Thermodynamics and heat Books

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Book SynopsisEnables engineers to understand the most important aspects of rotating machine vibrations, from basic explanations to more accurate numerical models and analysis. This book, together with the the associated MATLAB software, will give engineers the confidence to base their designs on calculations and understand any dynamic phenomena that might occur.Table of Contents1. Introduction; 2. Introduction to vibration analysis; 3. Free lateral response of simple rotor models; 4. Finite element modeling; 5. Free lateral response of complex systems; 6. Forced lateral response and critical speeds; 7. Asymmetric rotors and other sources of instability; 8. Balancing; 9. Axial and torsional vibration; 10. More complex rotordynamic models.

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Book SynopsisAn account of the concepts and intellectual structure of classical thermodynamics that reveals the subject's simplicity and coherence.Students of physics, chemistry, and engineering are taught classical thermodynamics through its methods—a “problems first” approach that neglects the subject's concepts and intellectual structure. In Thermodynamic Weirdness, Don Lemons fills this gap, offering a nonmathematical account of the ideas of classical thermodynamics in all its non-Newtonian “weirdness.” By emphasizing the ideas and their relationship to one another, Lemons reveals the simplicity and coherence of classical thermodynamics. Lemons presents concepts in an order that is both chronological and logical, mapping the rise and fall of ideas in such a way that the ideas that were abandoned illuminate the ideas that took their place. Selections from primary sources, including writings by Daniel Fahrenheit, Antoine Lavoisier, James Joule

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Book SynopsisA new edition of the bestseller on convection heat transfer A revised edition of the industry classic, Convection Heat Transfer, Fourth Edition, chronicles how the field of heat transfer has grown and prospered over the last two decades. This new edition is more accessible, while not sacrificing its thorough treatment of the most up-to-date information on current research and applications in the field. One of the foremost leaders in the field, Adrian Bejan has pioneered and taught many of the methods and practices commonly used in the industry today. He continues this book''s long-standing role as an inspiring, optimal study tool by providing: Coverage of how convection affects performance, and how convective flows can be configured so that performance is enhanced How convective configurations have been evolving, from the flat plates, smooth pipes, and single-dimension fins of the earlier editions to new populations of configurationsTrade ReviewThe book is very useful for students, practicing engineers, and for researchers. It is highly recommended (Zeitschrift fur Angewandte Mathematik und Mechanik, September 2014)Table of ContentsPreface xv Preface to the Third Edition xvii Preface to the Second Edition xxi Preface to the First Edition xxiii List of Symbols xxv 1 Fundamental Principles 1 1.1 Mass Conservation / 2 1.2 Force Balances (Momentum Equations) / 4 1.3 First Law of Thermodynamics / 8 1.4 Second Law of Thermodynamics / 15 1.5 Rules of Scale Analysis / 17 1.6 Heatlines for Visualizing Convection / 21 References / 22 Problems / 25 2 Laminar Boundary Layer Flow 30 2.1 Fundamental Problem in Convective Heat Transfer / 31 2.2 Concept of Boundary Layer / 34 2.3 Scale Analysis / 37 2.4 Integral Solutions / 42 2.5 Similarity Solutions / 48 2.5.1 Method / 48 2.5.2 Flow Solution / 51 2.5.3 Heat Transfer Solution / 53 2.6 Other Wall Heating Conditions / 56 2.6.1 Unheated Starting Length / 57 2.6.2 Arbitrary Wall Temperature / 58 2.6.3 Uniform Heat Flux / 60 2.6.4 Film Temperature / 61 2.7 Longitudinal Pressure Gradient: Flow Past a Wedge and Stagnation Flow / 61 2.8 Flow Through the Wall: Blowing and Suction / 64 2.9 Conduction Across a Solid Coating Deposited on a Wall / 68 2.10 Entropy Generation Minimization in Laminar Boundary Layer Flow / 71 2.11 Heatlines in Laminar Boundary Layer Flow / 74 2.12 Distribution of Heat Sources on a Wall Cooled by Forced Convection / 77 2.13 The Flow of Stresses / 79 References / 80 Problems / 82 3 Laminar Duct Flow 96 3.1 Hydrodynamic Entrance Length / 97 3.2 Fully Developed Flow / 100 3.3 Hydraulic Diameter and Pressure Drop / 103 3.4 Heat Transfer To Fully Developed Duct Flow / 110 3.4.1 Mean Temperature / 110 3.4.2 Fully Developed Temperature Profile / 112 3.4.3 Uniform Wall Heat Flux / 114 3.4.4 Uniform Wall Temperature / 117 3.5 Heat Transfer to Developing Flow / 120 3.5.1 Scale Analysis / 121 3.5.2 Thermally Developing Hagen–Poiseuille Flow / 122 3.5.3 Thermally and Hydraulically Developing Flow / 128 3.6 Stack of Heat-Generating Plates / 129 3.7 Heatlines in Fully Developed Duct Flow / 134 3.8 Duct Shape for Minimum Flow Resistance / 137 3.9 Tree-Shaped Flow / 139 References / 147 Problems / 153 4 External Natural Convection 168 4.1 Natural Convection as a Heat Engine in Motion / 169 4.2 Laminar Boundary Layer Equations / 173 4.3 Scale Analysis / 176 4.3.1 High-Pr Fluids / 177 4.3.2 Low-Pr Fluids / 179 4.3.3 Observations / 180 4.4 Integral Solution / 182 4.4.1 High-Pr Fluids / 183 4.4.2 Low-Pr Fluids / 184 4.5 Similarity Solution / 186 4.6 Uniform Wall Heat Flux / 189 4.7 Effect of Thermal Stratification / 192 4.8 Conjugate Boundary Layers / 195 4.9 Vertical Channel Flow / 197 4.10 Combined Natural and Forced Convection (Mixed Convection) / 200 4.11 Heat Transfer Results Including the Effect of Turbulence / 203 4.11.1 Vertical Walls / 203 4.11.2 Inclined Walls / 205 4.11.3 Horizontal Walls / 207 4.11.4 Horizontal Cylinder / 209 4.11.5 Sphere / 209 4.11.6 Vertical Cylinder / 210 4.11.7 Other Immersed Bodies / 211 4.12 Stack of Vertical Heat-Generating Plates / 213 4.13 Distribution of Heat Sources on a Vertical Wall / 216 References / 218 Problems / 221 5 Internal Natural Convection 233 5.1 Transient Heating from the Side / 233 5.1.1 Scale Analysis / 233 5.1.2 Criterion for Distinct Vertical Layers / 237 5.1.3 Criterion for Distinct Horizontal Jets / 238 5.2 Boundary Layer Regime / 241 5.3 Shallow Enclosure Limit / 248 5.4 Summary of Results for Heating from the Side / 255 5.4.1 Isothermal Sidewalls / 255 5.4.2 Sidewalls with Uniform Heat Flux / 259 5.4.3 Partially Divided Enclosures / 259 5.4.4 Triangular Enclosures / 262 5.5 Enclosures Heated from Below / 262 5.5.1 Heat Transfer Results / 263 5.5.2 Scale Theory of the Turbulent Regime / 265 5.5.3 Constructal Theory of B´enard Convection / 267 5.6 Inclined Enclosures / 274 5.7 Annular Space Between Horizontal Cylinders / 276 5.8 Annular Space Between Concentric Spheres / 278 5.9 Enclosures for Thermal Insulation and Mechanical Strength / 278 References / 284 Problems / 289 6 Transition to Turbulence 295 6.1 Empirical Transition Data / 295 6.2 Scaling Laws of Transition / 297 6.3 Buckling of Inviscid Streams / 300 6.4 Local Reynolds Number Criterion for Transition / 304 6.5 Instability of Inviscid Flow / 307 6.6 Transition in Natural Convection on a Vertical Wall / 313 References / 315 Problems / 318 7 Turbulent Boundary Layer Flow 320 7.1 Large-Scale Structure / 320 7.2 Time-Averaged Equations / 322 7.3 Boundary Layer Equations / 325 7.4 Mixing Length Model / 328 7.5 Velocity Distribution / 329 7.6 Wall Friction in Boundary Layer Flow / 336 7.7 Heat Transfer in Boundary Layer Flow / 338 7.8 Theory of Heat Transfer in Turbulent Boundary Layer Flow / 342 7.9 Other External Flows / 347 7.9.1 Single Cylinder in Cross Flow / 347 7.9.2 Sphere / 349 7.9.3 Other Body Shapes / 350 7.9.4 Arrays of Cylinders in Cross Flow / 351 7.10 Natural Convection Along Vertical Walls / 356 References / 359 Problems / 361 8 Turbulent Duct Flow 369 8.1 Velocity Distribution / 369 8.2 Friction Factor and Pressure Drop / 371 8.3 Heat Transfer Coefficient / 376 8.4 Total Heat Transfer Rate / 380 8.4.1 Isothermal Wall / 380 8.4.2 Uniform Wall Heating / 382 8.4.3 Time-Dependent Heat Transfer / 382 8.5 More Refined Turbulence Models / 383 8.6 Heatlines in Turbulent Flow Near a Wall / 387 8.7 Channel Spacings for Turbulent Flow / 389 References / 390 Problems / 392 9 Free Turbulent Flows 398 9.1 Free Shear Layers / 398 9.1.1 Free Turbulent Flow Model / 398 9.1.2 Velocity Distribution / 401 9.1.3 Structure of Free Turbulent Flows / 402 9.1.4 Temperature Distribution / 404 9.2 Jets / 405 9.2.1 Two-Dimensional Jets / 406 9.2.2 Round Jets / 409 9.2.3 Jet in Density-Stratified Reservoir / 411 9.3 Plumes / 413 9.3.1 Round Plume and the Entrainment Hypothesis / 413 9.3.2 Pulsating Frequency of Pool Fires / 418 9.3.3 Geometric Similarity of Free Turbulent Flows / 421 9.4 Thermal Wakes Behind Concentrated Sources / 422 References / 425 Problems / 426 10 Convection with Change of Phase 428 10.1 Condensation / 428 10.1.1 Laminar Film on a Vertical Surface / 428 10.1.2 Turbulent Film on a Vertical Surface / 435 10.1.3 Film Condensation in Other Configurations / 438 10.1.4 Drop Condensation / 445 10.2 Boiling / 447 10.2.1 Pool Boiling Regimes / 447 10.2.2 Nucleate Boiling and Peak Heat Flux / 451 10.2.3 Film Boiling and Minimum Heat Flux / 454 10.2.4 Flow Boiling / 457 10.3 Contact Melting and Lubrication / 457 10.3.1 Plane Surfaces with Relative Motion / 458 10.3.2 Other Contact Melting Configurations / 462 10.3.3 Scale Analysis and Correlation / 464 10.3.4 Melting Due to Viscous Heating in the Liquid Film / 466 10.4 Melting By Natural Convection / 469 10.4.1 Transition from the Conduction Regime to the Convection Regime / 469 10.4.2 Quasisteady Convection Regime / 472 10.4.3 Horizontal Spreading of the Melt Layer / 474 References / 478 Problems / 482 11 Mass Transfer 489 11.1 Properties of Mixtures / 489 11.2 Mass Conservation / 492 11.3 Mass Diffusivities / 497 11.4 Boundary Conditions / 499 11.5 Laminar Forced Convection / 501 11.6 Impermeable Surface Model / 504 11.7 Other External Forced Convection Configurations / 506 11.8 Internal Forced Convection / 509 11.9 Natural Convection / 511 11.9.1 Mass-Transfer-Driven Flow / 512 11.9.2 Heat-Transfer-Driven Flow / 513 11.10 Turbulent Flow / 516 11.10.1 Time-Averaged Concentration Equation / 516 11.10.2 Forced Convection Results / 517 11.10.3 Contaminant Removal from a Ventilated Enclosure / 520 11.11 Massfunction and Masslines / 527 11.12 Effect of Chemical Reaction / 527 References / 531 Problems / 532 12 Convection in Porous Media 537 12.1 Mass Conservation / 537 12.2 Darcy Flow Model and the Forchheimer Modification / 540 12.3 First Law of Thermodynamics / 542 12.4 Second Law of Thermodynamics / 546 12.5 Forced Convection / 547 12.5.1 Boundary Layers / 547 12.5.2 Concentrated Heat Sources / 552 12.5.3 Sphere and Cylinder in Cross Flow / 553 12.5.4 Channel Filled with Porous Medium / 554 12.6 Natural Convection Boundary Layers / 555 12.6.1 Boundary Layer Equations: Vertical Wall / 555 12.6.2 Uniform Wall Temperature / 556 12.6.3 Uniform Wall Heat Flux / 558 12.6.4 Spacings for Channels Filled with Porous Structures / 559 12.6.5 Conjugate Boundary Layers / 562 12.6.6 Thermal Stratification / 563 12.6.7 Sphere and Horizontal Cylinder / 566 12.6.8 Horizontal Walls / 567 12.6.9 Concentrated Heat Sources / 567 12.7 Enclosed Porous Media Heated from the Side / 571 12.7.1 Four Heat Transfer Regimes / 571 12.7.2 Convection Results / 575 12.8 Penetrative Convection / 577 12.8.1 Lateral Penetration / 577 12.8.2 Vertical Penetration / 578 12.9 Enclosed Porous Media Heated from Below / 579 12.9.1 Onset of Convection / 579 12.9.2 Darcy Flow / 583 12.9.3 Forchheimer Flow / 585 12.10 Multiple Flow Scales Distributed Nonuniformly / 587 12.10.1 Heat Transfer / 590 12.10.2 Fluid Friction / 591 12.10.3 Heat Transfer Rate Density: The Smallest Scale for Convection / 591 12.11 Natural Porous Media: Alternating Trees / 592 References / 595 Problems / 598 Appendixes 607 A Constants and Conversion Factors / 609 B Properties of Solids / 615 C Properties of Liquids / 625 D Properties of Gases / 633 E Mathematical Formulas / 639 Author Index 641 Subject Index 653

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Book Synopsis

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Book SynopsisMany practical operations, such as environment depollution, blood dialysis or product purification, require matter transfer. With an emphasis on the aforementioned subjects, this book revisits the founding principles of materials transfer on the basis of Fick’s first law, which constitutes the foundation of diffusional phenomena. Additionally, continuity equations translating the macroscopic balances of systems are established. These balances constitute Fick’s second law, which can be applied to quantify the fluxes of matter transferred in each situation, provided physical data is available. To this end, Mass Transfers and Physical Data Estimation pays particular attention to methods of data estimation. Methods presented in this book are applied to several practical cases, such as diffusion in catalytic reactions or the reconstitution of cartilage in human bone joints.Table of ContentsPreface ix Introduction xi Chapter 1. Determination of Physical Data 1 1.1. Introduction 1 1.2. Estimating critical properties 2 1.2.1. Estimating critical temperature 2 1.2.2. Estimating critical pressure 5 1.2.3. Estimating the critical volume: Benson correlation (Benson, 1948) 8 1.2.4. Estimating the critical compressibility factor 10 1.3. Methods for estimating boiling temperature 11 1.4. Methods for estimating density 14 1.4.1. Estimating liquid densities 14 1.5. Methods for estimating viscosity 15 1.5.1. Estimating viscosities of pure liquids 15 1.5.2. Correlations for the viscosity of liquid mixtures 17 1.5.3. Estimating gas viscosities 18 1.6. Methods for estimating specific heat 19 1.6.1. Heat capacities of petroleum oils 19 1.6.2. Heat capacities of petroleum vapors 20 1.6.3. Estimations for anthracite and bituminous coals 20 1.6.4. Heat capacities for cement, mortar and sand 21 1.6.5. Heat capacities of organic liquids 21 1.7. Estimating latent heat of vaporization 22 1.7.1. Rapid estimations 22 1.7.2. Calculating latent heat from critical data 23 1.7.3. Chen correlation 23 1.7.4. Calculations at different temperatures 24 1.8. Estimating expansion coefficients β 24 1.9. Methods for estimating heat conductivity 25 1.9.1. Heat conductivity of metals and alloys 25 1.9.2. Heat conductivity of wood 26 1.9.3. Conductivity of chains of liquid hydrocarbons 26 1.9.4. Conductivity of gases and vapors 27 1.9.5. Conductivity of monatomic gases 28 1.9.6. Conductivity of non-polar gases with linear molecules 28 1.10. Physical properties of water 29 1.10.1. Correlation of density 29 1.10.2. Heat capacity 29 1.10.3. Correlation of heat conductivity 29 1.10.4. Correlation of viscosity 29 1.10.5. Correlation of thermal diffusivity 30 1.10.6. Correlation of the Prandtl number 30 1.10.7. Correlation for calculating the expansion coefficient 30 1.10.8. Correlation for calculating the saturating pressure 30 1.10.9. Correlation for calculating latent heat 31 1.11. Physical properties of air 31 1.11.1. Correlation of density 32 1.11.2. Heat capacity 32 1.11.3. Correlation of heat conductivity 32 1.11.4. Correlation of viscosity 33 1.11.5. Correlation of thermal diffusivity 33 1.11.6. Correlation of the Prandtl number 33 1.11.7. Correlation for calculating the expansion coefficient 33 Chapter 2. Determinants and Parameters of Mass Transfer 35 2.1. Introduction 35 2.2. Relative transfer velocities 36 2.2.1. Velocity relating to average mass velocity 36 2.2.2. Velocity relative to average molar velocity. 37 2.3. Amount of matter transferred 38 2.4. Expressions of flux density 39 2.4.1. Total flux 39 2.4.2. Specific fluxes 41 2.5. Operations on diffusion flux densities 44 2.5.1. Total density as a function of the specific densities 44 2.5.2. Sum of mass densities with respect to v 45 2.5.3. Sum of molar flux densities with respect to v* 46 2.5.4. Sum of mass flux densities with respect to a mobile reference frame at v* 46 2.6. Relations between flux densities fi and ji 47 2.7. Relations between flux densities Fi and Ji* 47 Chapter 3. Fick’s First Law: Diffusion Coefficients 49 3.1. Introduction 49 3.2. Fick’s first law 50 3.2.1. Expressing the flux density vector 50 3.2.2. Similarities to energy and momentum transfer laws 51 3.2.3. Convective analogy 52 3.3. Fick’s first law in different forms 52 3.4. Determining diffusion coefficients from tabulated data 53 3.4.1. Gaseous binary diffusion coefficients 53 3.4.2. Illustration: diffusion coefficients of CO2 in air and in water vapor 54 3.4.3. Diffusion coefficients for liquid binaries 58 3.5. Estimating diffusion coefficients from correlations 60 3.5.1. Estimating gaseous binary diffusion coefficients 60 3.5.2. Estimating diffusion coefficients of liquid binaries 71 3.6. Diffusion coefficients for multicomponent mixtures 81 3.6.1. Stefan–Maxwell equation 81 3.6.2. Effective diffusion coefficient for complex mixtures 82 Chapter 4. Fick’s Second Law: Macroscopic Balances 85 4.1. Introduction 85 4.2. Overall continuity equation 85 4.2.1. The accumulation term 86 4.2.2. The generation term 86 4.2.3. The term I – O 87 4.2.4. The balance equation 87 4.2.5. The balance equation in Cartesian coordinates 88 4.3. Particular continuity equations 88 4.3.1. The term Ii – Oi 88 4.3.2. The accumulation term 89 4.3.3. The generation term 89 4.3.4. Continuity equations in molar terms 90 4.4. Illustration: diffusion with chemical reaction 92 4.5. Illustration: diffusion of a component in a stagnant mixture 94 4.6. Reading: background to Fick’s Laws 97 Chapter 5. Exercises and Solutions 101 Appendices 153 Appendix 1 155 Appendix 2 187 References 191 Index 205

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Book SynopsisConvection heat transfer is an important topic both for industrial applications and fundamental aspects. It combines the complexity of the flow dynamics and of the active or passive scalar transport process. It is part of many university courses such as Mechanical, Aeronautical, Chemical and Biomechanical Engineering. The literature on convective heat transfer is large, but the present manuscript differs in many aspects from the existing ones, particularly from the pedagogical point of view. Each chapter begins with a brief yet complete presentation of the related topic. This is followed by a series of solved problems. The latter are scrupulously detailed and complete the synthetic presentation given at the beginning of each chapter. There are about 50 solved problems, which are mostly original with gradual degree of complexity including those related to recent findings in convective heat transfer phenomena. Each problem is associated with clear indications to help the reader to handle independently the solution. The book contains nine chapters including laminar external and internal flows, convective heat transfer in laminar wake flows, natural convection in confined and no-confined laminar flows, turbulent internal flows, turbulent boundary layers, and free shear flows.Trade Review"The variety of theoretical methods is shown and a great number of relevant problems is treated. The book is highly recommended for students and researchers." (ZAMM, March 2011) Table of ContentsForeword xiii Preface xv Chapter 1. Fundamental Equations, Dimensionless Numbers 1 1.1. Fundamental equations 1 1.2. Dimensionless numbers 8 1.3. Flows with variable physical properties: heat transfer in a laminar Couette flow 9 1.4. Flows with dissipation 14 1.5. Cooling of a sphere by a gas flow 20 Chapter 2. Laminar Fully Developed Forced Convection in Ducts 31 2.1. Hydrodynamics 31 2.2. Heat transfer 33 2.3. Heat transfer in a parallel-plate channel with uniform wall heat flux 35 2.3.3. Solution 37 2.4. Flow in a plane channel insulated on one side and heated at uniform temperature on the opposite side 46 Chapter 3. Forced Convection in Boundary Layer Flows 53 3.1. Hydrodynamics 53 3.2. Heat transfer 58 3.3. Integral method 62 3.4. Heated jet nozzle 65 3.5. Asymptotic behavior of thermal boundary layers 68 3.6. Protection of a wall by a film of insulating material 74 3.7. Cooling of a moving sheet 83 3.8. Heat transfer near a rotating disk 93 3.9. Thermal loss in a duct 106 3.10. Temperature profile for heat transfer with blowing 117 Chapter 4. Forced Convection Around Obstacles 119 4.1. Description of the flow 119 4.2. Local heat-transfer coefficient for a circular cylinder 121 4.3. Average heat-transfer coefficient for a circular cylinder 123 4.4. Other obstacles 125 4.5. Heat transfer for a rectangular plate in cross-flow 126 4.6. Heat transfer in a stagnation plane flow. Uniform temperature heating 128 4.7. Heat transfer in a stagnation plane flow. Step-wise heating at uniform flux 131 4.8. Temperature measurements by cold-wire 135 Chapter 5. External Natural Convection 141 5.1. Introduction 141 5.2. Boussinesq model 142 5.3. Dimensionless numbers. Scale analysis 142 5.4. Natural convection near a vertical wall 145 5.5. Integral method for natural convection 149 5.6. Correlations for external natural convection 152 5.7. Mixed convection 152 5.8. Natural convection around a sphere 155 5.9. Heated jet nozzle 157 5.10. Shear stress on a vertical wall heated at uniform temperature 161 5.11. Unsteady natural convection 164 5.12. Axisymmetric laminar plume 176 5.13. Heat transfer through a glass pane 183 5.14. Mixed convection near a vertical wall with suction 189 Chapter 6. Internal Natural Convection 195 6.1. Introduction 195 6.2. Scale analysis 195 6.3. Fully developed regime in a vertical duct heated at constant temperature 197 6.4. Enclosure with vertical walls heated at constant temperature 198 6.5. Thermal insulation by a double-pane window 199 6.6. Natural convection in an enclosure filled with a heat generating fluid 201 6.7. One-dimensional mixed convection in a cavity 206 Chapter 7. Turbulent Convection in Internal Wall Flows 211 7.1. Introduction 211 7.2. Hydrodynamic stability and origin of the turbulence 211 7.3. Reynolds averaged Navier-Stokes equations 213 7.4. Wall turbulence scaling 215 7.5. Eddy viscosity-based one point closures 216 7.6. Some illustrations through direct numerical simulations 227 7.7. Empirical correlations 231 7.8. Exact relations for a fully developed turbulent channel flow 233 7.9. Mixing length closures and the temperature distribution in the inner and outer layers 243 7.10. Temperature distribution in the outer layer 252 7.11. Transport equations and reformulation of the logarithmic layer 255 7.12. Near-wall asymptotic behavior of the temperature and turbulent fluxes 261 7.13. Asymmetric heating of a turbulent channel flow 264 7.14. Natural convection in a vertical channel in turbulent regime 270 Chapter 8. Turbulent Convection in External Wall Flows 281 8.1. Introduction 281 8.2. Transition to turbulence in a flat plate boundary layer 281 8.3. Equations governing turbulent boundary layers 282 8.4. Scales in a turbulent boundary layer 284 8.5. Velocity and temperature distributions 284 8.6. Integral equations 285 8.7. Analogies 286 8.8. Temperature measurements in a turbulent boundary layer 289 8.9. Integral formulation of boundary layers over an isothermal flat plate with zero pressure gradient 292 8.10. Prandtl-Taylor analogy 297 8.11. Turbulent boundary layer with uniform suction at the wall 301 8.12. Turbulent boundary layers with pressure gradient. Turbulent Falkner-Skan flows 306 8.13. Internal sublayer in turbulent boundary layers subject to adverse pressure gradient 312 8.14. Roughness 319 Chapter 9. Turbulent Convection in Free Shear Flows 323 9.1. Introduction 323 9.2. General approach of free turbulent shear layers 323 9.3. Plumes 326 9.4. Two-dimensional turbulent jet 328 9.5. Mixing layer 335 9.6. Determination of the turbulent Prandtl number in a plane wake 340 9.7. Regulation of temperature 348 List of symbols 363 References 367 Index 371

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