Two-Phase Heat Transfer

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 xvii1 Introduction 11.1 Scope and Objectives of the Book 11.2 Basic Definitions 11.3 Various Models 21.3.1 Homogeneous Model 21.3.2 Separated Flow Models 21.3.3 Flow Pattern-Based Models 31.4 Classification of Channels 31.4.1 Based on Physical Dimensions 31.4.2 Based on Condensation Studies 31.4.3 Based on Boiling Flow Studies 41.4.4 Based on Two-Component Flow 41.4.5 Discussion 51.4.6 Recommendation 51.5 Flow Patterns in Channels 51.5.1 Horizontal Channels 51.5.1.1 Description of Flow Patterns 51.5.1.2 Flow Pattern Maps 61.5.2 Vertical Channels 71.5.3 Inclined Channels 71.5.4 Annuli 81.5.5 Minichannels 81.5.6 Horizontal Tube Bundles with Crossflow 91.5.7 Vertical Tube Bundles 101.5.8 Effect of Low Gravity 101.5.9 Recommendations 121.6 Heat Transfer in Single-Phase Flow 121.6.1 Flow Inside Channels 121.6.2 Vertical Tube/Rod Bundles with Axial Flow 131.6.3 Various Geometries 141.6.4 Liquid Metals 141.7 Calculation of Pressure Drop 141.7.1 Single-Phase Pressure Drop in Pipes 141.7.2 Two-Phase Pressure Drop in Pipes 151.7.3 Annuli and Vertical Tube Bundles 171.7.4 Horizontal Tube Bundles 171.7.5 Recommendations 171.8 Calculation of Void Fraction 171.8.1 Flow Inside Pipes 171.8.2 Flow in Tube Bundles 181.8.3 Recommendations 181.9 CFD Simulation 181.10 General Information 19Nomenclature 19References 202 Heat Transfer During Condensation 252.1 Introduction 252.2 Condensation on Plates 252.2.1 Nusselt Equations 252.2.2 Modifications to the Nusselt Equations 262.2.3 Condensation with Turbulent Film 272.2.4 Condensation on Underside of a Plate 272.2.5 Recommendations 282.3 Condensation Inside Plain Channels 282.3.1 Laminar Condensation in Vertical Tubes 282.3.2 The Onset of Turbulence 282.3.3 Prediction of Heat Transfer in Turbulent Flow 292.3.3.1 Analytical Models 292.3.3.2 CFD Models 302.3.3.3 Empirical Correlations 302.3.3.4 Correlations Applicable to Both Macro and Minichannels 342.3.4 Recommendation 412.4 Condensation Outside Tubes 412.4.1 Single Tube 412.4.1.1 Stagnant Vapor 412.4.1.2 Moving Vapor 422.4.2 Bundles of Horizontal Tubes 422.4.2.1 Vapor Entry from Top 422.4.2.2 Vapor Entry from Side 442.4.3 Recommendations 442.5 Condensation with Enhanced Tubes 442.5.1 Condensation on Outside Surface 442.5.1.1 Single Tubes 442.5.1.2 Tube Bundles 462.5.2 Condensation Inside Enhanced Tubes 472.5.3 Recommendations 492.6 Condensation of Superheated Vapors 492.6.1 Stagnant Vapor on External Surfaces 492.6.2 Forced Flow on External Surfaces 492.6.3 Flow inside Tubes 502.6.4 Plate-Type Heat Exchangers 502.6.5 Recommendations 512.7 Miscellaneous Condensation Problems 512.7.1 Condensation on Stationary Cone 512.7.2 Condensation on a Rotating Disk 512.7.3 Condensation on Rotating Vertical Cone 522.7.4 Condensation on Rotating Tubes 522.7.5 Plate-Type Condensers 532.7.5.1 Recommendation 542.7.6 Effect of Oil in Refrigerants 542.7.6.1 Recommendation 552.7.7 Effect of Gravity 552.7.7.1 Some Formulas for Zero Gravity 552.7.7.2 Experimental Studies 552.7.7.3 Conclusion 552.7.8 Effect of Non-condensable Gases 562.7.8.1 Prediction Methods 562.7.8.2 Recommendation 572.7.9 Flooding in Upflow 572.7.10 Condensation in Thermosiphons 582.7.11 Condensation in Helical Coils 582.8 Condensation of Vapor Mixtures 592.8.1 Physical Phenomena 592.8.2 Prediction Methods 602.8.3 Recommendation 612.9 Liquid Metals 612.9.1 Stagnant Vapors 612.9.2 Interfacial Resistance 622.9.3 Moving Vapors 622.9.4 Recommendation 622.10 Dropwise Condensation 632.10.1 Prediction of Mode of Condensation 632.10.2 Theories of Dropwise Condensation 632.10.3 Methods to Get Dropwise Condensations 632.10.4 Some Experimental Studies 642.10.5 Prediction of Heat Transfer 642.10.6 Recommendations 66Nomenclature 66References 673 Pool Boiling 773.1 Introduction 773.2 Nucleate Boiling 773.2.1 Mechanisms of Nucleate Boiling 773.2.1.1 Bubble Agitation 773.2.1.2 Vapor–Liquid Exchange 773.2.1.3 Evaporative Mechanism 783.2.2 Bubble Nucleation 783.2.2.1 Inception of Boiling 783.2.2.2 Bubble Nucleation Cycle 793.2.2.3 Active Nucleation Site Density 813.2.2.4 Recommendations 813.2.3 Correlations for Heat Transfer 813.2.3.1 Conclusion and Recommendation 833.2.4 Multicomponent Mixtures 833.2.4.1 Physical Phenomena 833.2.4.2 Prediction of Heat Transfer 843.2.4.3 Recommendation 863.2.5 Liquid Metals 863.2.5.1 Physical Phenomena 863.2.5.2 Prediction of Heat Transfer 873.2.5.3 Recommendations 883.3 Critical Heat Flux 903.3.1 Models of Mechanisms 903.3.1.1 Bubble Interference Model 903.3.1.2 Hydrodynamic Instability Model 903.3.1.3 Macrolayer Dryout Model 913.3.1.4 Dry Spot Model 913.3.1.5 Interfacial Lift-off Model 923.3.2 Correlations for Inclined Surfaces 923.3.3 Various Correlations 933.3.4 Effect of Subcooling 933.3.5 Various Other Factors Affecting CHF 943.3.6 Evaluation of CHF Prediction Methods 943.3.7 Recommendations 943.3.8 Multicomponent Mixtures 953.3.8.1 Physical Phenomena and Prediction Methods 953.3.8.2 Recommendation 953.3.9 Liquid Metals 953.3.9.1 Physical Phenomena 973.3.9.2 Prediction of CHF 983.3.9.3 Recommendations 1023.4 Transition Boiling 1023.5 Minimum Film Boiling Temperature 1043.5.1 Prediction Methods 1043.5.1.1 Analytical Models 1043.5.1.2 Empirical Correlations 1053.5.2 Recommendations 1063.6 Film Boiling 1063.6.1 Methods for Predicting Heat Transfer 1063.6.1.1 Vertical Plates 1063.6.1.2 Horizontal Cylinders 1073.6.1.3 Horizontal Plates 1083.6.1.4 Inclined Plates 1083.6.1.5 Spheres 1093.6.2 Liquid Metals 1093.6.3 Recommendations 1103.7 Various Topics 1103.7.1 Effect of Gravity 1103.7.1.1 Scaling Method of Raj et al. 1103.7.1.2 Scaling for Hydrogen 1123.7.1.3 Some Other Studies 1123.7.1.4 Recommendations 1133.7.2 Effect of Oil in Refrigerants 1133.7.2.1 Mechanisms 1143.7.2.2 Correlations 1143.7.2.3 Recommendation 1153.7.3 Thermosiphons 1153.7.4 Effect of Some Organic Additives 115Nomenclature 115References 1164 Forced Convection Subcooled Boiling 1234.1 Introduction 1234.2 Inception of Boiling in Channels 1234.2.1 Analytical Models and Correlations 1234.2.2 Minichannels 1254.2.3 Effect of Dissolved Gases 1264.2.4 Recommendations 1264.3 Prediction of Subcooled Boiling Regimes in Channels 1264.3.1 Recommendation 1274.4 Prediction of Void Fraction in Channels 1274.4.1 Recommendations 1294.5 Heat Transfer in Channels 1294.5.1 Visual Observations and Mechanisms 1294.5.2 Prediction of Heat Transfer 1304.5.2.1 Some Dimensional Correlations 1304.5.2.2 The Shah Correlation 1304.5.2.3 Various Correlations 1324.5.2.4 Recommendations 1354.6 Single Cylinder with Crossflow 1354.6.1 Experimental Studies 1354.6.2 Prediction of Heat Transfer 1354.6.2.1 Shah Correlation 1354.6.2.2 Other Correlations 1374.6.3 Recommendation 1384.7 Various Geometries 1384.7.1 Tube Bundles with Axial Flow 1384.7.2 Tube Bundles with Crossflow 1384.7.3 Flow Parallel to a Flat Plate 1384.7.4 Helical Coils 1384.7.5 Bends 1394.7.6 Rotating Tube 1394.7.7 Jets Impinging on Hot Surfaces 1414.7.7.1 Experimental Studies and Correlations 1424.7.7.2 Recommendations 1454.7.8 Spray Cooling 145Nomenclature 146References 1465 Saturated Boiling with Forced Flow 1515.1 Introduction 1515.2 Boiling in Channels 1515.2.1 Effect of Various Parameters 1515.2.2 Prediction of Heat Transfer 1525.2.2.1 Correlations for Macro Channels 1525.2.2.2 Correlations for Minichannels 1585.2.2.3 Correlations for Both Minichannels and Macrochannels 1595.2.2.4 Recommendations 1625.3 Plate-Type Heat Exchangers 1625.3.1 Herringbone Plate Type 1625.3.1.1 Longo et al. Correlation 1635.3.1.2 Almalfi et al. Correlation 1635.3.1.3 Ayub et al. Correlation 1645.3.1.4 Recommendation 1645.3.2 Plane Plate Heat Exchangers 1645.3.3 Serrated Fin Plate Heat Exchangers 1645.3.4 Plate Fin Heat Exchangers 1655.4 Boiling in Various Geometries 1665.4.1 Helical Coils 1665.4.1.1 Correlations for Heat Transfer 1665.4.1.2 Evaluation of Correlations 1675.4.1.3 Discussion 1675.4.1.4 Recommendation 1675.4.2 Rotating Disk 1685.4.3 Cylinder Rotating in a Liquid Pool 1695.4.3.1 Recommendation 1695.4.4 Bends 1705.4.5 Spiral Wound Heat Exchangers (SWHE) 1705.4.6 Falling Thin Film on Vertical Surfaces 1715.4.6.1 Various Studies and Correlations 1715.4.6.2 Recommendation 1715.4.7 Vertical Tube/Rod Bundles with Axial Flow 1725.4.8 Spiral Plate Heat Exchangers 1725.5 Horizontal Tube Bundles with Upward Crossflow 1725.5.1 Physical Phenomena 1725.5.2 Prediction Methods for Heat Transfer 1735.5.2.1 Shah Correlation 1755.5.3 Conclusion and Recommendation 1765.6 Horizontal Tube Bundles with Falling Film Evaporation 1775.6.1 Flow Patterns/Modes 1775.6.2 Heat Transfer 1785.6.3 Conclusion and Recommendation 1805.7 Boiling of Multicomponent Mixtures 1805.7.1 Boiling in Tubes 1805.7.2 Boiling in Various Geometries 1825.7.3 Conclusions and Recommendations 1825.8 Liquid Metals 1825.8.1 Inception of Boiling 1825.8.2 Heat Transfer 1845.8.2.1 Sodium 1845.8.2.2 Potassium 1845.8.2.3 Mercury 1865.8.2.4 Cesium and Rubidium 1865.8.2.5 Mixtures of Liquid Metals 1875.8.3 Conclusions and Recommendations 1875.9 Effect of Gravity 1875.9.1 Experimental Studies 1885.9.2 Conclusions and Recommendation 1895.9.3 Effect of Oil in Refrigerants 1895.9.3.1 Heat Transfer with Immiscible Oils 1895.9.3.2 Heat Transfer with Miscible Oils 1905.9.3.3 Conclusions and Recommendations 190Nomenclature 191References 1926 Critical Heat Flux in Flow Boiling 2016.1 Introduction 2016.2 CHF in Tubes 2016.2.1 Types of Boiling Crisis and Mechanisms 2016.2.2 Prediction Methods 2016.2.2.1 Analytical Models 2016.2.2.2 Lookup Tables of CHF 2026.2.2.3 Dimensional Correlations for Water 2036.2.2.4 General Correlations 2036.2.2.5 Fluid-to-Fluid Modeling 2136.2.2.6 Non-uniform Heat Flux 2146.2.3 Recommendations 2166.3 CHF in Annuli 2166.3.1 Vertical Annuli with Upflow 2166.3.1.1 Dimensional Correlations for Water 2166.3.1.2 General Correlations 2176.3.1.3 Recommendations 2206.3.2 Horizontal Annuli 2216.3.3 Eccentric Annuli 2216.4 CHF in Various Geometries 2226.4.1 Single Cylinder with Crossflow 2226.4.2 Horizontal Tube Bundles 2246.4.2.1 Recommendation 2266.4.3 Vertical Tube/Rod Bundles 2276.4.3.1 Mixed Flow Analyses 2276.4.3.2 Subchannel Analysis 2286.4.3.3 Phenomenological Analyses 2286.4.4 Falling Films on Vertical Surfaces 2296.4.5 Flow Parallel to a Flat Plate 2306.4.6 Helical Coils 2306.4.6.1 Recommendation 2326.4.7 Spiral Wound Heat Exchangers (SWHE) 2326.4.8 Rotating Liquid Film 2326.4.9 Bends 2336.4.10 Jets Impinging on Hot Surfaces 2346.4.10.1 Correlations for CHF in Free Stream Jets 2346.4.10.2 Effect of Contact Angle 2356.4.10.3 Multiple Jets 2366.4.10.4 Effect of Heater Thickness 2366.4.10.5 Confined Jets 2366.4.10.6 Submerged Jets 2366.4.10.7 Recommendations 2366.4.11 Spray Cooling 2366.4.12 Effect of Gravity 2376.4.12.1 Terrestrial Studies 2376.4.12.2 Experimental Studies at Low Gravities 2386.4.12.3 CHF Prediction Methods 2396.4.12.4 Recommendation 239Nomenclature 239References 2407 Post-CHF Heat Transfer in Flow Boiling 2477.1 Introduction 2477.2 Film Boiling in Vertical Tubes 2477.2.1 Physical Phenomena 2477.2.2 Prediction of Dispersed Flow Film Boiling in Upflow 2487.2.2.1 Empirical Correlations 2487.2.2.2 Mechanistic Analyses 2497.2.2.3 Phenomenological Correlations 2497.2.2.4 Lookup Tables 2547.2.2.5 Recommendations 2567.2.3 Prediction of Inverted Annular Film Boiling in Upflow 2567.2.3.1 Recommendations 2577.2.4 Film Boiling in Downflow 2577.3 Film Boiling in Horizontal Tubes 2577.3.1 Prediction Methods 2587.3.2 Recommendations 2597.4 Film Boiling in Various Geometries 2597.4.1 Annuli 2597.4.2 Vertical Tube Bundles 2607.4.3 Single Horizontal Cylinder 2617.4.3.1 Recommendation 2627.4.4 Spheres 2627.4.5 Jets Impinging on Hot Surfaces 2647.4.6 Bends 2657.4.7 Helical Coils 2657.4.8 Chilldown of Cryogenic Pipelines 2667.4.9 Flow Parallel to a Plate 2677.4.10 Spray Cooling 2677.5 Minimum Film Boiling Temperature and Heat Flux 2687.5.1 Flow in Channels 2687.5.2 Jets Impinging on Hot Surfaces 2687.5.3 Chilldown of Cryogenic Lines 2697.5.4 Spheres 2697.5.5 Spray Cooling 2707.6 Transition Boiling 2707.6.1 Flow in Channels 2707.6.2 Jets on Hot Surfaces 2717.6.3 Spheres 2727.6.4 Spray Cooling 272Nomenclature 273References 2748 Two-Component Gas–Liquid Heat Transfer 2798.1 Introduction 2798.2 Pre-mixed Mixtures in Channels 2798.2.1 Flow Pattern-Based Prediction Methods 2798.2.1.1 Bubbly Flow 2798.2.1.2 Slug Flow 2818.2.1.3 Annular Flow 2828.2.1.4 Post-dryout Dispersed Flow 2838.2.2 General Correlations 2838.2.2.1 Horizontal Channels 2838.2.2.2 Vertical Channels 2868.2.2.3 Horizontal and Vertical Channels 2888.2.2.4 Inclined Channels 2898.2.3 Recommendations 2898.3 Gas Flow through Channel Walls 2908.3.1 Experimental Studies 2908.3.2 Heat Transfer Prediction 2928.3.3 Conclusions 2928.4 Cooling by Air–Water Mist 2928.4.1 Single Cylinders in Crossflow 2928.4.2 Flow over Tube Banks 2948.4.3 Flow Parallel to Plates 2948.4.4 Wedges 2958.4.5 Jets 2958.4.6 Sphere 2978.5 Evaporation from Water Pools 2978.5.1 Introduction 2978.5.2 Empirical Correlations 2978.5.3 Analytical Models 2988.5.3.1 Shah Model 2988.5.3.2 Other Models 3008.5.4 CFD Models 3018.5.5 Occupied Swimming Pools 3018.5.6 Conclusions and Recommendations 3018.6 Various Topics 3018.6.1 Jets Impinging on Hot Surfaces 3018.6.2 Vertical Tube Bundle 3028.6.3 Effect of Gravity 3028.7 Liquid Metal–Gas in Channels 3038.7.1 Mercury 3038.7.2 Various Liquid Metals 3048.7.3 Discussion 305Nomenclature 305References 3069 Gas-Fluidized Beds 3119.1 Introduction 3119.2 Regimes of Fluidization 3119.2.1 Regime Transition Velocities 3129.2.1.1 Minimum Fluidization Velocity 3129.2.1.2 Various Regime Transition Velocities 3129.2.2 Void Fraction and Bed Expansion 3139.3 Properties of Solid Particles 3139.3.1 Density 3139.3.2 Particle Diameter 3139.3.3 Particle Shape Factor 3149.3.4 Classification of Particles 3149.4 Parameters Affecting Heat Transfer to Surfaces 3159.4.1 Gas Velocity 3159.4.2 Particle Size and Shape 3159.4.3 Pressure and Temperature 3169.4.4 Heat Transfer Surface Diameter 3179.4.5 Properties of Gas and Solid 3179.4.6 Gas Distribution 3179.4.7 Length and Location of Tube 3179.4.8 Bed Diameter and Height 3189.4.9 Tube Inclination 3189.5 Theories of Heat Transfer 3189.5.1 Film Theory 3189.5.2 Penetration Theory 3189.5.2.1 Particle Theory 3199.5.2.2 Packet Theory 3199.6 Prediction Methods for Single Tubes and Spheres 3199.6.1 Analytical Models 3199.6.1.1 Particle Models 3199.6.1.2 Packet Models 3209.6.2 Empirical Correlations 3219.6.2.1 Maximum Heat Transfer 3219.6.2.2 Correlations for the Entire Range 3249.6.3 Recommendations 3259.7 Tube Bundles 3269.7.1 Horizontal Tube Bundles 3269.7.2 Vertical Tube Bundles 3289.7.3 Recommendations 3289.8 Radiation Heat Transfer 3299.8.1 Radiation Heat Transfer Coefficient and Effective Emissivity 3299.8.2 Temperature for Significant Radiation Contribution 3299.8.3 Conclusions and Recommendations 3309.9 Heat Transfer to Bed Walls 3309.9.1 Prediction Methods 3309.9.2 Conclusions and Recommendations 3319.10 Heat Transfer in Freeboard Region 3319.10.1 Experimental Studies and Prediction Methods 3329.10.2 Recommendation 3329.11 Heat Transfer Between Gas and Particles 3329.12 Gas–Solid Flow in Pipes 3339.12.1 Regimes of Gas–Solid Flow 3339.12.2 Experimental Studies of Heat Transfer 3349.12.3 Prediction of Heat Transfer 3349.12.3.1 Various Methods 3349.12.3.2 Shah Correlation 3369.12.4 Recommendation 3379.13 Solar Collectors with Particle Suspensions 337Nomenclature 338References 340Appendix 347Index 357