Convective Heat Transfer Solved Problems

Michel FAVRE-MARINET is a professor emeritus at Grenoble Institute of Technology, where he has taught courses in convective heat transfer during many years. His research activities were focused on turbulence, microfluidics and heat transfer. He published about eighty papers in journals or in international conferences.

Sedat TARDU is an associate professor at the University J. Fourier-Grenoble where he is teaching fluid dynamics, turbulence, heat transfer and dynamical systems. His main research areas include, wall turbulence in canonical and non-canonical flows, active and passive control of the turbulent drag and microfluidics. He published about two hundred papers in peer reviewed journals and international conferences.

Foreword 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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