Two-Phase Heat Transfer

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 authora noted expert in this fieldalso 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:

Mirza Mohammed Shah, PhD, PE, has over 50 years experience of research and engineering. His more than 100 publications include his general predictive techniques for two-phase heat transfer which are widely used in the industry. He is Fellow of ASME and ASHRAE. Presently he is Director of Engineering Research Associates, an organization dedicated to promoting and performing research for developing practically useable solutions to problems.

Preface

Chapter 1

INTRODUCTION

1.1 SCOPE AND OBJECTIVE OF THE BOOK

1.2 BASIC DEFINITIONS: Mass flux, heat flux, mass quality, void fraction, liquid holdup, etc.

1.3 VARIOUS MODELS

1.3.1 Homogeneous Model

1.3.2 Separated Flow Models

1.3.3 Two Fluid Model

1.4 CLASSIFICATION OF CHANNELS

1.4.1 Classifications Based on Physical Dimensions

1.4.2 Classifications Based on Condensation Studies

1.4.3 Classifications Based on Boiling Flow Studies

1.4.4 Classifications Based on Gas-Liquid Flows

1.4.5 Discussion

1.4.6 Recommendation

1.5 FLOW PATTERNS IN CHANNELS

1.5.1 Horizontal Channels

1.5.1.1 Description of Flow Patterns

1.5.1.2 Flow Pattern Maps

1.5.2 Vertical Channels

1.5.3 Inclined Channels

1.5.4 Annuli

1.5.5 Minichannels

1.5.6 Horizontal Tube Bundles with Crossflow

1.5.7 Vertical Tube Bundles

1.5.8 Effect of Low Gravity

1.5.9 Recommendations

1.6 HEAT TRANSFER IN SINGLE PHASE FLOW

1.6.1 Flow inside channels

1.6.2 Vertical Tube/Rod Bundles with Axial Flow

1.6.3 Various Geometries

1.6.4 Liquid Metals

1.7 CALCULATION OF PRESSURE DROP

1.7.1 Single-Phase Pressure Drop in Pipes

1.7.2 Two-Phase Pressure Drop in Pipes

1.7.3 Annuli and Vertical Tube Bundles

1.7.4 Horizontal Tube Bundles

1.7.5 Recommendations

1.8 CALCULATION OF VOID FRACTION

1.8.1 Flow inside Pipes

1.8.2 Flow in Tube Bundles

1.8.3 Recommendations

1.9 CFD MODELLING

1.10 GENERAL INFORMATION

Chapter 2 Heat Transfer During Condensation

2.1 INTRODUCTION

2.2 CONDENSATION ON FLAT PLATES

 2.2.1 Nusselt Equations

 2.2.2 Modifications of Nusselt Equations

2.2.3 Condensation with Turbulent Condensate

2.2.4 Condensation on Underside of Plate

2.2.5 Recommendations

2.3 CONDENSATION INSIDE PLAIN CHANNELS

2.3.1 Laminar condensation in vertical tubes

2.3.2 Onset of turbulence

2.3.3 Prediction of heat transfer in turbulent flow

2.3.3.1 Analytical Models

 2.3.3.2 CFD Models

2.3.3.2 Empirical Correlations

2.3.3.2.1Correlations for conventional (macro) channels.

2.3.3.2.2 Correlations for minichannels

2.3.3.2.3 Correlations for both mini and macro channels

2.3.3.2.4 Inclined channels

2.3.4 Recommendations

2.4 CONDENSATION OUTSIDE PLAIN TUBES

2.4.1 Single Tubes

2.4.1.1 Stagnant Vapor

2.4.1.2 Moving Vapor

2.4.2 Horizontal Tube Bundles

2.4.2.1 Vapor Entry from Top

2.4.2.2 Vapor Entry from Side

 2.4.3 Recommendations

2.5 CONDENSATION WITH ENHANCED TUBES

2.5.1 Condensation on outside surface

2.5.1.1 Single tubes

2.5.1.2 Tube bundles

2.5.3 Condensation inside enhanced tubes

2.5.4 Recommendations

2.6 CONDENSATION OF SUPERHEATED VAPORS

2.6.1 Stagnant vapor on external surfaces

2.6.2 Moving vapor on external surfaces

2.6.3 Forced convection in tubes

2.6.4 Plate type heat exchangers

2.6.5 Recommendations

2.7 MISCELLANEOUS CONDENSATION PROBLEMS

2.7.1 Condensation on stationary vertical cone

2.7.2 Condensation on rotating disc

2.7.3 Condensation on rotating cone

2.7.4 Condensation on rotating tubes

2.7.5 Plate type condensers

2.7.6 Effect of oil in refrigerants

2.7.7 Effect of gravity

2.7.8 Effect of non-condensable gases

2.7.9 Flooding in Upflow

2.7.10 Condensation in Thermosiphons

2.7.11 Condensation in Helical Coils

2.8 CONDENSATION OF VAPOR MIXTURES

2.8.1 Physical phenomena

2.8.2 Prediction methods

2.8.3 Recommendations

2.9 CONDENSATION OF LIQUID METALS

2.9.1 Condensation from stagnant vapor

2.9.2 Interfacial resistance

2.9.2 Condensation from moving vapors

2.9.3 Recommendations

2.10 DROPWISE CONDENSATION

2.10.1 Prediction of mode of condensation

2.10.2 Theories of dropwise condensation

2.10.3 Methods to get dropwise condensation

2.10.4 Some experimental studies

2.10.5 Prediction methods

2.10.6 Recommendations

CHAPTER 3 POOL BOILING

3.1 INTRODUCTION

3.2 NUCLEATE BOILING

3.2.1 Mechanisms of Nucleate Boiling

3.2.2 Bubble Nucleation

3.2.2.1 Inception of Boiling

3.2.2.2 Bubble Nucleation Cycle

3.2.2.3 Active Nucleation Site Density

3.2.2.4 Recommendations

3.2.3 Correlations for Heat Transfer

3.2.3.1 Various Correlations

3.2.3.2 Recommendations

3.2.4 Multi-Component Mixtures

3.2.4.1 Physical Phenomena

3.2.4.2 Prediction Methods

3.2.4.3 Recommendations

3.2.5 Liquid metals

3.2.5.1 Physical Phenomena

3.2.5.2 Prediction Methods

3.2.5.3 Recommendations

3.3 CRITICAL HEAT FLUX

3.3.1 Models of Mechanisms

3.3.2 Correlations for Inclined Surfaces

3.3.3 Various Correlations

3.3.4 Effect of Subcooling

3.3.5 Various Other Factors Affecting CHF

3.3.6 Evaluation of CHF Prediction Methods

3.3.7 Recommendations

3.3.8 Mixtures of Fluids

3.3.8.1 Physical Phenomena and Prediction Methods

3.3.8.2 Recommendations

3.3.9 Liquid Metals

3.3.9.1 Physical Phenomena

3.3.9.2 Prediction Methods

3.3.9.3 Recommendations

 3.4 TRANSITION BOILING

3.5 MINIMUM FILM BOILING TEMPERATURE

3.5.1 Prediction Methods

3.5.1.1 Analytical Models

3.5.1.2 Empirical Correlations

3.5.2 Recommendations

3.6 FILM BOILING

3.6.1 Methods for Predicting Heat Transfer

3.6.1.1 Vertical Plates

3.6.1.2 Horizontal Cylinders

3.6.1.3 Horizontal Plates

3.6.1.4 Inclined Surfaces

3.6.1.5 Spheres

3.6.2 Liquid Metals

3.6.3 Recommendations

3.7 MISCELLANEOUS TOPICS

3.7.1 Effect of Gravity

3.7.1.1 Scaling Method of Raj et al.

3.7.1.2 Scaling for Hydrogen   

3.7.1.3 Some Other Studies

3.7.1.4 Recommendations

3.7.2 Effect of Oil in Refrigerants

3.7.2.1 Mechanisms

3.7.2.2 Correlations

3.7.2.3 Recommendations

3.7.3 Thermosiphons

3.7.4 Effect of Some Organic Additives

CHAPTER 4 FORCED CONVECTION SUBCOOLED BOILING

4.1 INTRODUCTION

4.2 INCEPTION OF BOILING IN CHANNEL FLOW

4.2.1 Analytical Models and Correlations

4.2.2 Minichannels

4.2.3 Effect of Dissolved Gases

4.2.3 Recommendations

4.3 PREDICTION OF SUBCOOLED BOILING REGIMES IN CHANNELS

4.3.1 Recommendations

4.4 PREDICTION OF VOID FRACTION IN CHANNELS

4.4.1 Recommendations

4.5 HEAT TRANSFER IN CHANNELS

4.5.1 Visual Observations and Mechanisms

4.5.2 Prediction of Heat Transfer

4.5.2.1 Some Dimensional Correlations

4.5.2.2 The Shah Correlation

4.5.2.3 Various Correlations

4.5.2.4 Recommendations

4.6 SINGLE CYLINDER WITH CROSSFLOW

4.6.1 Experimental Studies

4.6.2 Prediction of Heat Transfer

4.6.3 Recommendation

4.7 MISCELLANEOUS GEOMETRIES

4.7.1 Tube Bundles with Axial Flow

4.7.2 Tube Bundles with Crossflow

4.7.3 Flow Parallel to a Flat Plate

4.7.4 Helical Coils

4.7.5 Bends

4.7.6 Rotating Tube

4.7.7 Jets Impinging on Hot Surfaces

4.7.7.1 Experimental Studies and Correlations

4.7.7.2 Recommendations

4.7.8 Spray Cooling

CHAPTER 5 SATURATED BOILING WITH FORCED FLOW

5.1 INTRODUCTION

5.2 BOILING IN CHANNELS

5.2.1 Effect of Various Parameters

5.2.2 Prediction of Heat Transfer

5.2.2.1 Correlations for Macro Channels

5.2.2.1.1 Chen Correlation

5.2.2.1.2 Shah Correlation

5.2.2.1.3 Kandlikar Correlation

5.2.2.1.4 Correlations of Winterton et al.

5.2.2.1.5 Steiner-Taborek Correlation

5.2.2.1.6 EPFL Flow Pattern-Based Correlations

5.2.2.2 Correlations for Mini Channels

5.2.2.2.1 Kim-Mudawar Correlation

5.2.2.2.2 Various Correlations for Minichannels

5.2.2.3 Correlations for both Mini and Macro Channels

5.2.2.3.1 Kandlikar et al. Correlation

5.2.2.3.2 Shah Correlation

5.2.2.4 Recommendations

5.3 PLATE TYPE HEAT EXCHANGERS

5.3.1 Herringbone Plate Heat Exchangers

5.3.2 Plane Plate Heat Exchangers

5.3.2 Serrated Fin Plate Heat Exchangers

5.3.3 Pin-Fin Plate Heat Exchangers

5.4 BOILING IN VARIOUS GEOMETRIES

5.4.1 Helical Coils

5.4.2 Rotating Disk

5.4.3 Cylinder Rotating in a Liquid Pool

5.4.4 Bends

5.4.5 Spiral Wound Heat Exchangers (SWHE)

5.4.6 Falling Thin Film on a Vertical Surface

5.4.7 Vertical Tube/Rod Bundles with Axial Flow

5.4.8 Spiral Plate Heat Exchangers

5.5 HORIZONTAL TUBE BUNDLES WITH UPWARD CROSS-FLOW

5.5.1 Physical Phenomena

5.5.2 Predictive Techniques for Heat Transfer

5.5.3 Conclusions and Recommendations

5.6 HORIZONTAL TUBE BUNDLES WITH FALLING FILM EVAPORATION

5.6.1 Flow Patterns/Modes

5.6.2 Heat Transfer

5.6.3 Conclusions and Recommendations

5.7 BOILING OF MULTI-COMPONENT MIXTURES

5.7.1 Physical Phenomena

5.7.2 Predictive Techniques

5.7.3 Conclusions and Recommendations

5.8 LIQUID METALS

5.8.1 Inception of Boiling

5.8.2 Heat Transfer

5.8.2.1 Sodium

5.8.2.2 Potassium

5.8.2.3 Mercury

5.8.2.4 Cesium and Rubidium

5.8.2.5 Mixtures of Liquid Metals

5.8.3 Conclusions and Recommendations

5.9 VARIOUS TOPICS

5.9.1 Effect of Gravity

5.9.1.1 Experimental Studies

5.9.1.2 Conclusions and Recommendations

5.9.2 Effect of Oil in Refrigerants

Chapter 6 CRITICAL HEAT FLUX IN FLOW BOILING

6.1 INTRODUCTION

6.2 CHF IN TUBES

6.2.1 Types of Boiling Crisis and Mechanisms

6.2.2 Prediction Methods

6.2.2.1 Analytical Methods

6.2.2.2 Lookup Tables of CHF

6.2.2.3 Dimensional Correlations for Water

6.2.2.4 General Correlations

6.2.2.4.1 Vertical tubes

6.2.2.4.2 Horizontal tubes

6.2.2.4.3 Inclined Tubes

6.2.2.4.4 Critical Quality Correlations

6.2.2.4.5 Mini channels

6.2.2.5 Fluid to Fluid Modelling

6.2.2.6 Non-Uniform Heat Flux

 6.2.3 Recommendations

6.3 CHF IN ANNULI

6.3.1 Vertical Annuli with Upflow

6.3.1.1 Dimensional Correlations for Water

6.3.1.2 General Correlations

6.3.1.3 Recommendations

6.3.2 Horizontal Annuli

6.3.3 Effect of Eccentricity

6.4 CHF IN VARIOUS GEOMETRIES

6.4.1 Single Cylinder with Crossflow

6.4.2 Horizontal Tube Bundles with Upward Crossflow

6.4.3 Vertical Tube/Rod Bundles

6.4.4 Falling films on Vertical Surfaces

6.4.5 Flow Parallel to a Flat Plate

6.4.6 Helical Coils

6.4.7 Spiral Wound Heat Exchangers (SWHE)

6.4.8 Rotating Liquid Film

6.4.9 Bends

6.4.10 Jets Impinging on Hot Surfaces

6.4.11 Spray Cooling

6.4.12 Effect of Gravity

Chapter 7 POST-CHF HEAT TRANSFER IN FLOW BOILING

7.1 INTRODUCTION

7.2 FILM BOILING IN VERTICAL TUBES

7.2.1 Physical Phenomena

7.2.2 Prediction of Dispersed Flow Film Boiling in Upflow

7.2.2.1 Equilibrium Correlations

7.2.2.2 Analytical Models

7.2.2.3 Non-Equilibrium Correlations

7.2.2.4 Look-up Tables

7.2.2.5 Recommendations

7.2.3 Prediction of Inverted Annular Film Boiling in Upflow

7.2.3.1 Recommendations

7.2.4 Film Boiling in Downflow

7.3 FILM BOILING IN HORIZONTAL TUBES

7.3.1 Prediction Methods for Dispersed Flow Film Boiling

7.3.2 Recommendations

7.4 FILM BOILING IN VARIOUS GEOMETRIES

7.4.1 Annuli

7.4.2 Vertical Tube Bundles

7.4.3 Single Horizontal Cylinder

7.4.4 Spheres

7.4.5 Jets Impinging on Hot Surfaces

7.4.6 Bends

7.4.7 Helical Coils

7.4.8 Chilldown of Cryogenic Pipelines

7.4.9 Flow Parallel to a Plate

7.4.10 Spray Cooling

7.5 MINIMUM FILM BOILING TEMPERATURE AND HEAT FLUX

7.5.1 Flow in Channels

7.5.2 Jets Impinging on Hot Surfaces

7.5.3 Chilldown of Cryogenic Lines

7.5.4 Spheres

7.5.5 Spray Cooling

7.6 TRANSITION BOILING

7.6.1 Flow in Channels

7.6.2 Jets Impinging on Hot Surfaces

7.6.3 Spheres

7.6.4 Spray Cooling

Chapter 8 TWO-COMPONENT GAS-LIQUID HEAT TRANSFER

8.1 INTRODUCTION

8.2 PRE-MIXED MIXTURES IN CHANNELS

8.2.1 Flow Pattern-Based Prediction Methods

 8.2.1.1 Bubble Flow

8.2.1.2 Slug Flow

8.2.1.3 Annular Flow

8.2.1.4 Post-Dryout Dispersed Flow

8.2.2 General Correlations

8.2.2.1 Horizontal Channels

8.2.2.2 Vertical Channels

8.2.2.3 Horizontal and Vertical Channels

8.2.2.4 Inclined Channels

8.2.3 Recommendations

8.3 GAS FLOW THROUGH CHANNEL WALLS

8.3.1 Experimental Data

8.3.2 Prediction of Heat Transfer

8.3.3 Conclusions

8.4 Cooling by Air-Water Mist

8.4.1 Single Cylinders in Crossflow

8.4.2 Flow Over Tube Banks

8.4.3 Flow Parallel to Plates

8.4.4 Wedges

8.4.5 Jets

8.4.6 Sphere

8.5 EVAPORATION FROM WATER POOLS

8.5.1 Introduction

8.5.2 Empirical Correlations

8.5.3 Analytical Models

8.5.3.1 Shah Model

8.5.3.2 Other Models

8.5.4 CFD Models

8.5.5 Occupied Swimming Pools

8.5.6 Conclusions and Recommendations

8.6 VARIOUS TOPICS

8.6.1 Jets Impinging on Hot Surfaces

8.6.2 Vertical Tube Bundle

8.6.3 Effect of Gravity

8.7 LIQUID METAL-GAS FLOW IN CHANNELS

8.7.1 Mercury

8.7.2 Various Liquid Metals

8.7.3 Discussion

Chapter 9 GAS-FLUIDIZED BEDS

9.1 INTRODUCTION

9.2 REGIMES OF FLUIDIZATION

9.2.1 Regime Transition Velocities

9.2.1.1 Minimum Fluidization Velocity

9.2.1.2 Various Regime Transition Velocities

9.2.2 Void Fraction

9.3 PROPERTIES OF SOLID PARTICLES

9.3.1 Density

9.3.2 Particle Diameter

9.3.3 Particle Shape Factor

9.3.4 Classification of Particles

9.4 PARAMETERS AFFECTING HEAT TRANSFER TO SURFACES

9.4.1 Gas Velocity

9.4.2 Particle Size and Shape

9.4.3 Pressure and Temperature

9.4.4 Heat Transfer Surface Diameter

9.4.5 Properties of Gas and Solid

9.4.6 Gas Distribution

9.4.7 Length and Location of Tube

9.4.8 Bed Diameter and Height

9.4.9 Tube Inclination

9.5 THEORIES OF HEAT TRANSFER

9.5.1 Film Theory

9.5.2 Penetration Theory

9.5.2.1 Particle Theory

9.5.2.2 Packet Theory

9.6 PREDICTION METHODS FOR SINGLE TUBES AND SPHERES

9.6.1 Analytical Models

9.6.1.1 Particle Models

9.6.1.1 Packet Models

9.6.2 Empirical Correlations

9.6.2.1 Maximum Heat Transfer

9.6.2.2 Correlations for the Entire Range

9.6.3 Recommendations

9.7 TUBE BUNDLES

9.7.1 Horizontal Tube Bundle

9.7.2 Vertical Tube Bundles

9.7.3 Conclusions and Recommendations

9.8 RADIATION HEAT TRANSFER

9.8.1 Radiation Heat Transfer Coefficient and Effective Emissivity

9.8.2 Results of Various Studies

9.8.3 Conclusions and Recommendations

9.9 HEAT TRANSFER TO BED WALLS

9.9.1 Prediction Methods

9.9.2 Conclusions and Recommendations

9.10 HEAT TRANSFER IN FREEBOARD REGION

9.10.1 Experimental Studies and Prediction Methods

9.11.3 Recommendations

9.11 HEAT TRANSFER BETWEEN GAS AND PARTICLES

9.12 GAS-SOLID FLOW IN PIPES

9.12.1 Regimes of Gas-Solid Flow

9.12.2 Experimental Studies of Heat Transfer

9.12.3 Prediction of Heat Transfer

9.12.4 Recommendation

9.13 SOLAR COLLECTORS WITH PARTICLE SUSPENSIONS

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