.0
et al. 2.61 0.442 -17.1
(1998)
Zurcher et 0.01 0.0024 106 21.9
al. (1998) 1.36 0.473 1.7
Steiner and 0.05 0.031 42 58.6
Schlunder 2.2 3.3 -58.6
(1977)
Klein 0.02 0.35 21 29.3
(1976) 0.74 0.61 -19.7
Mohr and 0.05 0.11 15 48.4
Runge 0.49 00.28 -48.4
(1977)
Wright and 1.88 587 18 17.6
Walters 4.15 4822 2.0
(1959)
Muller 0.05 0.064 33 23.4
et al. 1.79 1.35 -0.3
(1983)
All data 0.01 0.0008 1086 17.5
1000 4822 -6.4
Mean Deviation, %
Average Deviation, % ([dagger])
Data of G-W L-W Kandlikar S-T Chen-Cooper
Mumm (1954) 10.9 13.2 13.3 31.8 32.2
-0.2 -6.1 -10.1 -31.1 -30.9
Chawla 19.9 28.3 13.9 36.1 21.2
(1967) -15.1 -28.3 -7.6 -34.1 -20.7
14.6 19.0 12.0 58.7 30.0
-4.7 -3.4 10.9 51.4 24.7
12.5 17.3 17.9 105.4 54.8
1.2 -0.9 13.2 103.6 54.8
Haynes and 13.2 35.3 19.2 73.8 25.1
Fletcher -5.2 -35.3 10.6 -73.8 -25.1
(2003)
Wattalet et 15.5 16.2 11.8 20.2 8.5
al. (1994) -12.8 -10.4 -2.7 2.4 -3.7
13.3 13.5 NA 25.1 12.7
-12.0 -7.2 14.5 -3.4
Uchida and 20.8 15.6 15.7 18.3 18.3
Yamaguchi -19.9 -11.7 -10.4 -19.2 -18.1
(1966)
Chaddock 13.0 15.6 12.8 11.6 21.7
and -5.5 2.3 -2.4 -7.9 -17.1
Noerager
(1966)*
Ebisu, and 22.5 17.5 20.6 12.2 16.5
Torikoshi -22.5 -17.5 -3.9 4.1 -16.5
(1998)
Mathur 18.4 18.4 48.0 22.7 16.9
(1976) -2.8 3.4 43.5 1.3 -10.4
Johnston 21.4 50.1 86.3 18.5 25.9
and -20.4 -50.1 86.3 -15.4 25.3
Chaddock
(1964)*
Muzzio et 17.8 17.6 9.1 10.9 19.6
al. (1998)* -10.4 -10.4 9.1 -7.4 -16.5
Pierre 11.6 22.3 41.7 34.2 2.3
(1957)* 0.3 -2.9 41.7 34.2 1.9
6.9 8.0 41.8 30.0 1.8
6.9 8.0 41.8 30.0 -0.8
Jung et al. 14.5 13.7 37.0 12.3 25.3
(1989a, -8.9 -10.5 33.0 -2.7 -18.3
1989b) 14.7 14.4 12.5 29.9 5.6
10.4 13.7 10.7 29.9 -4.8
13.0 60.2 9.3 35.9 10.4
-3.6 60.2 -7.0 35.9 -9.7
Reid et al. 13.5 14.5 9.9 25.7 18.4
(1987) -11.4 -9.9 -8.8 -24.1 -18.4
Shin et al. 13.4 12.7 51.5 23.4 6.5
(1997) 4.9 9.0 50.9 17.9 -6.2
9.0 13.6 NA 22.7 8.3
3.0 10.6 1.2 -8.3
14.3 14.2 NA 28.4 7.3
7.3 9.9 20.3 -7.1
16.3 26.9 NA 32.6 1.9
14.2 26.9 32.5 0.8
20.2 33.2 NA 46.5 3.7
18.4 33.2 43.5 3.2
Gouse and 18.8 41.4 23.6 24.6 9.2
Coumo 18.8 41.4 23.6 21.4 -9.2
(1965)
Murata and 9.1 14.1 9.2 18.6 27.7
Hashizume -9.1 -14.1 -9.2 -13.4 -27.7
(1990)
14.0 11.1 NA 16.1 17.1
-11.2 -4.1 -1.4 -17.1
Hambreaus 17.3 20.6 NA 40.3 12.3
(1995) 1.3 14.2 40.2 2.3
Chaddock 15.2 16.3 NA 29.4 9.7
and 6.1 4.7 28.5 3.3
Buzzard
(1986)
Kattan 15.5 26.5 NA 32.7 8.7
et al. -7.0 -9.8 -22.2 -7.0
(1998)
Zurcher et 23.4 25.5 NA 29.8 27.5
al. (1998) -4.7 -9.7 17.9 13.5
Steiner and 52.2 44.4 51.4 26.0 46.6
Schlunder -52.2 -42.1 45.8 -6.8 -44.9
(1977)
Klein 33.8 29.2 120.2 23.0 29.0
(1976) -17.5 -16.1 106.1 6.4 -29.0
Mohr and 40.4 63.4 52.4 56.8 60.0
Runge -40.4 -63.4 43.6 -56.8 -60.0
(1977)
Wright and 18.5 27.0 NA 13.2 45.7
Walters 11.5 -27.0 -4.3 -46.7
(1959)
Muller 38.4 116.2 NA 169.7 38.0
et al. 24.5 114.9 164.7 28.5
(1983)
All data 18.9 26.0 27.8 36.8 23.7
-4.9 -4.9 +6.6 +9.8 -7.5
* Reported heat transfer coefficients are mean for the tube length. All
other data are local heat transfer coefficients.
([dagger]) For each data set, the upper row gives the mean deviation and
the lower row gives the average deviation.
Table 2. Results of Comparison of Data for Vertical Tubes and Annuli
with Various Correlations
Dia., Material
Data of mm (Heating by) Fluid [p.sub.r]
Naitoh (1974) 16.5 SS Water 0.783
(Liquid)
Wright (1961) 18.2 SS Water 0.0053
(Elec.) 0.0078
12.0 0.0068
0.014
Dengler and 25.4 Copper Water 0.011
Addoms (1956) (Steam)
Piret and Isbin 27.1 Copper Water 0.0046
(1954)* (Elec.)
C[Cl.sub.4] 0.022
n-butanol 0.0204
Isopropyl 0.011
Alcohol
Adorni et al. 3.2 (a) SS Water 0.32
(1961) (Elec.)
3.2 (b) 0.32
8.5 (c) 0.32
Morozov (1969) 13.8 (d) SS water 0.228
(Elec.)
Robertson and 10.0 Copper Ethanol 0.0244
Wadekar (1988) (Elec.)
Staub and Zuber 10.0 Copper R-22 0.121
(1966) (Elec.)
Lazarek and 3.15 SS R-113
Black (1982) (Elec.)
Johannes (1972) 2.1 Monel Helium 0.477
(Elec.)
Keilin et al. 2.0 Copper Helium 0.57
(1975) (Elec.) 0.68
Ogata and Sato 1.1 SS Helium 0.477
(1974) (Elec.)
Pappel and 2.0 SS Nitrogen 0.64
Hendricks (Elec)
(1978)
Klimenko and 10.0 SS Nitrogen 0.087
Sudarchikov (Elec.) 0.203
(1983)
Klimenko et al. 9.0 SS Nitrogen 0.14
(1987) (Elec.) 0.26
Bennet 20.4 Ethylene 0.026
(1976) (e) glycol
Talty (1953) 19 Brass Heptane 0.037
(Liquid)
25.3
19.0 Pentane 0.030
25.3
19.0 Methanol 0.0156
25.3
25.4 Cyclohexane 0.025
19.0
25.4 Benzene .0203
19.0
All data 1.1 0.0053
27.1 0.783
G, q,
Data of kg/[m.sup.2]s kW/[m.sup.2] x, % Bo x [10.sup.4]
Naitoh (1974) 1250 100 0.0 0.96
523 60.0 5.02
Wright (1961) 434 99 1.0 0.56
796 154 11.8 1.5
666 118 1.4 0.52
2437 274 10.0 1.07
Dengler and 721 95 1.7 0.6
Addoms (1956) 448 13.5 2.83
Piret and Isbin 394 19.4 0.19 0.22
(1954)* 822 165 0.45 0.84
347 5.9 0.64 0.29
943 55.3 2.4 0.99
555 16.9 0.4 0.51
706 70.0 1.5 1.73
681 10.8 0.26 0.29
779 85.7 1.6 1.8
Adorni et al. 980 420 14.0 0.66
(1961) 3000 1250 69.6 5.9
980 91 7.4 0.65
3800 688 70.1 4.5
1010 137 21.0 0.9
2954 812 70.1 2.34
Morozov (1969) 6085 261 0.0 0.24
11071 375 20.0 0.26
Robertson and 145 25.5 3.0 2.1
Wadekar 290 104.6 56.0 7.0
(1988)
Staub and Zuber 153 12.1 4.0 3.95
(1966) 896 70.7 21.0 3.98
Lazarek and 502 64.0 4.0 16.1
Black (1982) 60.0 25.2
Johannes (1972) 130 0.5 3.2 2.0
1.5 25.0 5.8
Keilin et al. 28 0.1 1.3 1.3
(1975) 96 3.0 39.4 40.3
Ogata and Sato 87 0.2 2.0 0.9
(1974) 1.4 40.0 8.1
Pappel and 2210 212 0.00 9.2
Hendricks (1978)
Klimenko and 310 13.7 0 2.2
Sudarchikov 490 20.3 0.08 3.3
(1983)
Klimenko et al. 220 9.0 2.0 2.35
(1987) 27.0 70.0 7.05
Bennet 206 136 0.0
(1976) (e) 1030 576 26.9
Talty (1953) 231 7.7 0.14 0.99
454 31.7 8.1 1.73
266 13.6 0.20 0.69
391 35.6 5.00 1.59
251 9.1 0.28 0.85
408 22.9 8.3 2.16
266 13.6 0.61 1.11
399 38.4 11.7 3.74
280 26.2 0.12 0.85
459 49.7 4.3 1.40
314 20.3 0.19 0.60
553 53.5 4.3 1.09
335 10.1 0.5 0.58
488 41.6 10.0 3.02
390 7.9 0.36 0.46
482 24.1 6.1 1.86
347 12.7 0.20 0.59
600 41.4 8.5 2.58
293 16.5 0.26 1.34
521 43.1 8.7 2.75
All data 28 0.2 0.00 0.22
11071 1250 70.1 40.3
No. of
Data
Data of Co Point Shah
Naitoh (1974) 0.34 7 8.8
1000 -8.8
Wright (1961) 0.15 71 10.1
1.0 1.4
0.18 37 21.5
6.4 19.8
Dengler and 0.15 5 11.5
Addoms (1956) 0.98 8.8
Piret and Isbin 1.27 4 9.7
(1954)* 3.4 9.7
1.17 4 9.1
3.43 -8.5
1.62 4 7.8
4.6 -7.8
1.02 4 6.5
4.43 -6.5
Adorni et al. 0.18 39 22.2
(1961) 1.68 -14.7
0.11 38 18.1
1.68 -11.2
0.11 8 46.8
0.63 -46.8
Morozov (1969) 0.55 6 20.9
1000 4.4
Robertson and 0.05 51 21.3
Wadekar (1988) 0.90 -21.3
Staub and Zuber 0.41 8 40.0
(1966) 1.12 -40.0
Lazarek and 0.06 10 10.4
Black (1982) 1.14 5.4
Johannes (1972) 0.92 7 27.2
5.86 19.2
Keilin et al. 0.49 15 28.5
(1975) 11.0 9.5
Ogata and Sato 0.53 14 11.2
(1974) 8.62 -5.5
Pappel and 1000 1 0.10
Hendricks -0.10
(1978)
Klimenko and 1.0 14 15.3
Sudarchikov 4.5 15.3
(1983)
Klimenko et al. 0.09 20 13.9
(1987) 7.05 -3.7
Bennet 101 21.4
(1976) (e) -7.4
Talty (1953) 0.53 33 18.6
6.9 0.8
0.77 28 16.9
3.98 -15.5
0.48 51 13.1
16.6 -0.9
0.35 54 11.3
16.7 -10.6
0.48 22 25.9
7.3 -25.9
0.65 54 35.2
5.5 -35.2
0.37 52 15.9
4.46 -15.9
0.57 23 8.9
5.71 -5.2
0.39 55 13.7
8.4 -11.2
0.4 48 11.7
6.8 -5.9
All data 0.09 888 18.0
1000 -9.0
Mean Deviation, %
Average Deviation, % ([dagger])
Kand- Chen-
Data of G-W L-W likar S-T Cooper
Naitoh (1974) 8.0 110.8 15.9 28.8 38.4
-0.2 110.8 -15.2 -28.8 -38.4
Wright (1961) 11.4 14.5 8.7 25.0 12.6
-8.6 11.2 -6.6 23.0 12.3
24.0 37.1 15.1 43.9 10.8
21.9 36.8 12.3 42.8 0.0
Dengler and 21.3 34.7 13.1 40.1 12.2
Addoms (1956) 21.3 34.7 9.9 40.1 12.2
Piret and Isbin 40.9 88.3 10.2 53.4 6.4
(1954)* 40.9 88.3 10.2 53.4 -3.6
13.5 80.8 NA 26.9 5.6
13.5 80.8 26.9 0.2
3.7 47.9 NA 13.0 22.8
-1.5 47.9 -12.2 -22.8
7.8 90.7 NA 10.3 12.9
7.8 90.7 8.0 -12.9
Adorni et al. 15.0 15.4 24.5 29.3 32.2
(1961) -4.2 -5.5 -15.2 -22.2 -27.4
14.9 19.5 19.5 22.7 17.0
5.9 -0.2 -13.8 -0.5 -11.7
42.3 41.7 50.3 38.9 45.4
-42.3 -40.6 -50.3 -38.9 -45.4
Morozov (1969) 28.6 16.7 30.5 58.5 35.9
25.5 9.6 -17.5 32.0 11.8
Robertson and 17.7 23.3 NA 20.6 9.4
Wadekar -17.7 23.3 -19.6 -6.6
(1988)
Staub and Zuber 33.8 34.8 33.5 57.5 45.2
(1966) -33.8 -34.8 33.4 -57.7 -45.2
Lazarek and 32.5 23.1 38.2 54.5 24.4
Black (1982) 32.5 -23.1 37.6 -54.5 -24.4
Johannes (1972) 35.6 35.1 NA 25.9 51.5
31.6 -35.1 -25.9 -51.5
Keilin et al. 41.1 24.8 NA 19.5 39.7
(1975) 41.1 -24.8 -13.5 -39.7
Ogata and Sato 12.3 15.1 NA 14.7 29.5
(1974) 9.1 -14.1 11.3 -29.4
Pappel and 19.6 14.3 436.3 12.5 52.0
Hendricks (1978) 19.6 -14.3 436.3 12.5 -52.5
Klimenko and 21.7 16.6 397 39.5 6.4
Sudarchikov 21.7 15.8 397 39.5 4.8
(1983)
Klimenko et al. 19.7 16.1 269.8 32.3 14.7
(1987) 6.8 7.8 269.8 11.3 -7.2
Bennet 23.4 21.9 NA
(1976) (e) 2.0 12.1
Talty (1953) 18.6 19.7 NA 13.6 27
8.9 17.4 -9.1 -27
10.5 17.1 NA 18.9 34.3
-6.8 7.9 -16.1 34.3
11.4 24.5 NA 12.2 20.5
9.1 24.0 -1.8 -20.0
5.4 10.9 NA 17.4 36.4
-2.1 7.5 -16.5 -36.4
16.7 38.8 NA 18.7 13.3
-16.7 38.8 -17.0 -1.4
21.9 33.6 NA 12.1 22.2
-21.9 33.6 -10.7 -22.2
6.8 24.0 NA 16.8 26.0
-6.4 24.0 -15.6 -26.0
9.8 51.4 NA 15.4 9.6
9.1 51.4 6.0 -9.2
9.3 24.7 NA 9.9 28.0
-0.3 24.6 -3.6 -28.0
8.2 17.2 NA 16.6 22.0
1.2 16.8 -16.3 -21.3
All data 15.9 24.8 65.4 20.4 22.7
+9.5
* Reported heat transfer coefficients are mean for the tube length. All
other data are local heat transfer coefficients.
([dagger]) For each data set, the upper row gives the mean deviation and
the lower row gives the average deviation.
a. Annulus, 8.2/5.0 OD/ID, bilateral heating, data for outer tube.
b. Annulus, 8.2/5.0 OD/ID, bilateral heating, data for inner tube.
c. Annulus, 8.2/5.0 OD/ID, heating on inner tube only.
d. Annulus, 20.0/14.2 OD/ID, inner tube heated.
e. Results are as reported in Liu and Winterton (1991).
Table 3. Summary of Results for Both Horizontal and Vertical Channels
Mean Dev. %
Correlation of a b
Shah 17.7 17.3
Gungor and Winterton 17.6 18.6
Chen-Cooper 23.2 22.4
Liu and Winterton 25.5 37.5
Steiner and Taborek 30.0 36.5
Kandlikar 32.3 55.0
a. Giving equal weight to each data point.
b. Giving equal weight to each data set.
Table 4. Complete Range of Data Satisfactorily Predicted by the
Correlation of Shah (1982)
Parameter Range of Data
Fluids Water, R-11, R-12, R-22, R-32, R-113, R-114,
R-123, R-134a, R-152a, R-502, ammonia, propane,
isobutane, carbon tetrachloride, isopropyl
alcohol, ethanol, methanol, n-butanol,
cyclohexane, benzene, heptane, pentane, ethylene
glycol, argon, hydrogen, nitrogen, and helium
Test channels Tubes and annuli (heated on inside, outside, and
bilateral); horizontal and vertical
Heating method Electric, condensing steam, liquid
Diameter, mm 1.1 to 27.1
Reduced pressure 0.0053 to 0.78
G, kg/[m.sup.2]s 10 to 11,071
q, kW/[m.sup.2] 0.2 to 1,250
x, percent 0 to 95
[B.sub.o] x [10.sup.4] 0.22 to 74.2
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