HEAT TRANSFER Principles and Applications BINAY K. DUTTA West Bengal Pollution Control Board Kolkata PHI Learning PfcO too1 Delhi-110092 2014
Contents Preface Notations ix xiii 1. Introduction 1-8 1.1 Modes of Heat Transfer 3 1.1.1 Conduction 3 1.1.2 Convection 3 1.1.3 Radiation 3 1.2 Heat Transfer Equipment 4 1.3 Systems of Measurement, Units and Dimensions 4 1.3.1 English Engineering System 5 1.3.2 The International System (SI) of Units (The Systeme Internationale (SI) de Unites) 6 1.4 Examples of Unit Conversion 6 2. Steady State Conduction in One Dimension 9-49 2.1 The Basic Law of Heat Conduction Fourier's Law 9 2.2 Thermal Conductivity 10 2.3 Steady State Conduction of Heat through a Composite Solid 12 2.4 Steady State Heat Conduction through a Variable Area 16 2.4.1 The Cylinder 16 2.4.2 The Sphere 23 2.5 Steady State Heat Conduction in Bodies with Heat Sources 25 2.5.1 The Plane Wall 25 2.5.2 The Cylinder 33 2.5.3 The Sphere 38 2.6 Average Temperature of a Solid 39 2.7 Application of Conduction Calculation 40 Short Questions 42 Problems 44 References and Further Reading 49 3. Heat Transfer Coefficient 50-97 3.1 Convective Heat Transfer and the Concept of Heat Transfer Coefficient 50 3.2 Overall Heat Transfer Coefficient 57 3.2.1 Heat Transfer between Fluids Separated by 3.2.2 Heat Transfer between Fluids Separated by a Cylindrical Wall 59 a Plane Wall 57 iii
iv CONTENTS 3.3 Heat Transfer from Extended Surfaces The Fins 74 3.4 Thermal Contact Resistance 80 3.5 Critical Insulation Thickness 82 3.6 Economic (or Optimum) Insulation Thickness 85 Short Questions 89 Problems 90 References and Further Reading 97 4. Forced Convection 98-148 4.1 Forced Convection in Systems of Simple Geometries 98 4.1.1 Flow over a Flat Plate 99 4.1.2 Thermal Boundary Layer 100 4.1.3 Flow across a Cylinder 101 4.2 Dimensional Analysis 103 4.2.1 Statement of Buckingham Pi Theorem 103 4.2.2 Dimensionless Groups in Convective Heat Transfer to a Fluid Flowing through a Circular Pipe 104 4.3 Dimensionless Groups in Heat Transfer 105 4.4 Experimental Determination of the Heat Transfer Coefficient 107 4.5 Correlations for the Heat Transfer Coefficient Internal Flows 108 4.5.1 Laminar Flow through a Circular Pipe 109 4.5.2 Turbulent Flow through a Circular Pipe 109 4.5.3 Flow through a Non-circular Duct 110 4.6 Correlations for the Heat Transfer Coefficient External Flows 111 4.6.1 Flow over a Flat Plate 111 4.6.2 Flow across a Cylinder 113 4.6.3 Flow past a Sphese 116 4.6.4 Flow across a Bank of Tubes 119 4.6.5 Heat Transfer Coefficient in a Packed and a Fluidized Bed 121 4.7 Heat Transfer with a Variable Driving Force Cocurrent and Countercurrent Operations 122 4.8 Momentum and Heat Transfer Analogies 136 Short Questions 142 Problems 143 References and Further Reading 147 5. Free Convection 149-169 5.1 Qualitative Description of Free Convection Flows 149 5.2 Heat Transfer Correlations for Free Convection 151 5.2.1 Free Convection from a Flat Surface 152 5.2.2 Free Convection from a Cylinder 155 5.2.3 Free Convection from a Sphere 160 5.2.4 Free Convection in an Enclosure 160 5.3 Combined Free and Forced Convection 162 Short Questions 164 Problems 165 References and Further Reading 169
CONTENTS V 6. Boiling and Condensation 170-206 6.1 The Boiling Phenomenon 170 6.2 Hysteresis in the Boiling Curve 174 6.3 The Mechanism of Nucleate Boiling 174 6.4 Correlations for Pool Boiling Heat Transfer 178 6.4.1 Nucleate Boiling 178 6.4.2 Critical Heat Flux 179 6.4.3 Stable Film Boiling 180 6.5 Forced Convection Boiling 186 6.6 The Condensation Phenomenon 190 6.7 Film Condensation on a Vertical Surface 191 6.8 Turbulent Film Condensation 194 6.9 Condensation Outside a Horizontal Tube or a Tube Bank 197 6.10 Condensation Inside a Horizontal Tube 200 6.11 Effect of Non-condensable Gases 201 6.12 Dropwise Condensation 202 Short Questions 202 Problems 203 References and Further Reading 205 7. Radiation Heat Transfer 207-274 7.1 Basic Concepts of Radiation from a Surface 208 7.1.1 Blackbody Radiation 209 7.1.2 Planck's Law 210 7.1.3 Wein's Displacement Law 212 7.1.4 The Stefan-Boltzmann Law 213 7.1.5 Kirchhoff s Law 216 7.1.6 Gray Body 217 7.2 Radiation Intensity of a Blackbody 220 7.3 Spectral Emissive Power of a Blackbody over a Hemisphere 222 7.4 Radiative Heat Exchange between Surfaces The View Factor 222 7.5 View Factor Algebra 229 7.6 Rate of Radiation Exchange between Blackbodies 237 7.7 Exchange of Radiation between Diffuse Gray Surfaces 239 7.7.1 Radiation Exchange in a Gray Enclosure 240 7.7.2 Radiation Exchange in a Two-surface Gray Enclosure 242 7.7.3 Emissivity Factor 243 7.7.4 A Gray Enclosure with Re-radiating Surfaces 244 7.7.5 Use of the Network Diagram to Calculate Radiation Exchange 245 7.8 Radiation Shield 254 7.9 Radiation Combined with Conduction and Convection 257 7.10 Absorption and Emission in a Gaseous Medium 261 7.10.1 The Absorptivity and Emissivity of a Gas 261 7.10.2 Radiation Exchange between a Non-luminous Gas and Black Surface of Enclosing Walls 265 7.11 Greenhouse Effect 267 Short Questions 268 Problems 269 References and Further Reading 274
CONTENTS Heat Exchangers 275-360 8.1 Construction of a Shell-and-Tube Heat Exchanger 275 8.1.1 The Shell 277 8.1.2 The Tubes 277 8.1.3 The Tube Sheets 278 8.1.4 The Bonnet and the Channel 279 8.1.5 The Pass Partition Plate 279 8.1.6 Nozzles 280 8.1.7 Baffles 281 8.1.8 Tie Rods and Baffle Spacers 282 8.1.9 Flanges and Gaskets 283 8.1.10 Expansion Joint 283 8.2 Process Design Considerations 283 8.2.1 Fouling of a Heat Exchanger The Dirt Factor or Fouling Factor 284 8.2.2 Log Mean Temperature Difference Correction Factor 285 8.2.3 Temperature Distribution in Multi-pass Exchangers and Temperature Cross 291 8.2.4 The Caloric Temperature 293 8.2.5 Individual and Overall Heat Transfer Coefficients 293 8.2.6 Pressure Drop Calculation 298 8.3 Double-pipe Heat Exchanger Design Procedure 300 8.3.1 Energy Balance and Heat Duty Calculation 301 8.3.2 The Design Procedure 302 8.4 Shell-and-Tube Heat Exchanger Design Procedure 306 8.5 The Effectiveness NTU'Method of Heat Exchanger Analysis 317 8.6 Other Types of Shell-and-Tube Exchangers 321 8.6.1 Floating-head Exchangers 322 8.6.2 Heat Exchanger with a U-bundle 324 8.6.3 Reboilers and Condensers 324 8.6.4 The RODbaffle Exchanger 326 8.6.5 Air-cooled Exchangers 327 8.7 Classification of Shell-and-Tube Exchangers 327 8.8 Materials of Construction 329 8.9 Cleaning of Heat Exchangers 331 8.10 Heat Transfer in an Agitated Vessel 332 8.10.1 Heating and Cooling Arrangements 332 8.10.2 Thermal Design of an Agitated Vessel 335 8.10.3 Correlations for Individual Coefficients 336 8.11 Compact Heat Exchangers 339 8.11.1 Plate Heat Exchangers 340 8.11.2 Spiral-plate and Spiral-tube Heat Exchangers 347 8.12 Other Common Heat Exchange Devices 350 8.13 Pipe Tracing 351 8.13.1 Steam Jacketing 351 8.13.2 Electrical Heating 352 8.13.3 Steam Tracing 352 8.14 Heat Transfer Fluids 353 Short Questions 354 Problems 356 References and Further Reading 358
CONTENTS vii 9. Evaporation and Evaporators 361-420 9.1 Types of Evaporators Their Construction and Operation 361 9.1.1 Natural-circulation Evaporators 361 9.1.2 Forced-circulation Evaporators 366 9.1.3 Falling-film Evaporators 369 9.1.4 Climbing- or Rising-film Evaporator 371 9.1.5 Agitated Thin-film Evaporators 372 9.1.6 The Plate Evaporator 373 9.2 Evaporator Auxiliaries 374 9.2.1 Vacuum Devices 374 9.2.2 Steam Traps 377 9.2.3 Entrainment Separators 381 9.3 Principles of Evaporation and Evaporators 382 9.3.1 Single- and Multiple-effect Evaporators 382 9.3.2 Capacity and Economy 385 9.3.3 Boiling Point Elevation (BPE) 385 9.3.4 Temperature Driving Force 387 9.3.5 Heat Transfer Coefficient 388 9.3.6 Enthalpy of a Solution 389 9.4 Single-effect Evaporator Calculation 389 9.5 Multiple-effect Evaporators 395 9.5.1 Classification Based on the Mode of Feed Supply 395 9.5.2 Comparison between the Forward and Backward Feed Modes 397 9.5.3 Effect of Boiling Point Elevation in a Multiple-effect Evaporator 398 9.5.4 Multiple-effect Evaporator Calculations 400 9.6 Evaporator Selection 411 9.7 Vapour Recompression 411 Short Questions 415 Problems 418 References and Further Reading 419 10. Unsteady State and Multidimensional Heat Conduction 421-464 10.1 Mathematical Formulation and Initial and Boundary Conditions 422 10.2 Techniques of Analytical Solution 428 10.3 Types of Boundary Conditions 435 10.4 Determination of the Average Temperature of a Solid 443 10.5 Numerical Calculation of Unsteady State Heat Conduction 443 10.6 Unsteady or Steady State Heat Conduction in a Multidimensional Solid 450 10.7 The Graetz Problem 454 10.8 Similarity Solution 455 10.9 Numerical Solution of Heat Conduction Problems 460 Short Questions 461 Problems 461 References and Further Reading 464
viii CONTENTS 11. Boundary Layer Heat Transfer 465-511 11.1 The Equation of Continuity 465 11.2 The Equation of Motion 467 11.3 Boundary Layer Flow over a Flat Plate 472 11.3.1 Differential Equations for Laminar Boundary Layer Flow 472 11.3.2 Solution of the Boundary Layer Equations 474 11.3.3 Boundary Layer Thickness and Drag Coefficient 476 11.3.4 The Momentum Integral Equation 479 11.4 Forced Convection Heat Transfer in Laminar Boundary Layer Flow over a Flat Plate 483 11.4.1 Boundary Layer Temperature Equation 483 11.4.2 The Energy Integral Equation 491 11.5 Application to Free Convection Heat Transfer 495 11.6 Heat Transfer in Turbulent Boundary Layer Flow 498 11.6.1 Mean and Fluctuating Quantities 499 11.6.2 The Concept of Eddy Viscosity 502 11.6.3 The Prandtl Mixing-Length Theory 502 11.6.4 The Prandtl Analogy 506 11.6.5 The von Kantian Analogy 508 Short Questions 509 Problems 510 References and Further Reading 511 Answers to Selected Problems 513 liidi-x 521