Theory of Heat Transfer with Forced Convection Film Flows (eBook)

Preface 4
Contents 6
Nomenclature 13
Greek Symbols 17
Subscripts 20
1 Introduction 21
1.1 Scope 22
1.2 Application Background 23
1.3 Previous Developments of the Research 23
1.3.1 Laminar Forced Convection Boundary Layer 23
1.3.2 Laminar Forced Film Condensation of Pure Vapour 24
1.3.3 Laminar Forced Film Condensation of Vapour–Gas Mixture 25
1.4 Challenges Associated with Investigations of Laminar Forced Convection and Film Condensation 25
1.4.1 Investigation of the Laminar Forced Convection Boundary Layer 25
1.4.2 Investigation of Laminar Forced Film Condensation of Pure Vapour 26
1.4.3 Investigation of Laminar Forced Film Condensation of Vapour–Gas Mixture 26
1.5 Limitations of Falkner-Skan Type Transformation 27
1.6 Recent Developments of Research in This Book 28
1.6.1 New Similarity Analysis Method 28
1.6.2 Treatment of Variable Physical Properties 29
1.6.3 Coupled Effect of Variable Physical Properties on Heat and Mass Transfer 29
1.6.4 Extensive Study of Effect of Viscous Thermal Dissipation on Laminar Forced Convection 30
1.6.5 Laminar Forced Film Condensation of Vapour 31
1.6.6 Laminar Forced Film Condensation of Vapour–Gas Mixturer 32
References 34
Part I Theoretical Foundation 38
2 Basic Conservation Equations for Laminar Convection 39
2.1 Continuity Equation 39
2.2 Momentum Equation (Navier–Stokes Equations) 41
2.3 Energy Equation 44
2.4 Governing Partial Differential Equations of Laminar Forced Convection Boundary Layers with Consideration of Variable Physical Properties 48
2.4.1 Principle of the Quantitative Grade Analysis 48
2.4.2 Continuity Equation 49
2.4.3 Momentum Equations (Navier–Stokes Equations) 49
2.4.4 Energy Equations 51
2.5 Summary 54
3 Review of Falkner-Skan Type Transformation for Laminar Forced Convection Boundary Layer 56
3.1 Introduction 56
3.2 Basic Conservation Equations 56
3.3 Derivation Review of Similarity Variables of Falkner-Skan Transformation on Laminar Forced Convection 57
3.4 Example of Similarity Transformation with Falkner-Skan Transformation 61
3.5 Summary 63
3.6 Limitations of the Falkner-Skan Type Transformation 63
Exercises 65
References 66
4 A New Similarity Analysis Method for Laminar Forced Convection Boundary Layer 67
4.1 Introduction 67
4.2 Typical Basis Conservation Equations of Laminar Forced Convection 68
4.3 Brief Review on Determination of Dimensionless Similarity Parameters (Number) 69
4.3.1 Select Whole Physical Independent Variables Dominating the Physical Phenomenon 69
4.3.2 Select Basic Dimension System 70
4.3.3 Determine the Dimensionless Similarity Parameters p1, p2, and p3 70
4.4 Investigation of the Dimensionless Similarity Variables on the Velocity Field 72
4.4.1 Derivation of Dimensionless Coordinate Variable 73
4.4.2 Derivation for Dimensionless Velocity Components 74
4.5 Application Example of the New Similarity Analysis Method 79
4.5.1 Similarity Transformation of (3.1) 79
4.5.2 Similarity Transformation of (3.2) 80
4.5.3 Similarity Transformation of (3.3) 81
4.6 Comparison of the Two Similarity Methods 83
4.6.1 Different Derivation Process of the Dimensionless Similarity Variables on Momentum Field 84
4.6.2 Different Dimensionless Expressionson Momentum Field 84
4.6.3 Different Similarity Analysis Governing Mathematical Models 84
4.7 Remarks 85
Exercises 86
References 86
Part II Laminar Forced Convection 88
5 Heat Transfer on Laminar Forced Convection with Ignoring Variable Physical Properties and Viscous Thermal Dissipation 89
5.1 Introduction 89
5.2 Basic Conservation Equations of Laminar Forced Convection 90
5.2.1 Governing Partial Differential Equations 90
5.2.2 Similarity Transformation Variables 91
5.2.3 Governing Ordinary Differential Equations 91
5.3 Numerical Results 92
5.3.1 Velocity Fields 92
5.3.2 Temperature Fields 93
5.4 Skin-Friction Coefficient 93
5.5 Heat Transfer 96
5.5.1 Heat Transfer Analysis 96
5.5.2 Dimensionless Wall Temperature Gradient 98
5.6 Summary 100
5.7 Remarks 103
5.8 Calculation Example 103
Exercise 106
References 106
6 Heat Transfer of Laminar Forced Convection with Consideration of Viscous Thermal Dissipation 107
6.1 Introduction 107
6.2 Governing Partial Differential Equations of Laminar Forced Convection 108
6.2.1 Governing Partial Differential Equations 108
6.2.2 Similarity Variables 109
6.2.3 Governing Ordinary Differential Equations 109
6.3 Numerical Results 112
6.3.1 Velocity Field 112
6.3.2 Temperature Fields 112
6.4 Heat Transfer Analysis 115
6.5 Formulated Equation of Dimensionless Wall Temperature Gradient 117
6.6 Heat Transfer Prediction Equation 119
6.7 Heat Transfer Prediction Deviation Caused by Ignoring the Viscous Thermal Dissipation 120
6.8 Adiabatic Eckert Numbers 122
6.9 Summary 124
6.10 Remarks 126
6.11 Calculation Examples 126
Exercise 131
References 131
7 Heat Transfer of Gas Laminar Forced Convection with Consideration of Variable Physical Properties 132
7.1 Introduction 132
7.2 Governing Equations 133
7.2.1 Governing Partial Differential Equations 133
7.2.2 Similarity Transformation Variables 134
7.2.3 Similarity Transformation of the Governing Partial Differential Equations 135
7.3 Treatment of Gas Variable Physical Properties 141
7.4 Velocity and Temperature Fields 144
7.5 Skin-Friction Coefficient with Consideration of Variable Physical Properties 146
7.6 Heat Transfer 148
7.6.1 Heat Transfer Analysis 149
7.6.2 Dimensionless Wall Temperature Gradient 150
7.6.3 Prediction Equations on Heat Transfer 153
7.7 Remarks 154
7.8 Calculation Examples 155
Exercises 159
References 159
8 Heat Transfer of Liquid Laminar Forced Convection with Consideration of Variable Physical Properties 161
8.1 Introduction 161
8.2 Governing Equations 162
8.2.1 Governing Partial Differential Equations 162
8.2.2 Similarity Transformation Variables 163
8.2.3 Governing Ordinary Differential Equations 163
8.3 Treatment of Liquid Variable Physical Properties 164
8.4 Velocity and Temperature Fields 166
8.5 Skin-Friction Coefficient with Consideration of Variable Physical Properties 168
8.6 Heat Transfer Analysis 169
8.7 Dimensionless Wall Temperature Gradient 171
8.8 Prediction Equations on Heat Transfer 176
8.9 Summary 176
8.10 Remarks 179
8.11 Calculation Examples 180
Exercises 183
References 184
Part III Laminar Forced Film Condensation 185
9 Complete Similarity Mathematical Models on Laminar Forced Film Condensation of Pure Vapour 186
9.1 Introduction 186
9.2 Governing Partial Differential Equations 188
9.2.1 Physical Model and Coordinate System 188
9.2.2 Governing Partial Differential Equations 188
9.3 Similarity Variables 190
9.3.1 For Liquid Film 190
9.3.2 For Vapour Film 191
9.4 Similarity Transformation of Governing Partial Differential Equations 191
9.4.1 For Liquid Film 191
9.4.2 For Vapour Film 197
9.4.3 For Boundary Conditions 201
9.5 Remarks 204
Exercises 205
References 205
10 Velocity and Temperature Fields on Laminar Forced Film Condensation of Pure Vapour 207
10.1 Introduction 207
10.2 Treatment of Temperature-Dependent Physical Properties 208
10.2.1 For Liquid Film Medium 208
10.2.2 For Vapour Film Medium 210
10.3 Numerical Solutions 211
10.3.1 Calculation Procedure 211
10.3.2 Velocity and Temperature Fields of the Two-Phase Film Flows 212
10.4 Remarks 215
Exercises 216
References 216
11 Heat and Mass Transfer on Laminar Forced Film Condensation of Pure Vapour 218
11.1 Introduction 219
11.2 Condensate Heat Transfer Analysis 219
11.3 Wall Dimensionless Temperature Gradient 221
11.4 Prediction Equations on Heat Transfer 222
11.5 Mass Transfer Analysis 224
11.6 Mass Flow Rate Parameter 226
11.7 Prediction Equations on Condensate Mass Transfer 233
11.8 Condensate Mass–Energy Transformation Equation 234
11.8.1 Derivation on Condensate Mass–Energy Transformation Equation 234
11.8.2 Mass–Energy Transformation Coefficient 236
11.9 Summary 239
11.10 Remarks 239
11.11 Calculation Example 246
Exercises 248
12 Complete Similarity Mathematical Models on Laminar Forced Film Condensation of Vapour–Gas Mixture 249
12.1 Introduction 249
12.2 Governing Partial Differential Equations 250
12.2.1 Physical Model and Coordinate System 250
12.2.2 Governing Partial Differential Equations 251
12.3 Similarity Variables 253
12.3.1 For Liquid Film 253
12.3.2 For Vapor–Gas Mixture Film 254
12.4 Similarity Transformation of Governing Partial Differential Equations 255
12.4.1 For Liquid Film 255
12.4.2 For Vapour–Gas Mixture Film 261
12.4.3 For Boundary Conditions 271
12.5 Remarks 278
Exercises 278
References 279
13 Velocity, Temperature, and Concentration Fields on Laminar Forced Film Condensation of Vapour–Gas Mixture 281
13.1 Introduction 282
13.2 Treatment of Variable Physical Properties 282
13.2.1 Treatment of Temperature-Dependent Physical Properties of Liquid Film 283
13.2.2 Treatment of Concentration-Dependent Densities of Vapour--Gas Mixture 283
13.2.3 Treatment of Other Concentration-Dependent Physical Properties of Vapour–Gas Mixture 285
13.2.4 Treatment of Temperature-Dependent Physical Properties of Vapour–Gas Mixture 286
13.3 Numerical Calculation Procedure 288
13.4 Numerical Solutions 289
13.4.1 Interfacial Vapour Saturation Temperature 289
13.4.2 Effect of the Interfacial Vapour Saturation Temperature on Wall Subcooled Temperature 289
13.4.3 Velocity, Concentration, and Temperature Fields of the Two-Phase Film Flows 290
13.5 Remarks 295
Exercises 297
References 297
14 Heat and Mass Transfer on Laminar Forced Film Condensation of Vapour–Gas Mixture 298
14.1 Introduction 299
14.2 Heat Transfer Analysis 299
14.3 Wall Dimensionless Temperature Gradient 301
14.4 Determination of Interfacial Vapour Saturation Temperature 304
14.5 Simple and Reliable Prediction Equations of Heat Transfer 307
14.6 Condensate Mass Transfer Analysis 309
14.7 Mass Flow Rate Parameter 311
14.8 Prediction Equations of Condensate Mass Transfer 317
14.9 Equation of Interfacial Vapour Saturation Temperature 317
14.9.1 For Laminar Forced Film Condensation of Vapour–Gas Mixture 317
14.9.2 For Laminar Forced Film Condensation of Water Vapour–Air Mixture 318
14.10 Evaluation of Condensate Mass–Energy Transformation Coefficient 319
14.11 Summary 320
14.12 Remarks 328
14.13 Calculation Examples 329
Exercises 334
Part IV Appendix 335
Appendix A Tables with Physical Properties 336
Physical Properties of Gases at Atmospheric Pressure 336
Physical Properties of Some Saturated Liquid 341
Temperature Parameters of Gases [5--7] 344
References 345
Index 346