Table Of ContentEnergy Transfers by Convection
Energy Engineering Set
coordinated by
Abdelhanine Benallou
Volume 3
Energy Transfers by
Convection
Abdelhanine Benallou
First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1. Methods for Determining Convection
Heat Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Characterizing the motion of a fluid . . . . . . . . . . . . . . . . . . . . . 1
1.3. Transfer coefficients and flow regimes . . . . . . . . . . . . . . . . . . . 3
1.4. Using dimensional analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4.1. Dimensionless numbers used in convection . . . . . . . . . . . . . . 4
1.4.2. Dimensional analysis applications in convection . . . . . . . . . . . 7
1.5. Using correlations to calculate h . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.1. Correlations for flows in forced convection . . . . . . . . . . . . . . 14
1.5.2. Correlations for flows in natural convection . . . . . . . . . . . . . . 14
Chapter 2. Forced Convection inside Cylindrical Pipes . . . . . . . . . 15
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2. Correlations in laminar flow . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1. Reminders regarding laminar-flow characteristics inside a pipe . . 16
2.2.2. Differential energy balance . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3. Illustration: transportation of phosphate slurry
in a cylindrical pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.4. Correlations for laminar flow at pipe entrance . . . . . . . . . . . . . 25
2.3. Correlations in transition zone . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4. Correlations in turbulent flow . . . . . . . . . . . . . . . . . . . . . . . . . 30
vi Energy Transfers by Convection
2.4.1. Dittus–Boelter–McAdams relation. . . . . . . . . . . . . . . . . . . . 31
2.4.2. Colburn–Seider–Tate relation . . . . . . . . . . . . . . . . . . . . . . 32
2.4.3. Illustration: improving transfer by switching to turbulent flow . . . 33
2.4.4. Specific correlations in turbulent flow . . . . . . . . . . . . . . . . . 34
2.4.5. Illustration: industrial-grade cylindrical pipe . . . . . . . . . . . . . . 38
2.5. Dimensional correlations for air and water . . . . . . . . . . . . . . . . . 39
Chapter 3. Forced Convection inside Non-cylindrical Pipes . . . . . 43
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2. Concept of hydraulic diameter. . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3. Hydraulic Nusselt and Reynolds numbers . . . . . . . . . . . . . . . . . . 45
3.4. Correlations in established laminar flow . . . . . . . . . . . . . . . . . . . 45
3.4.1. Pipes with rectangular or square cross-sections in laminar flow . . 45
3.4.2. Pipes presenting an elliptical cross-section in laminar flow . . . . . 46
3.4.3. Pipes presenting a triangular cross-section in laminar flow . . . . . 47
3.4.4. Illustration: air-conditioning duct design . . . . . . . . . . . . . . . . 48
3.4.5. Annular pipes with laminar flow . . . . . . . . . . . . . . . . . . . . . 51
3.5. Correlations in turbulent flow for non-cylindrical pipes . . . . . . . . . 57
3.5.1. Pipes with rectangular or square cross-sections in turbulent flow . 57
3.5.2. Pipes with elliptical or triangular cross-sections in turbulent flow . 58
3.5.3. Illustration: design imposes the flow regime . . . . . . . . . . . . . . 60
3.5.4. Annular pipes in turbulent flow . . . . . . . . . . . . . . . . . . . . . 62
Chapter 4. Forced Convection outside Pipes or around Objects . . 69
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2. Flow outside a cylindrical pipe . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3. Correlations for the stagnation region . . . . . . . . . . . . . . . . . . . . 71
4.4. Correlations beyond the stagnation zone . . . . . . . . . . . . . . . . . . . 72
4.5. Forced convection outside non-cylindrical pipes . . . . . . . . . . . . . . 72
4.5.1. Pipes with a square cross-section area . . . . . . . . . . . . . . . . . . 72
4.5.2. Pipes presenting an elliptical cross-section area . . . . . . . . . . . . 74
4.5.3. Pipes presenting a hexagonal cross-section area . . . . . . . . . . . . 74
4.6. Forced convection above a horizontal plate . . . . . . . . . . . . . . . . . 76
4.6.1. Plate at constant temperature . . . . . . . . . . . . . . . . . . . . . . . 76
4.6.2. Plate with constant flow density . . . . . . . . . . . . . . . . . . . . . 77
4.7. Forced convection around non-cylindrical objects . . . . . . . . . . . . . 79
4.7.1. Forced convection around a plane parallel to the flow . . . . . . . . 79
4.7.2. Forced convection around a sphere . . . . . . . . . . . . . . . . . . . 80
4.8. Convective transfers between falling films and pipes . . . . . . . . . . . 80
4.8.1. Vertical tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.8.2. Horizontal tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Contents vii
4.9. Forced convection in coiled pipes . . . . . . . . . . . . . . . . . . . . . . . 83
4.9.1. Convection heat transfer coefficient inside the coil . . . . . . . . . . 84
4.9.2. Convection heat transfer coefficient with the
outer wall of the coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.9.3. Convection heat transfer coefficient between
the fluid and the tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Chapter 5. Natural Convection Heat Transfer . . . . . . . . . . . . . . . . 89
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2. Characterizing the motion of natural convection . . . . . . . . . . . . . . 89
5.3. Correlations in natural convection . . . . . . . . . . . . . . . . . . . . . . 91
5.4. Vertical plates subject to natural convection . . . . . . . . . . . . . . . . 92
5.5. Inclined plates subject to natural convection . . . . . . . . . . . . . . . . 94
5.6. Horizontal plates subject to natural convection . . . . . . . . . . . . . . . 95
5.6.1. Case of underfloor heating . . . . . . . . . . . . . . . . . . . . . . . . 95
5.6.2. Ceiling cooling systems . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.7. Vertical cylinders subject to natural convection . . . . . . . . . . . . . . 97
5.8. Horizontal cylinders subject to natural convection . . . . . . . . . . . . . 98
5.9. Spheres subject to natural convection . . . . . . . . . . . . . . . . . . . . 99
5.10. Vertical conical surfaces subject to natural convection . . . . . . . . . 100
5.11. Any surface subject to natural convection . . . . . . . . . . . . . . . . . 101
5.12. Chambers limited by parallel surfaces . . . . . . . . . . . . . . . . . . . 101
5.12.1. Correlation of Hollands et al. for horizontal chambers . . . . . . . 103
5.12.2. Correlation of El-Sherbiny et al. for vertical chambers . . . . . . . 104
5.13. Inclined-plane chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.13.1. For large aspect ratios and low-to-moderate inclinations . . . . . . 105
5.13.2. For lower aspect ratios and inclinations
below the critical inclination . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.13.3. For lower aspect ratios and inclinations
greater than the critical inclination . . . . . . . . . . . . . . . . . . . . . . . 106
5.14. Chambers limited by two concentric cylinders . . . . . . . . . . . . . . 107
5.15. Chambers limited by two concentric spheres . . . . . . . . . . . . . . . 109
5.16. Simplified correlations for natural convection in air . . . . . . . . . . . 111
5.16.1. Vertical cylinder or plane under natural convection in air . . . . . 111
5.16.2. Horizontal cylinder or plane under natural convection in air. . . . 111
5.16.3. Horizontal plane under natural convection in air . . . . . . . . . . . 112
5.16.4. Sphere under natural convection in air . . . . . . . . . . . . . . . . . 112
5.16.5. Circuit boards under natural convection in air . . . . . . . . . . . . 112
5.16.6. Electronic components or cables under natural convection in air . 113
viii Energy Transfers by Convection
5.17. Finned surfaces: heat sinks in electronic systems . . . . . . . . . . . . . 113
5.17.1. Dissipation systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.17.2. Thermal resistance of a heat sink . . . . . . . . . . . . . . . . . . . . 115
5.18. Optimizing the thermal resistance of a heat sink . . . . . . . . . . . . . 117
5.18.1. Determining the heat-sink/air heat transfer coefficient . . . . . . . 119
5.18.2. Calculating the optimum spacing between fins . . . . . . . . . . . . 120
5.18.3. Practical expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.18.4. Calculating the evacuated heat flux . . . . . . . . . . . . . . . . . . 120
5.18.5. Implementation algorithm . . . . . . . . . . . . . . . . . . . . . . . . 120
5.18.6. Illustration: optimum design of a heat sink . . . . . . . . . . . . . . 122
5.19. Optimum circuit-board assembly . . . . . . . . . . . . . . . . . . . . . . 125
5.19.1. Calculating the optimum spacing between electronic boards . . . 126
5.19.2. Heat transfer coefficient between electronic boards and air . . . . 126
5.19.3. Calculating the evacuated heat flux . . . . . . . . . . . . . . . . . . 127
5.19.4. Implementation algorithm . . . . . . . . . . . . . . . . . . . . . . . . 127
5.19.5. Illustration: optimum evacuation of heat
generated by electronic boards . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.20. Superimposed forced and natural convections . . . . . . . . . . . . . . 130
5.20.1. Vertical-tube scenario: Martinelli-Boelter correlation . . . . . . . 131
5.20.2. Horizontal-tube scenario: Proctor-Eubank correlation . . . . . . . 132
5.20.3. Cylinders, disks or spheres in rotation . . . . . . . . . . . . . . . . . 133
Chapter 6. Convection in Nanofluids,
Liquid Metals and Molten Salts . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2. Transfers in nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.1. Physical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.2.2. Nanofluids circulating in tubes . . . . . . . . . . . . . . . . . . . . . . 142
6.2.3. Nanofluids circulating within annular pipes . . . . . . . . . . . . . . 144
6.2.4. Superposition of natural and forced convections in nanofluids . . . 145
6.3. Transfers in liquid metals . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3.1. Physical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3.2. Liquid metals in forced convection within cylindrical pipes . . . . 147
6.3.3. Liquid metals in forced convection within an annular space . . . . 147
6.3.4. Liquid metals flowing along a horizontal plane . . . . . . . . . . . . 149
6.3.5. Liquid metals in forced convection between two parallel planes . . 149
6.3.6. Liquid metals subject to natural convection . . . . . . . . . . . . . . 149
6.4. Transfers in molten salts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.4.1. Physical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.4.2. Molten salts under forced convection in laminar flow
within cylindrical pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Contents ix
6.4.3. Molten salts under forced convection in the transition zone
within cylindrical pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.4.4. Molten salts under forced convection in turbulent flow
within cylindrical pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.5. Reading: Eugène Péclet and Lord Rayleigh . . . . . . . . . . . . . . . . . 154
6.5.1. Eugène Péclet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.5.2. Lord Rayleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Chapter 7. Exercises and Solutions . . . . . . . . . . . . . . . . . . . . . . 157
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Appendix 1. Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Appendix 2. Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Preface
“The secret of change is to focus all
your energy not on fighting the
old, but on building the new.”
Dan Millman (1946–), artist, author,
record-holder and sportsman
For several years, I have cherished the wish of devoting enough time to the
writing of a series of books on energy engineering. The reason is simple: for having
practiced for years teaching as well as consulting in different areas ranging from
energy planning to rational use of energy and renewable energies, I have always
noted the lack of formal documentation in these fields to constitute a complete and
coherent source of reference, both as a tool for teaching to be used by engineering
professors and as a source of information summarizing, for engineering students and
practicing engineers, the basic principles and the founding mechanisms of energy
and mass transfers leading to calculation methods and design techniques.
But between the teaching and research tasks (first as a teaching assistant at the
University of California and later as a professor at the École des mines de Rabat,
Morocco) and the consulting and management endeavors conducted in the private
and in the public sectors, this wish remained for more than twenty years in my long
list of priorities, without having the possibility to make its way up to the top. Only
providence was able to unleash the constraints and provide enough time to achieve a
lifetime objective.
This led to a series consisting of nine volumes:
– Volume 1: Energy and Mass Transfers;
xii Energy Transfers by Convection
– Volume 2: Energy Transfers by Conduction;
– Volume 3: Energy Transfers by Convection;
– Volume 4: Energy Transfers by Radiation;
– Volume 5: Mass Transfers and Physical Data Estimation;
– Volume 6: Design and Calculation of Heat Exchangers;
– Volume 7: Solar Thermal Engineering;
– Volume 8: Solar Photovoltaic Energy Engineering;
– Volume 9: Rational Energy Use Engineering.
The present book is the third volume of this series. It concerns the study of
convection heat transfer.
As we will see, the calculation methods established in this book present multiple
applications in engineering: heat exchanger calculation, demand-side energy,
improvement of heat dissipation in electronic circuits, etc.
A series of exercises is presented at the end of the book, aimed at enabling
students to implement new concepts as rapidly as possible. These exercises are
designed to correspond as closely as possible to real-life situations occurring in
industrial practice or everyday life.
Abdelhanine BENALLOU
October 2018
