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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley-ASME Press Series
- Sprache: Englisch
A guide to two-phase heat transfer theory, practice, and applications Designed primarily as a practical resource for design and development engineers, Two-Phase Heat Transfer contains the theories and methods of two-phase heat transfer that are solution oriented. Written in a clear and concise manner, the book includes information on physical phenomena, experimental data, theoretical solutions, and empirical correlations. A very wide range of real-world applications and formulas/correlations for them are presented. The two-phase heat transfer systems covered in the book include boiling, condensation, gas-liquid mixtures, and gas-solid mixtures. The author a noted expert in this field also reviews the numerous applications of two-phase heat transfer such as heat exchangers in refrigeration and air conditioning, conventional and nuclear power generation, solar power plants, aeronautics, chemical processes, petroleum industry, and more. Special attention is given to heat exchangers using mini-channels which are being increasingly used in a variety of applications. This important book: * Offers a practical guide to two-phase heat transfer * Includes clear guidance for design professionals by identifying the best available predictive techniques * Reviews the extensive literature on heat transfer in two-phase systems * Presents information to aid in the design and analysis of heat exchangers. Written for students and research, design, and development engineers, Two-Phase Heat Transfer is a comprehensive volume that covers the theory, methods, and applications of two-phase heat transfer.
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Veröffentlichungsjahr: 2021
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Table of Contents
Cover
Wiley-ASME Press Series
Title Page
Copyright
Preface
1 Introduction
1.1 Scope and Objectives of the Book
1.2 Basic Definitions
1.3 Various Models
1.4 Classification of Channels
1.5 Flow Patterns in Channels
1.6 Heat Transfer in Single‐Phase Flow
1.7 Calculation of Pressure Drop
1.8 Calculation of Void Fraction
1.9 CFD Simulation
1.10 General Information
References
2 Heat Transfer During Condensation
2.1 Introduction
2.2 Condensation on Plates
2.3 Condensation Inside Plain Channels
2.4 Condensation Outside Tubes
2.5 Condensation with Enhanced Tubes
2.6 Condensation of Superheated Vapors
2.7 Miscellaneous Condensation Problems
2.8 Condensation of Vapor Mixtures
2.9 Liquid Metals
2.10 Dropwise Condensation
Nomenclature
References
3 Pool Boiling
3.1 Introduction
3.2 Nucleate Boiling
3.3 Critical Heat Flux
3.4 Transition Boiling
3.5 Minimum Film Boiling Temperature
3.6 Film Boiling
3.7 Various Topics
Nomenclature
References
4 Forced Convection Subcooled Boiling
4.1 Introduction
4.2 Inception of Boiling in Channels
4.3 Prediction of Subcooled Boiling Regimes in Channels
4.4 Prediction of Void Fraction in Channels
4.5 Heat Transfer in Channels
4.6 Single Cylinder with Crossflow
4.7 Various Geometries
References
5 Saturated Boiling with Forced Flow
5.1 Introduction
5.2 Boiling in Channels
5.3 Plate‐Type Heat Exchangers
5.4 Boiling in Various Geometries
5.5 Horizontal Tube Bundles with Upward Crossflow
5.6 Horizontal Tube Bundles with Falling Film Evaporation
5.7 Boiling of Multicomponent Mixtures
5.8 Liquid Metals
5.9 Effect of Gravity
Nomenclature
References
6 Critical Heat Flux in Flow Boiling
6.1 Introduction
6.2 CHF in Tubes
6.3 CHF in Annuli
6.4 CHF in Various Geometries
References
7 Post‐CHF Heat Transfer in Flow Boiling
7.1 Introduction
7.2 Film Boiling in Vertical Tubes
7.3 Film Boiling in Horizontal Tubes
7.4 Film Boiling in Various Geometries
7.5 Minimum Film Boiling Temperature and Heat Flux
7.6 Transition Boiling
References
8 Two‐Component Gas–Liquid Heat Transfer
8.1 Introduction
8.2 Pre‐mixed Mixtures in Channels
8.3 Gas Flow through Channel Walls
8.4 Cooling by Air–Water Mist
8.5 Evaporation from Water Pools
8.6 Various Topics
8.7 Liquid Metal–Gas in Channels
References
9 Gas‐Fluidized Beds
9.1 Introduction
9.2 Regimes of Fluidization
9.3 Properties of Solid Particles
9.4 Parameters Affecting Heat Transfer to Surfaces
9.5 Theories of Heat Transfer
9.6 Prediction Methods for Single Tubes and Spheres
9.7 Tube Bundles
9.8 Radiation Heat Transfer
9.9 Heat Transfer to Bed Walls
9.10 Heat Transfer in Freeboard Region
9.11 Heat Transfer Between Gas and Particles
9.12 Gas–Solid Flow in Pipes
9.13 Solar Collectors with Particle Suspensions
References
Appendix
Index
End User License Agreement
List of Tables
Chapter 1
1.4.1 Criteria for macro to mini transition by various authors.
1.5.1 Range of data with which flow pattern map of Mandhane et al. was verified.
Chapter 2
2.3.1 Range of data with which Shah (2019a) was verified.
2.3.2 Deviations of various correlations.
2.3.3 Salient features of studies on inclined tubes.
Chapter 3
3.2.1 Some experimental studies on pool boiling of mercury.
3.2.2 Some experimental studies on pool boiling of alkali metals.
3.3.1 Correction factors to the Zuber formula for CHF.
3.3.2 Liquid metal CHF data used in developing Shah correlation.
3.3.3 The range of data for which the Shah correlation (1996) was verified.
Chapter 4
4.5.1 Range of data for which Shah (2017a) correlation for subcooled boiling in channels was verified.
4.5.2 Results of evaluation of various correlations for subcooled boiling in channels.
4.6.1 The range of data with which the Shah (2005) correlation for subcooled boiling in crossflow was validated.
Chapter 5
5.2.1 Values of
F
fl
in the Kandlikar et al. correlation for surfaces other than stainless steel for which
F
fl
= 1 for all fluids.
5.2.2 The range of data analyzed by Shah (2017a).
5.2.3 Deviations of various correlations for boiling heat transfer in different ranges of parameters.
5.3.1 Verified range of the Almalfi et al. (2016b) correlation for boiling heat transfer in herringbone‐type plate heat exchangers.
5.4.1 The range of data for boiling in helical coils analyzed by Shah.
5.5.1 Range of data with which the Shah (2017b) correlation for horizontal tube bundle was verified.
5.5.2 Summary of comparison of data for horizontal tube bundles with the Shah (2017b) correlation.
5.8.1 Values of
B
and
n
in Eq. (5.8.10), the correlation of Fisher (1964) for boiling of rubidium
Chapter 6
6.2.1 Range of CHF data analyzed in Shah (1987).
6.2.2 Results of comparison of CHF data with various correlations.
6.2.3 Range of data used to validate the Shah correlation for CHF in horizontal channels.
6.2.4 Results of comparison of data for CHF in horizontal channels with various correlations by Shah (2015a).
6.2.5 Range of data for minichannels analyzed by Shah (2017).
6.3.1 The range of data satisfactorily predicted by the Shah correlation for annuli.
6.3.2 Summary of results of data analysis by Shah (2015b) for CHF in annuli.
6.4.1 The range of data on which some correlations for CHF in coils were based.
6.4.2 Summary of results of comparison of correlations with data for CHF in coils.
Chapter 7
7.2.1 Range of data for film boiling in vertical tubes analyzed by Shah.
7.2.2 Summary of results of comparison of data for film boiling in vertical tubes with various correlations.
7.3.1 Range of parameters in data for film boiling in horizontal tubes analyzed by Shah (2017).
7.3.2 Results of comparison of data for film boiling in horizontal tubes with various correlations done by Shah (2017).
Chapter 8
8.2.1 Constants and exponents in the flow pattern‐based correlation of Kim and Ghajar (2002).
8.2.2 Range of data with which the Shah correlation for horizontal pipes was verified.
8.2.3 Results of comparison of data for gas–liquid heat transfer in horizontal tubes with various correlations reported by Shah (2018a).
8.2.4 Range of data for heat transfer to gas–liquid mixtures flowing in vertical channels analyzed by Shah (2018b).
8.2.5 Deviations of various correlations with data for vertical channels in various ranges of
Re
LS
8.5.1 Constants and exponents for Eq. (8.5.1) for evaporation from calm water surfaces in various sources.
8.5.2 Range of data for which the Shah model for evaporation from water pools was verified.
Chapter 9
9.6.1 Values of accommodation coefficient
ϒ
at 25 °C in the Martin model.
9.6.2 Range of parameters in data for maximum heat transfer with which the Shah correlation was verified.
9.6.3 Deviations of various correlations for maximum heat transfer with test data.
9.12.1 The range of data for which the Shah (2020) correlation for heat transfer during gas–solid flow in pipes was verified.
9.12.2 Results of comparison of test data for heat transfer to gas–solid flowing in pipes with various correlations.
1
A.1 Unit conversion factors.
A.2 Physical properties of some fluids.
A.3 Properties of dry air at room temperature.
A.4 Properties of saturated ammonia.
A.5 Properties of saturated carbon dioxide.
A.6 Properties of saturated helium‐4.
A.7 Properties of saturated nitrogen.
A.8 Properties of saturated propane.
A.9 Properties of saturated R1234yf.
A.10 Properties of saturated R‐134a.
A.11 Properties of saturated water.
List of Illustrations
Chapter 1
Figure 1.5.1 Flow patterns during co‐current gas–liquid flow in horizontal tubes. Source: From Rouhani and Sohal (1983). © 1983 Elsevier.
Figure 1.5.2 Flow patterns during evaporation in horizontal tubes. (a) High mass velocity (400 kg s
−1
m
−2
), subcooled liquid at inlet. (b) Low mass velocity (200 kg s
−1
m
−2
), 20% flash gas at inlet. Source: From ASHRAE (2017).
Figure 1.5.3 Baker flow pattern map for co‐current gas–liquid flow in horizontal pipes. Source: From Rouhani and Sohal (1983). © 1983 Elsevier.
Figure 1.5.4 The Mandhane et al. flow pattern map for co‐current flow in horizontal pipes. Source: From Ghiaasiaan et al. and Cambridge University Press. © 1974 Elsevier.
Figure 1.5.5 Flow patterns during upflow in vertical pipes. Source: From Rouhani and Sohal (1983). © 1983 Elsevier.
Figure 1.5.6 Example of flow patterns according to the transition criteria of Mishima and Ishii. Source: From Mishima and Ishii (1984). © 1984 Elsevier.
Figure 1.5.7 Flow patterns predictions of McQuillan and Whalley for evaporating R‐11 during upflow in a vertical tube under the conditions shown. Source: From McQuillan and Whalley (1985). © 1985 Elsevier.
Figure 1.5.8 Effect of pipe inclination
β
on flow patterns during air–water flow in 51 mm diameter pipe at room temperature and pressure. The predictions are by Barnea (1987) and the data are of Shoham (1982). Source: From Barnea (1987). © 1987 Elsevier.
Figure 1.5.9 Flow patterns observed during flow of air–water across a horizontal tube bundle: (a) downflow and (b) upflow. Source: From Xu et al. (1998). © 1998 Elsevier.
Figure 1.5.10 Comparison of flow patterns under microgravity from several studies with the map by Dukler et al. (1988). Source: From Rezkallah (1990). © 1990 Elsevier.
Chapter 2
Figure 2.2.1 Condensation of stagnant vapor on a flat plate. Source: Rohsenow (1973a). © 1973 McGraw‐Hill.
Figure 2.3.1 Boundaries of heat transfer regimes for vertical and horizontal tubes in the Shah correlation (2009, 2013). Source: Reprinted from Shah (2016a). © 2016, with permission from Elsevier.
Figure 2.3.2 Comparison of the data of Jung et al. (2003) for R‐142b with various correlations.
D
= 8 mm,
T
SAT
= 40 °C, and
G
= 300 kg m
−2
s
—1
. “Present” is Shah (2014) flow pattern‐based correlation and “Shah” is Shah (2013) correlation. Source: Reprinted from Shah (2014). ©2014, with permission from Begell House, Inc.
Figure 2.3.3 Comparison of correlations with the data of Wang and Du (2000) for water in a horizontal tube.
D
= 4.98 mm,
T
SAT
= 105 °C,
G
= 14.1 kg m
−2
s
−1
, and
We
GT
= 24. Source: From Shah (2019a). © 2019 Elsevier.
Figure 2.3.4 Data of Fronk and Garimella (2016) for ammonia in a 1.44 mm diameter horizontal tube compared to various correlations.
T
SAT
= 40 °C,
G
= 75 kg m
−2
s
−1
, and
We
GT
= 39. “Present” is Shah (2019a) correlation. Source: From Shah (2019a). © 2019 Elsevier.
Figure 2.3.5 Comparison of the data of Son and Lee (2009) for R‐134a with correlations. Present 1 and 2 are correlations of Shah (2016c).
D
= 3.36 mm,
T
SAT
= 40 °C,
G
= 400 kg m
−2
s
−1
, and
We
GT
= 1757. Source: From Shah (2016c). © 2016 Elsevier.
Figure 2.3.6 Effect of inclination on heat transfer in a square channel with
D
HYD
= 1.25 mm. R‐134a with
T
SAT
= 40 °C. Source: From Del Col et al. (2014). © 2014 Elsevier.
Figure 2.4.1 Ratio of heat transfer coefficients of first and nth row of a tube bundle compared to three correlations. Source: From Belghazi et al. (2001). © 2001 Elsevier.
Figure 2.4.2 Downward flow of condensate: (a) in Nusselt model and (b) actual. Source: From Butterworth (1977). © 1977 American Society of Mechanical Engineers.
Figure 2.4.3 Comparison of heat transfer coefficients for lower tubes with those for the top tube in the bundle. Source: From Butterworth (1977). © 1977 American Society of Mechanical Engineers.
Figure 2.5.1 Definition of geometric variables for tube with trapezoidal fins. Source: From Marto (1988). © 1988 American Society of Mechanical Engineers.
Figure 2.5.2 Finned tube with condensate retention. Source: From Marto (1988). © 1988 American Society of Mechanical Engineers.
Figure 2.5.3 Variation of heat transfer with tube rows in a bundle of three‐dimensional tubes. Source: From Eckels (2005). © 2005 ASHRAE.
Figure 2.5.4 Internally enhanced tubes: (a) helical microfin tube and (b) herringbone tube. Source: From Cavallini et al. (2003). © 2003 Elsevier.
Figure 2.5.5 Geometrical parameters in the correlation of Cavallini et al. (2009). Source: From Cavallini et al. (2009). © 2009 Elsevier.
Figure 2.6.1 Effect of superheat on mean heat transfer coefficient in a brazed plate heat exchanger.
G
r
is the mass flux, kg m
−2
s
−1
, of condensing fluid pentane. Source: From Sarraf et al. (2016). © 2016 Elsevier.
Figure 2.7.1 Corrugated plate heat exchanger. Note that in many publications, chevron angle
β
is measured from the vertical axis. Source: From ASHRAE (2017). © 2017 ASHRAE.
Figure 2.7.2 Effect of non‐condensable gas on condensation of vapor on a vertical surface. Source: From Collier and Thome (1994). © 1994 Oxford University Press.
Figure 2.8.1 Effect of composition of mixture on heat transfer. CO
2
/DME mixture condensing in a 4.35 mm diameter horizontal tube. Source: From Afroz et al. (2008). © 2008 Elsevier.
Figure 2.9.1 Data from some early studies on condensation of stagnant liquid metal vapors compared to Nusselt theory and its modifications.
λ
is the latent heat. Source: From Sukhatme and Rohsenow (1966). © 1966 American Society of Mechanical Engineers.
Figure 2.10.1 Heat transfer measurements on dropwise condensation of steam at near atmospheric pressure. Source: From Rose (2002). © 2002 SAGE Publications.
Figure 2.10.2 Effect of surface inclination on heat transfer coefficient α during dropwise condensation. Source: From Koch et al. (1998). © 1998 Elsevier.
Chapter 3
Figure 3.1.1 Regimes of pool boiling and the flow behavior near the heating surface. Source: From Ghiaasiaan (2008).
Figure 3.2.1 Mechanisms of nucleate boiling. (a) Bubble agitation, (b) vapor–liquid exchange, and (c) evaporation. Source: From Wieland Heat Transfer Engineering Data Book III. © 2016 Wieland‐Werke AG.
Figure 3.2.2 Phase equilibria during boiling of binary mixture. Source: From Collier and Thome (1994). © 1994 Oxford University Press.
Figure 3.2.3 Heat transfer coefficients of aqueous mixtures of methanol and ethanol during pool boiling. (a) methanol‐water (b) ethanol‐water. Source: Fujita and Tsutsui (1994). © 1994 Elsevier.
Figure 3.2.4 Comparison of the data for pool boiling of pure mercury from four sources with the correlations of Shah (1992) (continuous line) and Subbotin et al. (1970) (dashed line). Data: (1) Bonilla et al. (1957), (2) Farmer (1952), (3) Wagner and Lykoudis (1981), and (4) Michiyoshi et al. (1975). Source: Reprinted from Shah (1992). © 1992, with permission from Elsevier.
Figure 3.2.5 Comparison of the data for pool boiling of sodium from five sources with the correlations of Shah (1992) (continuous line) and Subbotin et al. (1970) (dashed line). Source: Reprinted from Shah (1992). © 1992, with permission from Elsevier.
Figure 3.2.6 Comparison of the data for pool boiling of potassium from five sources with the correlations of Shah (1992) (continuous line) and Subbotin et al. (1970) (dashed line). Source: Reprinted from Shah (1992). © 1992, with permission from Elsevier.
Figure 3.2.7 Data of Wadkins (1984) for lithium compared with the correlations of Shah (1992) (continuous line) and Subbotin et al. (1970) (dashed line). (1) Measured data. (2) Data corrected for interfacial resistance. Source: Reprinted from Shah (1992). © 1992 with permission from Elsevier.
Figure 3.3.1 Zuber's hydrodynamic instability model for CHF in pool boiling. Source: From Lienhard and Dhir (1973). © 1973 American Society of Mechanical Engineers.
Figure 3.3.2 Effect of shape and size of heaters on CHF;
q
maxz
is the CHF predicted by Zuber formula. Source: Reproduced with permission from Lienhard (1988). © 1988 American Society of Mechanical Engineers.
Figure 3.3.3 Effect of surface tension variations on CHF of mixtures. (a) Ethanol/water, (b) methanol/water, (c) methanol/ethanol, (d) ethanol/
n
‐butanol, (e) methanol/benzene, and (f) benzene/
n
‐heptane. Thick continuous line is the correlation of Fujita and Bai, dashed line is the correlation of Reddy and Lienhard, and thin continuous line is the correlation of Yang. Source: Fujita and Bai (1997). © 1997 Elsevier
Figure 3.3.4 Comparison of data from various sources with various correlations. Data: (1) Subbotin et al. (1972) with argon cover gas, (2) Subbotin et al. (1972) without cover gas, (3) Subbotin et al. (1974), (4) Caswell and Balzhiser (1966), (5) Noyes and Lurie (1966), (6) Carbon (1964), (7) Kawamura et al. (1975), and (8) Sakurai et al. (1978). Correlations: (a) Shah for stable CHF. (b) Shah for unstable CHF. (c) Kutateladze–Zuber. (d) Subbotin et al. for stable CHF. (e) Caswell and Balzhiser. (f) Krillov. (g) Bankoff Fauske analysis. (h) Noyes. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.3.5 Critical heat flux data for potassium compared with various correlations. Data: (1) Subbotin et al. (1972), (2) Subbotin et al. (1974), (3) Michiyoshi et al. (1986), and (4) Colver and Balzhizer (1964). Correlations A through H, see caption of Figure 3.3.4. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.3.6 Cesium CHF data compared with various correlations. Data: (1) Subbotin et al. (1972) and (2) Avksentyuk and Mamontova (1973). Correlations A through H, see caption of Figure 3.3.4. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.3.7 Data of Caswell and Balzhiser (1966) for rubidium compared to various correlations. See caption of Figure 3.3.4 for A through H. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.3.8 Data for Subbotin et al. (1972) for mercury with fully wetted heater compared with various correlations. See caption of Figure 3.3.4 for A through H. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.3.9 Critical heat flux data for mercury with partially wetted heater surfaces compared with correlations for unstable boiling. Data: (1) Takahashi et al. (1980), (2) Lyon et al. (1955), (3) Lee (1968), and (4) Turner and Colver (1971). (a) Shah Eq. (3.3.35) and (b) Subbotin et al. Eq. (3.3.33) with
C
= 18. Source: From Shah (1996). © 1996 Taylor & Francis.
Figure 3.4.1 Pool boiling of pentane on a horizontal copper plate showing the effect of surface roughness. Source: From Berenson (1960). © 1960 Massachusetts Institute of Technology
Figure 3.5.1 Minimum film boiling temperature data and correlation.
T
wet
in the figure is
T
MFB
. For references in the figure, see Simon et al. (1968). Source: Simon et al. (1968)
Figure 3.6.1 Comparison of the correlation of Sakurai et al. [shown as Eq. (4)] with data from sources other than their own. Eq. (5) is an approximate form of Sakurai et al. correlation not included in this book. Source: Sakurai et al. (1990b). © 1990 American Society of Mechanical Engineers.
Figure 3.6.2 Effect of inclination of heater on film boiling heat transfer. Source: From Jung et al. (1987). © 1987 Elsevier.
Figure 3.6.3 Data of Lyon (1953) for film boiling of mercury and cadmium on a horizontal cylinder and prediction for mercury. Source: From Padilla (1966). © 1966 University of Michigan.
Figure 3.6.4 Film boiling heat transfer of potassium on a horizontal cylinder. Source: From Padilla (1966). © 1966 University of Michigan.
Figure 3.7.1 Effect of acceleration on pool boiling heat transfer of Helium‐I. Source: Ogata and Nakayama (1977). © 1977 Elsevier.
Figure 3.7.2 Effect of oil concentration on heat transfer during nucleate pool boiling of R‐134a on plain and enhanced tubes no. 1–4 or different types of enhanced tubes. Source: From Ji et al. (2010). © 2010 American Society of Mechanical Engineers
Chapter 4
Figure 4.1.1 Regimes of subcooled boiling in a tube. Source: From Delhaye et al. (2004). © 2004 Elsevier.
Figure 4.2.1 Effect of dissolved air on inception of boiling in an annulus. Source: From McAdams et al. (1949). © 1949 American Chemical Society.
Figure 4.3.1 Boundary between high and low subcooling regimes according to Shah (1977). Source: From Shah (1983). © 1983 Taylor & Francis.
Figure 4.4.1 Void fraction predictions of the Rouhani–Axelsson model compared with data of Rouhani (1966) for water in a tube.
θ
in
is inlet subcooling, and
θ
o
is local subcooling. Source: From Rouhani and Axelsson (1970). © 1970 Elsevier.
Figure 4.5.1 The correlation of Shah (1977) for subcooled boiling in graphical form. Source: From Shah (1983). © 1983 Taylor & Francis.
Figure 4.5.2 Data of Peng and Wang (1993) for a multichannel with
D
HYD
= 0.646 mm compared to various correlations:
T
SAT
= 100 °C,
G
= 3237 kg m
−2
s
−1
, subcooling 50 K. Source: Reprinted from Shah (2017a). © 2017, with permission from Elsevier.
Figure 4.5.3 Data of Lee and Mudawar (2008) for HFE‐7100 in a rectangular multichannel with
D
HYD
= 0.416 mm compared to various correlations:
T
sat
= 63.6 °C,
G
= 1010 kg m
−2
s
−1
, subcooling 89–93 °C, and
Re
LT
= 1300. Source: Reprinted from Shah (2017a). © 2017, with permission from Elsevier.
Figure 4.5.4 Data of Qu and Mudawar (2003) for water in a rectangular channel with
D
HYD
= 0.35 mm and
Re
LT
= 375 compared to various correlations. Source: Reprinted from Shah (2017a). © 2017, with permission from Elsevier.
Figure 4.5.5 Data of Alferov and Rybin (1969) for water in an annulus compared to various correlations: inner tube heated, annular gap = 5 mm,
T
SAT
= 340.2 °C,
G
= 1870 kg m
−2
s
−1
, and
Bo
= 4.25 × 10
−4
. Source: Reprinted from Shah (2017a). © 2017, with permission from Elsevier.
Figure 4.6.1 Effect of subcooling during crossflow boiling on a cylinder. Source: From Vliet (1962).
Figure 4.6.2 Correlation of heat transfer during crossflow at zero quality. Source: Reprinted from Shah (1984). © 1984, with permission from Elsevier.
Figure 4.6.3 The boundary between high and low subcooling in crossflow boiling. Source: Reprinted from Shah (1984). © 1984, with permission from Elsevier.
Figure 4.7.1 Wall temperature
T
w
at inner and outer surface of a 90° bend vs. fluid enthalpy
i
n
at average heat flux
q
av
:
G
= 400 kg m
−2
s
−1
, and
p
= 167 bar. Source: From Miropoloskiy and Pikus (1969).
Figure 4.7.2 Effect of subcooling and acceleration on heat transfer to a rotating vertical tube with water at atmospheric pressure.
T
sat,
w
is the saturation temperature at boiler wall. Source: From Marto and Gray (1971).
Figure 4.7.3 Effect of acceleration on heat transfer to a rotating vertical tube sprayed with water at atmospheric pressure, inlet subcooling 28 K. Source: Marto and Gray (1971).
Figure 4.7.4 Various types of jets. Source: From Wolf et al. (1993). © 1993 Elsevier.
Figure 4.7.5 Various regions in the impingement of a free surface jet on a flat surface. Source: From Karwa et al. (2011). © Elsevier.
Figure 4.7.6 Effect of subcooling and jet velocity on heat transfer. R‐113 submerged jet impinging on a horizontal plate.
T
s
is the saturation temperature. Source: From Ma and Bergles (1986).
Figure 4.7.7 Effect of subcooling with on heat transfer with a vertical water jet impinging on a horizontal disk. Source: From Liu et al. (2004). © 2004 American Society of Mechanical Engineers.
Figure 4.7.8 Effect of nozzle diameter
d
on mean heat transfer coefficient with horizontal jet on a vertical plate: plate temperature 500 °C, jet temperature 12 °C, and jet velocity 27.4 m s
−1
. Source: Reprinted from Lamvik and Iden (1982). © 1982, with permission from Begell House, Inc.
Chapter 5
Figure 5.2.1 Effect of quality and mass flow rate on heat transfer coefficient: R‐11 in 25 mm tube,
q
= 10 000 kcal m
−2
h
−1
, and
T
SAT
= 10 °C. Source: From Chawla (1967). Reproduced with permission of the Verein Deutscher Ingenieure e. V.
Figure 5.2.2 Effect of heat flux
q
and mass flux
M
on heat transfer coefficients during evaporation of R‐11 in horizontal tubes at
x
= 0.5 and
T
SAT
= 10 °C. Tube diameters are (a) 25 mm, (b) 14 mm, (c) 6 mm. Source: From Chawla (1967). Reproduced with permission of the Verein Deutscher Ingenieure e. V.
Figure 5.2.3 Effect of pressure on heat transfer for water flowing in a horizontal tube:
D
= 11.8 mm,
G
= 518 kg m
−2
s
−1
, and
q
= 79.4 kW m
−2
. Source: Based on Mumm (1954).
Figure 5.2.4 Correlation of Shah (1976) for boiling in horizontal and vertical tubes. Source: From Shah (1982). © ASHRAE.
Figure 5.2.5 (a) Predictions of Shah correlation for (a) (
ρ
g
/
ρ
f
) = 0.001 (b) (
ρ
g
/
ρ
f
) = 0.1. Source: From Shah (1982). © ASHRAE.
Figure 5.2.6 Transition Weber number during boiling in channels. Source: From Shah (2017a). © 2017 Elsevier.
Figure 5.2.7 Effect of Weber number on heat transfer at
p
r
= 0.0512, corresponds to R‐134a at −40 °C. Source: From Shah (2017a). © 2017 Elsevier.
Figure 5.2.8 Comparison of various correlations with the data of Ogata and Sato (1974) for helium in a vertical tube:
D
= 1.09 mm,
G
= 86 kg m
−2
s
−1
,
p
r
= 0.478, and
Bo
= 3.6 × 10
−4
. Source: From Shah (2017a). © 2017 Elsevier.
Figure 5.2.9 Comparison of various correlations with the data of Tran et al. (1996) for R‐12 in a horizontal tube:
D
= 2.46 mm,
G
= 89 kg m
−2
s
−1
,
p
r
= 0.1977,
We
GT
= 56, and
Bo
= 6.3 × 10
−4
. Source: From Shah (2017a). © 2017 Elsevier.
Figure 5.3.1 Typical rectangular offset‐fin plate‐fin heat exchanger. Source: From Wieting (1975). © 1975 American Society of Mechanical Engineers.
Figure 5.3.2 Heat transfer in a perforated fin plate heat exchanger. Source: Data of Feldman et al. (2000). © Elsevier.
Figure 5.4.1 Variations of heat transfer coefficients around the circumference of a coil. “4” is outer periphery of coil, “2” is inner periphery, “1” and “4” are top and bottom. Source: From Owhadi (1966).
Figure 5.4.2 Data for R‐134a boiling in a helical coil compared to various correlations.
T
SAT
= 20 °C,
G
= 600 kg m
−2
s
−1
,
q
= 7.1 kW m
−2
. Data of Chen et al. (2011). From Shah (2019). © 2019 American Society of Mechanical Engineers.
Figure 5.4.3 Effect of speed and wall superheat Δ
T
on boiling heat flux on a rotating tube in a pool of water. Source: From Nicol and Mclean (1968). © 1968 John Wiley & Sons.
Figure 5.4.4 Heat transfer during boiling on a rotating cylinder in water. Source: From Tang and McDonald (1971). © 1971 Elsevier.
Figure 5.5.1 Velocity vectors and stream lines during boiling of R‐113 in a tube bundle. Source: From Cornwell et al. (1980). © 1980 American Society of Mechanical Engineers.
Figure 5.5.2 Lines of constant heat transfer coefficients in a tube bundle with R‐113 at atmospheric pressure,
q
= 20 kW m
−2
. Heat transfer coefficients in kW m
−2
. Source: From Cornwell et al. (1980). © 1980 American Society of Mechanical Engineers.
Figure 5.5.3 The recirculation model of Brisbane et al. (1980). Source: From Brisbane et al. (1980). © 1980 American Society of Mechanical Engineers.
Figure 5.5.4 Comparison of the data of Webb and Chien (1994) for R‐113 in a plain tube bundle at two levels of heat flux with the Shah (2017b) correlation.
T
SAT
= 19 °C,
G
= 15.6 kg m
−2
s
−1
. Source: From Shah (2017b). © 2017 Elsevier.
Figure 5.5.5 Comparison of the Shah (2017b) correlation with the data of Kim et al. (2002) for a bundle of tubes with pores and gaps at two values of heat flux. Pore diameter 0.23 mm. R‐123,
T
SAT
= 26.7 °C,
G
= 26 kg m
−2
s
−1
. Source: From Shah (2017b). © 2017 Elsevier.
Figure 5.6.1 Schematic of a falling film evaporator. Source: From Wieland Data Book III. © 2016 Wieland‐Werke AG.
Figure 5.6.2 Flow modes in falling film evaporators according to Mitrovic (1986). (a) drop mode (b) jet/column mode (c) sheet mode From Hu and Jacobi (1995). Source: From Mitrovic (1986).
Figure 5.6.3 Heat transfer in a vertical row of horizontal enhanced tubes. Tube 1 is on top, and tube 7 at bottom. Source: From Zhao et al. (2018). © 2018 Elsevier.
Figure 5.6.4 Heat transfer coefficients with ammonia spray on a plain tube bundle. Source: From Zeng and Chyu (1995). © 1995.
Figure 5.7.1 Comparison of the data of Park et al. (2011) for a mixture of R123–R134a–R22 with the predictions of the Shah correlation with correction by Thome–Shakir factor only (TS) and by both Thome–Shakir and Bell–Ghaly factors (TSBG):
D
= 0.19 mm,
G
= 392 kg m
−2
s
−1
,
q
= 15 kW m
−2
,
T
SAT
= 33 °C, and glide = 16.8 K. Source: Reprinted from Shah (2015b). © 2015, with permission from Elsevier.
Figure 5.7.2 Comparison of data of Nellis et al. (2005) for mixture for cryocoolers with predictions of Shah correlation with correction by Thome–Shakir factor only (TS) and by both Thome–Shakir and Bell–Ghaly factors (TSBG). Glide = 156 °C,
T
SAT
= −160 °C,
G
= 840 kg m
−2
s
−1
,
q
= 79.5 kW m
−2
,
D
= 8.4 mm. Source: From Shah (2015b). Copyright Elsevier, reproduced with their permission.
Figure 5.8.1 Subcooled boiling heat transfer of sodium compared to pool boiling. Source: From Noyes and Lurie (1966). © 1966 Begell House Inc.
Figure 5.8.2 Effect of flow rate and direction of heating fluid on boiling of potassium in an annulus.
G
K
is mass flux of potassium, and
T
Ko
is the saturation temperature of potassium. Source: From Peterson (1967).
Figure 5.8.3 Heat transfer to boiling of mercury in a tube with swirl insert (
P
/
D
= 2). Source: From Hsia (1970). © 1970 American Society of Mechanical Engineers.
Figure 5.8.4 Data for boiling of mixtures and pure liquid metals from several sources.
T
c
is saturation temperature. “Present Data” are those of Mori et al. (1970) for a mixture. Amalgam data are those of Hsia (1970). Source: From Mori et al. (1970). © 1970 American Society of Mechanical Engineers.
Figure 5.9.1 Effect of gravity on heat transfer during boiling of HFE‐7100 in a minichannel 6 mm × 0.254 mm.
q
= 32 kW m
−2
, flow rate 0.26 g s
−1
, and exit quality 0.26.
X
is the distance from entrance. Source: From Luciani et al. (2008). © 2008 American Society of Mechanical Engineers.
Figure 5.9.2 Effect of 1% and 1.5% oil concentration on heat transfer to R‐600a in a horizontal tube. Source: From Momenifar et al. (2015). © 2015 Elsevier.
Chapter 6
Figure 6.2.1 Upstream condition correlation (UCC) of Shah for
Y
< 10
4
. Source: Reprinted from Shah (1987). © 1987, with permission from Elsevier.
Figure 6.2.2 Boiling number at
x
c
= 0 according to the local condition correlation (LCC) of Shah. Source: Reprinted from Shah (1987). © 1987, with permission from Elsevier.
Figure 6.2.3 Ratio of boiling numbers at
x
c
=
x
and
x
c
= 0 according to the local condition correlation (LCC) of Shah. Source: Reprinted from Shah (1987). © 1987, with permission from Elsevier.
Figure 6.2.4 Comparison of the Shah correlation with the data of Hewitt and Kearsey (1966) for water in a vertical tube:
D
= 12.62 mm,
L
C
/
D
= 290,
G
= 1355 kg m
−2
s
−1
, and
p
r
= 0.31.
Figure 6.2.5 Wall temperatures during boiling of water in a tube inclined 15° to horizontal. Source: Kefer et al. (1989). © 1989 Elsevier.
Figure 6.2.6 Effect of inclination angle on CHF of water flowing in a 20 mm ID tube. Source: Ami et al. (2014). © 2014 Taylor & Francis.
Figure 6.2.7 Effect of velocity and orientation on CHF in a rectangular channel with one side heated. Exit subcooling 3 K. Source: Zhang et al. (2002). ©2002 Elsevier.
Figure 6.2.8 Various methods for calculation of CHF in channels with non‐uniform axial flux distribution (AFD): (a) total power hypothesis, (b) local condition hypothesis, (c) F factor method, and (d) BLA method. Source: Yang et al. (2006). ©2006 Elsevier.
Figure 6.3.1 Comparison of quality at CHF in an annulus with
D
HYD
= 10 mm and round tubes of the same diameter. Source: Park et al. (1997). ©1997 Elsevier.
Figure 6.3.2 (a) Part 1 of the Shah correlation for annulus, critical boiling number at
Y
≤ 10
4
. Source: Shah (2015b). © 2015 Taylor & Francis (b) Part 2 of the Shah correlation for annuli Source: Shah (2015b). © 2016 Taylor & Francis.
Figure 6.3.3 Applicability limit of the Shah correlation for CHF in annuli to water and the range of water data in satisfactory agreement with the Shah correlation. Source: Shah (2015b). © 2015 Taylor & Francis.
Figure 6.4.1 Effect of velocity of water flowing across single cylinders on CHF. Source: Cochran and Andracchio (1974).
Figure 6.4.2 Vapor removal pattern during upflow and side flow on a heated cylinder. Source: Lienhard (1988). © 1988 ASME.
Figure 6.4.3 Comparison of the correlation of Cumo et al. for CHF in tube bundles with their test data. Source: Cumo et al. (1980). ©1980 Taylor & Francis.
Figure 6.4.4 Effect of mass flux on CHF in a horizontal tube bundle with
P
/
D
= 1.3. Source: Leroux and Jensen (1992). ©1992 ASME.
Figure 6.4.5 Effect of gap on the departure from nucleate boiling (DNBF) and transition to film boiling (SFBF) for horizontal bundles (
D
= 1.25 mm) cooled by helium. Source: Khalil (1982). © 1982 Elsevier.
Figure 6.4.6 Correlation of Palen and Small (1964) for bundle average CHF. Source: Palen and Small (1964).
Figure 6.4.7 Rod‐centered subchannels according to Gaspari et al. Source: Gaspari et al. (1970).
Figure 6.4.8 Critical heat flux vs. exit film flowrate for falling films on vertical tubes. Source: Ueda et al. (1981). ©1981 Elsevier.
Figure 6.4.9 Variation of wall temperatures with quality X in a straight tube and a coil with the same tube diameter, flow rate, and inlet quality. Source: Cumo et al. (1972). © 1972 Elsevier.
Figure 6.4.10 Effect of coil to tube diameter ratio on CHF (
d
i
is tube inside diameter). Fluid is R‐134a. Source: Chen et al. (2011) © Elsevier.
Figure 6.4.11 Critical heat flux with water in a 180° bend at various flow rates compared to CHF in straight tubes.
G
(kg m
−2
s
−1
) = 1–2000, 2–800, 3–400. Dashed lines are for straight tubes. Pressure 98 bar. Source: Miropolskiy and Pikus (1969).
Figure 6.4.12 Critical heat flux of a disk during quenching by a free surface round jet.
r
is the radial distance from the stagnation point,
d
is the jet diameter,
V
n
is the jet velocity, and
T
i
is the initial surface temperature. Source: Hall et al. (2001). ©2001 ASME.
Figure 6.4.13 Location of jets and definition of characteristic length in the tests of Monde and Mitsutake (1996).
N is the number of jets
. Source: Monde and Mitsutake (1996). ©1996 ASME.
Figure 6.4.14 Minimum flow rate required to overcome effect of gravity at various gravity levels X
e,in
is the inlet quality.. Source: Konishi et al. (2013b). © 2013 Elsevier.
Chapter 7
Figure 7.2.1 Film boiling regimes in a vertical tube following DNB‐type boiling crisis. Source: Mawatari et al. (2014). © Begell House.
Figure 7.2.2 Wall temperatures and heat transfer coefficient before and after CHF in a vertical tube of 19 mm ID with water upflow. Source: Shen et al. (2016). © 2016 Elsevier.
Figure 7.2.3 Estimated actual vapor quality
x
at various flow rates and heat fluxes.
L
is the location along the tube and
L
sat
is the tube length up to
x
E
= 1. Nitrogen boiling in a tube. Source: Laverty and Rohsenow (1964). © 1964 MIT.
Figure 7.2.4 Extreme scenarios of equilibrium following CHF. (a) Maximum degree of non‐equilibrium. (b) Complete thermal equilibrium. Source: Kohler and Hein (1986).
Figure 7.2.5 Effect of critical quality on wall temperature during film boiling of nitrogen in a vertical tube of 10.1 mm diameter. Source: Hynek et al. (1969). © 1969 MIT.
Figure 7.2.6 Shah correlation for heat transfer during film boiling in tubes. Source: Reproduced with permission from Shah (2017). © 2017 Elsevier.
Figure 7.2.7 Comparison of the data of Ogata and Sato (1974) for helium with various correlations:
D
= 1.09 mm,
T
SAT
= 4.35 K,
G
= 92 kg m
−2
s
−1
,
q
= 1.42 kW m
−2
,
x
C
= 0.38. Source: Shah (2017). © 2017 Elsevier.
Figure 7.2.8 Comparison of the data of Nijhawan et al. (1980) for water with various correlations:
D
= 14.1 mm,
p
= 2.65 bar,
G
= 42 kg m
−2
s
−1
,
x
c
= 0.20. Source: Shah (2017). © Elsevier.
Figure 7.2.9 Data of Annunziato et al. (1983) for water in a non‐uniformly heated tube compared to various correlations:
D
= 12.4 mm,
p
= 1.01 bar,
G
= 4 kg m
−2
s
−1
. Source: Shah and Siddiqui (2000). © 2000 Taylor & Francis.
Figure 7.2.10 Comparison of heat transfer coefficient
α
and wall temperature
T
during upward and downward flow of R‐134a in a vertical tube of 4.4 mm ID. Source: Mawatari et al. (2014). ©2014, with permission from Begell House, Inc.
Figure 7.3.1 Wall temperatures during film boiling of water in horizontal tubes. Source: Kohler and Hein (1986).
Figure 7.3.2 Comparison of the data of Kohler and Hein (1986) for top of tube with various correlations:
D
= 12.5 mm,
p
= 200.7 bar,
G
= 1054 kg m
−2
s
−1
,
q
= 405 kW m
−2
,
x
C
,TOP
= 0.19, (
z
/
D
) = 26–271. Source: From Shah (2017). © 2017 Elsevier..
Figure 7.3.3 Comparison of correlations with data of Schnittger (1982) for bottom of tube: R‐12,
D
= 24.3 mm,
p
= 27.5 bar,
G
= 960 kg m
−2
s
−1
,
q
= 62.5 kW m
−2
,
x
C
,TOP
= 0.5,
x
C
,BOT
= 0.7, (
z
/
D
) = 10–154. Source: Shah (2017). © 2017 Elsevier.
Figure 7.4.1 Effect of subcooling and velocity on heat transfer during film boiling on a horizontal cylinder. Source: Liu et al. (2009). 2009 ASME..
Figure 7.4.2 Comparison of the correlation of Liu et al. (2009) with some of their data for film boiling on cylinders. Source: Liu et al. (2009). © 2009 ASME..
Figure 7.4.3 Heat transfer regimes during quenching of a sphere with forced flow. Source: Orcozo and Witte (1984). © ASME.
Figure 7.4.4 Effect of jet velocity
V
s
and subcooling on film boiling heat transfer in the stagnation zone with 6 mm diameter water jet (a) at 15 K subcooling and (b) at
V
s
= 2.1 m s
−1
. The straight lines are the predictions of the Liu–Wang correlation. Source: Liu and Wang (2001). © 2001 Elsevier.
Figure 7.4.5 Post dryout temperature difference between the internal and external sides of a coil vs. the centrifugal acceleration of the mixture at various values of reduced pressure
π
. Source: Cumo et al. (1972). © 1972 Elsevier.
Figure 7.4.6 Heat transfer during chilldown of pipes with liquid nitrogen flowing in them:
G
≈ 240 kg m
−2
s
−1
. Source: Johnson and Shine (2015). © 2015 Elsevier.
Figure 7.4.7 Heat transfer coefficients as function of wall temperature
T
i
during quenching of a vertical tube with upflow and downflow of nitrogen. Source: Hu et al. (2012). © Elsevier.
Figure 7.4.8 Film boiling heat transfer coefficients
α
at Δ
T
f
≈ 700 K from several sources compared to the correlation of Wendelstorf et al. (2008). Source: Wendelstorf et al. (2008). © 2008 Elsevier.
Figure 7.5.1 Effect of Reynolds number on minimum film boiling temperature difference on spheres in R‐11 streams. Source: Rezakhany and El‐Wakil (1984).
Figure 7.6.1 Heat flux
φ
during transition boiling in reflooding of a rod bundle compared with various correlations. Source: Groeneveld and Gardiner (1977). © ASME.
Figure 7.6.2 Quenching of a surface with free stream jet of water: jet velocity of 0.8 m s
−1
, subcooling 16 K, and a nozzle‐to‐plate distance of 6 mm;
x
is the distance from the stagnation point. Source: Robidou et al. (2002). © 2002 Elsevier.
Chapter 8
Figure 8.2.1 Effect of liquid flow rate
M
and ratio of superficial velocities of gas and liquid,
V
g
and
V
l
, respectively, on heat transfer coefficient
α
. Air–water flowing up in a heated vertical tube 14.25 mm ID. Source: Groothius and Hendal (1959). © 1959, Elsevier.
Figure 8.2.2 Effect of gas and liquid superficial Reynolds numbers and flow patterns on heat transfer during air–water flow in a 26.6 mm ID horizontal pipe. Source: Ghajar and Tang (2010). © 2010, Taylor & Francis.
Figure 8.2.3 Heat transfer coefficients during slug flow at the top and bottom of a horizontal tube.
V
SL
is the superficial liquid velocity. Source: Deshpande et al. (1991). © 1991, American Chemical society.
Figure 8.2.4 Shah correlation for heat transfer during gas–liquid flow in horizontal pipes at
Re
LS
> 170. Source: Shah (2018a). © 2018, ASME.
Figure 8.2.5 Comparison of data of Nada (2017) for air–water mixtures in a horizontal pipe compared with three correlations. Source: Shah (2018a). © 2018, ASME.
Figure 8.2.6 The correlation of Shah (2018b) for heat transfer to gas-liquid flow in vertical pipes in graphical form.
Figure 8.2.7 Data of for hydrogen–water mixture at 6.9 bar in a 4 mm diameter vertical tube compared to various correlations.
u
LS
= 0.41 m s
−1
. Source: Shah (2018b). © 2018, ASME.
Figure 8.2.8 Comparison of various correlations with the data of Ravipudi (1976) for toluene–air mixture at atmospheric pressure in a 19 mm diameter tube. Source: Shah (2018b). © 2018, ASME.
Figure 8.2.9 Effect of downward inclination on ratio of two‐phase to single‐phase heat transfer. (a)
Re
SG
= 2800 and (b)
Re
SG
= 14 000. Source: John et al. (2015). © 2015 with permission from Begell House, Inc.
Figure 8.3.1 Effect of nitrogen injection through tube surface into water at various Reynolds numbers. Source: Gose et al. (1957). © 1957, AIP publishing.
Figure 8.3.2 Effect of air injection through tube wall into air–ethylene glycol mixtures flowing in a vertical tube. Panel (a) is at superficial liquid velocity
u
LS
= 4.5 ft s
−1
, and panel (b) is at
u
LS
= 1 ft s
−1
. Source: Kudirka (1964). © 1964, US Department of Energy.
Figure 8.3.3 Effect of air injection through tube wall into air–water mixtures flowing in a vertical tube.
ϕ
is the rate of air injection through tube surface, ft
3
s
−1
ft
−2
. Panel (a) is at superficial liquid velocity
u
LS
= 4.5 ft s
−1
and panel (b) is at
u
LS
= 1 ft s
−1
. Source: Kudirka (1964). © 1964, US Department of Energy.
Figure 8.3.4 Effect of nominal velocity of air bubbled through the wall
V
g
″ on heat transfer coefficient
α
o
at various water superficial velocities
U
f
. No air mixed with water at entrance to channel. Source: Martin and Sims (1971). © 1971, Elsevier.
Figure 8.4.1 Effect of water content in air flowing over a cylinder on heat transfer coefficients at various angles.
Re
TP
= 95 000. Source: Finlay and McMillan (1967–1968).
Figure 8.4.2 Effect of air Reynolds number and water to air mass flow ratio on circumferentially averaged Nusselt number for a cylinder in mist flow. Source: Hodgson et al. (1968). © 1968, ASME.
Figure 8.4.3 Heat transfer to a horizontal plate with vertical air–water jet impingement.
D
is the nozzle diameter,
r
the distance from stagnation point, and
f
is the water‐to‐air mass flow ratio. Reynolds number 4500,
H
/
D
= 5,
H
being the distance between nozzle and plate. Source: Quinn et al. (2017). © 2017, Elsevier.
Figure 8.4.4 Ratio of heat transfer to a sphere in mist flow to that in air alone.
j
is the mass flux of water spray. Natural convection in open space. Source: Abed et al. (2019). Licensed under CCBY 3.0.
Figure 8.5.1 Comparison of predicted evaporation by some empirical correlations from water pools without forced convection. Source: Shah (2018c). © 2018, Taylor & Francis.
Figure 8.5.2 Comparison of some empirical correlations for evaporation from water pools with forced air flow over them. Source: Shah (2018c). © 2018, Taylor & Francis.
Figure 8.5.3 Comparison of the predictions of Shah model with data of Boelter et al. (1946) for natural convection from a small calm water pool. Source: Shah (2014). © 2014, ASHRAE.
Figure 8.5.4 Deviations of various prediction methods for evaporation with test data for natural convection. Source: Reprinted from Shah (2012b). © 2012, with permission from Elsevier..
Figure 8.6.1 Boiling curves for quenching of a plate by an air–water free surface vertical jet,
r
is the distance from the stagnation point and
d
is the nozzle diameter. Source: Hall et al. (2001). © 2001, ASME.
Figure 8.6.2 Comparison of heat transfer at microgravity and Earth gravity during air–water flow in a vertical tube.
V
SL
is the superficial liquid velocity, and S, A, S–A are slug flow, annular, and slug–annular flow patterns. Source: Rite and Rezkallah (1997). © 1997, Elsevier.
Figure 8.7.1 Heat transfer to mercury–argon mixtures flowing up in an annulus. No magnetic field. Source: Michiyoshi et al. (1982). © 1982, Elsevier.
Figure 8.7.2 Effect of transverse magnetic field on heat transfer to mercury–argon mixture in a vertical annulus. Hartmann number = 110,
L
/
D
HYD
= 70. Source: Michiyoshi et al. (1982). © 1982, Elsevier.
Chapter 9
Figure 9.2.1 Regimes of fluidization and their appearance. The regimes are (a) fixed bed, (b) particulate, (c) bubbly, (d) slug, (e) turbulent, and (f) fast. Source: Grace (1982a).
Figure 9.3.1 Representation of Geldart classification of particles for air at normal temperature and pressure. Source: Geldart and Abrahamsen (1978). © 1978, Elsevier.
Figure 9.4.1 Effect of particle size and air velocity on heat transfer to vertical tubes in a fluidized bed at room temperature. Data of Wunder (1980). Solid lines are predictions of Martin model. Source: Martin (1984b). © 1984, Elsevier.
Figure 9.4.2 Effect of particle diameter d on maximum heat transfer coefficient h
m
to objects in a fluidized bed of corundum particles. (1) Horizontal cylinder 6 mm diameter. (2) Vertical plate 220 mm × 160 mm. (3) Vertical cylinder 40 mm diameter. Source: Baskakov et al. (1973). © 1973, Elsevier.
Figure 9.4.3 Effect of low pressure on heat transfer coefficient
α
(W m
−2
s
−1
) at superficial air velocity
w
(m s
−1
) on vertical cylinders in a bed of 0.2 mm sand. Pressure, Pa: (1) 10
5
, (2) 26 600, (3) 13 300, (4) 931, (5) 400, and (6) 266. Source: Shlapkova (1969). © 1969, Springer nature.
Figure 9.4.4 Effect of increase in pressure on maximum heat transfer coefficient in fluidized beds. Source: Botterill and Desai (1972). © 1972, Elsevier.
Figure 9.4.5 Effect of tube inclination on maximum heat transfer coefficient in fluidized beds of sand of particle diameters 150–350 μm. Source: Abid et al. (2011) © 2011 Elsevier.
Figure 9.6.1 The factor
F
t
for the effect of heat transfer surface in the Shah correlation. Source: Shah (2018b). © 2018, ASME.
Figure 9.6.2 The factor
F
k
for the effect of particle thermal conductivity in the Shah correlation. Source: Shah (2018b). © 2018, ASME.
Figure 9.6.3 Comparison of the Shah correlation with test data over the entire range of Archimedes number. Source: Reprinted from Shah (2018a). © 2018, with permission from Elsevier.
Figure 9.6.4 Effect of particle diameter on maximum heat transfer coefficient according to various correlations for silica sand fluidized by air at room conditions.
D
t
≥ 3 mm. Source: Reprinted from Shah (2018a). © 2018, with permission from Elsevier.
Figure 9.6.5 Comparison of the data of Baskakov et al. (1973) for corundum particles in air‐fluidized beds with the Shah correlation. Source: Reprinted from Shah (2018a). © 2018, with permission from Elsevier.
Figure 9.6.6 Predictions of some correlations for maximum heat transfer to wires in fluidized beds. Data of Turton (1986) for polythene particles. Source: Reprinted from Shah (2018a). © 2018, with permission from Elsevier.
Figure 9.6.7 Comparison of the Shah (2018a) and Zabrodsky et al. (1976) correlations with the data of Li et al. (1993). Silica sand,
D
p
= 1815 μm,
D
t
= 40 mm, and air at room pressure. Source: Reprinted from Shah (2018a). © 2018, with permission from Elsevier.
Figure 9.7.1 Common types of horizontal tube bundles: (a) in‐line bundle and (b) staggered bundle. Source: Lechner et al. (2014). © 2014, Elsevier.
Figure 9.7.2 Effect of
P
/
D
t
on heat transfer coefficients in a horizontal bundles of 12.7 mm diameter tubes arranged in equilateral triangle grid. Silica sand particles
D
p
= 504 μm. Source: Grewal and Saxena (1983). © 1983, American Chemical Society.
Figure 9.7.3 Heat transfer coefficients measured on vertical tube bundles in fluidized beds. Source: Borodulya et al. (1983). © 1983, Elsevier.
Figure 9.8.1 Fraction of total heat transfer provided by radiation as a function of wall temperature
t
w
. Chamotte particles in a bed at 850 °C Particle diameters 1–0.35 mm, 2–0.63 mm, and 3–1.25 mm. Source: Baskakov et al. (1973). © 1973 Elsevier.
Figure 9.9.1 The graphical correlation of Wender and Cooper (1958) for heat transfer to external walls of fluidized beds together with the equation fitted to it.
Figure 9.9.2 Variation of heat transfer with distance
X
1
from the distributor. Bed diameter 290 mm, 500 μm glass ballotini fluidized by air. Source: Gunn and Hilal (1994). © 1994, Elsevier.
Figure 9.10.1 Effect of superficial gas velocity
U
sg
and height
H
above bed surface on ratio of heat transfer coefficients in freeboard (
h
avg
) and inside the bed (
h
im
). Source: Biyikli et al. (1987). © 1987, Elsevier.
Figure 9.10.2 Heat transfer coefficients of a tube bundle as a function of distance from expanded bed surface. Staggered bundle with 1.9 cm horizontal and vertical pitch. Iron grit particles 0.2 mm diameter.
H
bo
is the bed height at minimum fluidization, cm (inch). Source: Dyrness et al. (1992). © 1992, Elsevier.
Figure 9.12.1 Flow regimes during gas–solid upward flow in vertical pipes. Source: Rabinovich and Kalman (2011). © Elsevier.
Figure 9.12.2 Effect of solid‐to‐gas ratio on Nusselt number for glass and lead particles flowing with air in a vertical tube at
x
/
D
= 8.45. Source: Tien and Quan (1962). © ASME.
Figure 9.12.3 Effect of solid‐to‐gas ratio on entrance length.
W
s
/
W
g
for the curves are
A
= 0,
B
= 6.9 (graphite),
C
= 24.2 (graphite),
D
= 3.35 (glass), and
E
= 1.17 (glass).
Re
t
= 10
4
to 3 × 10
4
. Source: Boothroyd and Haque (1970a). © SAGE.
Figure 9.12.4 Data of Tien and Quan (1962) for 200 μm lead particles with air in a pipe compared to various correlations.
Re
t
= 15 000. Source: Shah (2020). © 2020, ASME.
Figure 9.12.5 Data of Sukomel et al. (1967) for air–graphite mixture in horizontal pipe compared to various correlations.
D
p
= 65 μm. Source: Shah (2020). © 2020, ASME.
Figure 9.12.6 Data of Danziger (1963) for catalyst with air flowing up in a 28.5 mm diameter vertical tube compared to various correlations. Source: Shah (2020). © 2020, ASME.
Figure 9.13.1 Effect of particle mass flux
G
and receiver tube diameter on measured heat transfer coefficients in a concentrating solar collector with flowing dense phase gas–solid suspension. Source: Zhang et al. (2017). © 2017, Elsevier.
Guide
Cover Page
Two‐Phase Heat Transfer
Preface
Table of Contents
Begin Reading
Appendix
Index
WILEY END USER LICENSE AGREEMENT
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