Preface ........................................................ xv
Acknowledgments .............................................. xvii
Author ........................................................ xix
1 Fundamental Concepts
1.1 Introduction .......................................... 1-1
1.2 Mechanisms of Heat Transfer ........................... 1-1
1.3 Dimensions and Units .................................. 1-3
1.4 Fourier's Law of Heat Conduction ...................... 1-5
1.5 Thermal Conductivity .................................. 1-8
1.6 Convection Heat Transfer ............................. 1-13
1.7 Convection Heat-Transfer Coefficient ................. 1-16
1.8 Radiation Heat Transfer .............................. 1-18
1.9 Emissivity and Other Radiative Properties ............ 1-20
1.10 Combined Heat-Transfer Mechanisms .................... 1-21
1.11 Summary .............................................. 1-23
1.12 Problems ............................................. 1-24
1.12.1 Introduction to Conduction .................... 1-24
1.12.2 Introduction to Convection .................... 1-26
1.12.3 Introduction to Radiation ..................... 1-27
1.12.4 Combined Mechanism Problems ................... 1-29
2 Steady-State Conduction in One Dimension
2.1 Introduction .......................................... 2-1
2.2 One-Dimensional Conduction Equation ................... 2-2
2.3 Plane Geometry Systems ................................ 2-5
2.3.1 Thermal Circuit ................................ 2-7
2.3.2 Materials in Series ........................... 2-10
2.3.3 Materials in Parallel ......................... 2-13
2.3.4 Plane Wall with Heat Generation ............... 2-16
2.3.5 Overall Heat-Transfer Coefficient ............. 2-18
2.4 Polar Cylindrical Geometry Systems ................... 2-21
2.4.1 Pipe and Tube Specifications .................. 2-24
2.4.2 Materials in Series ........................... 2-26
2.4.3 Cylinder with Heat Generation ................. 2-29
2.4.4 Overall Heat-Transfer Coefficient ............. 2-31
2.4.5 Critical Thickness of Insulation .............. 2-34
2.5 Spherical Geometry Systems ........................... 2-37
2.6 Thermal Contact Resistance ........................... 2-39
2.7 Heat Transfer from Extended Surfaces ................. 2-44
2.7.1 General Differential Equation for Extended
Surfaces ...................................... 2-45
2.7.2 Analysis of Pin Fin ........................... 2-48
2.7.3 Analysis of Straight Fin of Rectangular
Profile ....................................... 2-58
2.7.4 Straight Fins of Triangular and Parabolic
Profile ....................................... 2-61
2.7.5 Circular Fin of Rectangular Profile ........... 2-65
2.8 Summary .............................................. 2-70
2.9 Problems ............................................. 2-71
2.9.1 One-Dimensional Planar Conduction ............. 2-71
2.9.2 One-Dimensional Conduction in Polar
Coordinates ................................... 2-75
2.9.3 Internal Heat Generation ...................... 2-76
2.9.4 One-Dimensional Conduction in Spherical
Coordinates ................................... 2-77
2.9.5 Contact Resistance ............................ 2-77
2.9.6 Pin Fins ...................................... 2-79
2.9.7 Straight Fins ................................. 2-81
2.9.8 Circular Fins ................................. 2-84
3 Steady-State Conduction in Multiple Dimensions
3.1 Introduction .......................................... 3-1
3.2 General Conduction Equation ........................... 3-1
3.2.1 Cartesian Coordinates .......................... 3-1
3.3 Analytical Method of Solution ......................... 3-3
3.4 Graphical Method of Solution ......................... 3-10
3.5 Conduction Shape Factor .............................. 3-15
3.6 Solution by Numerical Methods (Finite
Differences) ......................................... 3-24
3.6.1 Normalization of Equations .................... 3-25
3.6.2 Numerical Method of Solution for One-
Dimensional Problems .......................... 3-26
3.7 Numerical Method of Solution for Two-Dimensional
Problems ............................................. 3-37
3.8 Methods of Solving Simultaneous Equations ............ 3-47
3.9 Summary .............................................. 3-52
3.10 Problems ............................................. 3-53
3.10.1 Analytical Methods ........................... 3-53
3.10.2 Field Plotting: Graphical Method ............. 3-54
3.10.3 Shape Factor Method: Charts .................. 3-58
3.10.4 Normalization/Transformation of Equations .... 3-61
3.10.5 Numerical Methods for One-Dimensional
Problems ..................................... 3-63
3.10.6 Numerical Methods for Two-Dimensional
Problems ..................................... 3-64
4 Unsteady-State Heat Conduction
4.1 Introduction .......................................... 4-1
4.2 Systems with Negligible Internal Resistance ........... 4-2
4.3 Systems with Finite Internal and Surface
Resistances ........................................... 4-8
4.4 Solutions to Multidimensional Geometry Systems ....... 4-26
4.5 Approximate Methods of Solution to Transient-
Conduction Problems .................................. 4-35
4.5.1 Numerical Methods ............................. 4-35
4.5.2 Graphical Method .............................. 4-46
4.6 Summary .............................................. 4-50
4.7 Problems ............................................. 4-50
4.7.1 Lumped Capacitance Method ..................... 4-50
4.7.2 Chart Solutions: Slabs, Cylinders, Spheres .... 4-51
4.7.3 Semi-Infinite Slabs ........................... 4-53
4.7.4 Multidimensional Problems ..................... 4-53
4.7.5 Numerical Methods ............................. 4-54
4.7.6 Graphical Methods ............................. 4-54
4.7.7 Project Problems .............................. 4-55
5 Introduction to Convection
5.1 Introduction .......................................... 5-1
5.2 Fluid Properties ...................................... 5-1
5.2.1 Absolute Viscosity ............................. 5-2
5.2.2 Pressure ....................................... 5-3
5.2.3 Density ........................................ 5-3
5.2.4 Kinematic Viscosity ............................ 5-4
5.2.5 Surface Tension ................................ 5-5
5.2.6 Internal Energy ................................ 5-5
5.2.7 Enthalpy ....................................... 5-5
5.2.8 Specific Heat .................................. 5-6
5.2.9 Compressibility Factor ......................... 5-7
5.2.10 Volumetric Thermal-Expansion Coefficient ....... 5-8
5.3 Characteristics of Fluid Flow ......................... 5-9
5.4 Equations of Fluid Mechanics ......................... 5-10
5.4.1 Continuity Equation ........................... 5-10
5.4.2 Momentum Equation (or Equation of Motion) ..... 5-11
5.5 Thermal-Energy Equation .............................. 5-17
5.6 Applications to Laminar Flows ........................ 5-20
5.7 Applications to Turbulent Flows ...................... 5-23
5.8 Natural-Convection Problem ........................... 5-24
5.9 Dimensional Analysis ................................. 5-28
5.9.1 Internal Flows ................................ 5-31
5.9.2 External Flows ................................ 5-32
5.9.3 Natural Convection ............................ 5-33
5.10 Summary .............................................. 5-34
5.11 Problems ............................................. 5-36
5.11.1 Fluid Properties .............................. 5-36
5.11.2 Momentum Equation ............................. 5-36
5.11.3 Thermal-Energy Equation ....................... 5-37
5.11.4 Dimensional Analysis .......................... 5-39
5.11.5 Miscellaneous Problems ........................ 5-40
6 Convection Heat Transfer in a Closed Conduit
6.1 Introduction .......................................... 6-1
6.2 Heat Transfer to and from Laminar Flow in Circular
Conduit ............................................... 6-1
6.2.1 Constant Heat Flux at Wall ..................... 6-3
6.2.2 Constant Wall Temperature ..................... 6-11
6.2.3 Thermal Entry Length .......................... 6-17
6.2.4 Combined-Entry-Length Problem for Laminar
Flow in Circular Duct ......................... 6-26
6.3 Heat Transfer to and from Turbulent Flow in
Circular Conduit ..................................... 6-31
6.3.1 Constant Heat Flux at Wall and Constant
Wall Temperature .............................. 6-32
6.4 Heat-Transfer Correlations for Flow in Noncircular
Ducts ................................................ 6-37
6.4.1 Concentric Annular Duct ....................... 6-38
6.4.2 Rectangular Cross Sections .................... 6-41
6.5 Summary .............................................. 6-43
6.6 Problems ............................................. 6-43
6.6.1 Entrance Length ............................... 6-43
6.6.2 Constant Wall Flux ............................ 6-45
6.6.3 Constant Wall Temperature ..................... 6-46
6.6.4 Empirical Correlations ........................ 6-48
6.5.1 Noncircular Cross Sections .................... 6-52
6.6.1 Derivations and Theoretical Problems .......... 6-53
7 Convection Heat Transfer in Flows Past Immersed Bodies
7.1 Introduction .......................................... 7-1
7.2 Boundary-Layer Flow ................................... 7-1
7.2.1 Laminar-Boundary-Layer Flow over Flat
Plate ......................................... 7-4
7.2.2 Constant Wall Temperature ..................... 7-10
7.2.3 Constant Wall Flux ............................ 7-17
7.2.4 General Relationship .......................... 7-21
7.2.5 Reynolds Analogy .............................. 7-21
7.3 Turbulent Flow over Flat Plate ....................... 7-23
7.3.1 Laminar and Turbulent Flow over Flat
Plate ......................................... 7-24
7.4 Flow Past Various Two-Dimensional Bodies ............. 7-31
7.5 Flow Past a Bank of Tubes ............................ 7-42
7.6 Flow Past a Sphere ................................... 7-49
7.7 Summary .............................................. 7-50
7.8 Problems ............................................. 7-52
7.8.1 Flow Past a Flat Plate ........................ 7-52
7.8.2 Reynolds-Colburn Analogy ...................... 7-53
7.8.3 Flow Past Two-Dimensional Bodies .............. 7-53
7.8.4 Flow Past a Tube Bank ......................... 7-55
7.8.5 Derivations ................................... 7-56
8 Natural-Convection Systems
8.1 Introduction .......................................... 8-1
8.2 Natural Convection on a Vertical Surface: Laminar
Flow .................................................. 8-2
8.3 Natural Convection on a Vertical Surface:
Transition and Turbulence ............................ 8-14
8.4 Natural Convection on an Inclined Flat Plate ......... 8-16
8.5 Natural Convection on a Horizontal Flat Surface ...... 8-19
8.6 Natural Convection on Cylinders ...................... 8-22
8.6.1 Vertical Cylinders ............................ 8-22
8.6.2 Horizontal Cylinders .......................... 8-23
8.6.3 Inclined Cylinders ............................ 8-25
8.7 Natural Convection around Spheres and Blocks ......... 8-25
8.8 Natural Convection about an Array of Fins ............ 8-28
8.9 Combined Forced- and Natural-Convection Systems ...... 8-31
8.10 Summary .............................................. 8-32
8.11 Problems ............................................. 8-32
8.11.1 Natural Convection: Vertical Plane
Surfaces ...................................... 8-32
8.11.2 Natural Convection: Inclined Surfaces ......... 8-35
8.11.3 Natural Convection: Horizontal Plane
Surfaces ...................................... 8-35
8.11.4 Natural Convection: Cylinders ................. 8-36
8.11.5 Natural Convection: Miscellaneous
Geometries and Problems ....................... 8-38
8.11.6 Natural Convection: Fins ...................... 8-39
8.11.7 Derivations ................................... 8-40
8.12 Project Problems ..................................... 8-43
9 Heat Exchangers
9.1 Introduction .......................................... 9-1
9.2 Double-Pipe Heat Exchangers ........................... 9-2
9.2.1 Circular Duct .................................. 9-9
9.2.2 Annular Duct .................................. 9-10
9.2.3 Fouling Factors ............................... 9-14
9.3 Shell-and-Tube Heat Exchangers ....................... 9-19
9.3.1 Shells ........................................ 9-20
9.3.2 Tubes ......................................... 9-20
9.3.3 Baffles ....................................... 9-23
9.3.4 Modifications ................................. 9-23
9.3.5 Tube Side ..................................... 9-25
9.3.6 Shell Side .................................... 9-27
9.3.7 True Temperature Difference ................... 9-29
9.4 Effectiveness-Number of Transfer Units Method of
Analysis ............................................. 9-36
9.4.1 Effectiveness-Number of Transfer Units
Equations ..................................... 9-38
9.5 Crossflow Heat Exchangers ............................ 9-42
9.6 Efficiency of a Heat Exchanger ....................... 9-50
9.7 Summary .............................................. 9-51
9.7.1 Double-Pipe Heat Exchangers Suggested Order
of Calculations ............................... 9-51
9.7.2 Shell-and-Tube Heat Exchangers Suggested
Order of Calculations ......................... 9-54
9.7.3 Crossflow Heat Exchangers Suggested Order
of Calculations ............................... 9-56
9.8 Problems ............................................. 9-58
9.8.1 Double-Pipe Heat Exchangers ................... 9-58
9.8.2 Shell-and-Tube Heat Exchangers ................ 9-61
9.8.3 Crossflow Heat Exchangers ..................... 9-63
9.8.4 Miscellaneous Problems and Equations .......... 9-65
10 Condensation and Vaporization Heat Transfer
10.1 Introduction ......................................... 10-1
10.2 Condensation Heat Transfer ........................... 10-1
10.2.1 Laminar Film Condensation on a Vertical
Flat Surface .................................. 10-2
10.2.2 Turbulent Film Condensation on Vertical
Flat Surface ................................. 10-10
10.2.3 Laminar Film Condensation on an Inclined
Flat Surface ................................. 10-10
10.2.4 Film Condensation on a Vertical Tube ......... 10-11
10.2.5 Film Condensation on a Horizontal Tube and
on a Horizontal Tube Bank .................... 10-12
10.2.6 Film Condensation within Horizontal Tubes .... 10-14
10.3 Boiling Heat Transfer ............................... 10-15
10.3.1 Nucleate Pool Boiling ........................ 10-19
10.3.2 Nucleate Pool Boiling Critical Heat Flux ..... 10-19
10.4 Summary ............................................. 10-23
10.5 Problems ............................................ 10-23
10.5.1 Filmwise Condensation-Flat Plates ............ 10-23
10.5.2 Condensation on Tubes ........................ 10-25
10.5.3 Boiling ...................................... 10-26
11 Introduction to Radiation Heat Transfer
11.1 Introduction ......................................... 11-1
11.2 Electromagnetic Radiation Spectrum ................... 11-2
11.3 Emission and Absorption at the Surface of an
Opaque Solid ......................................... 11-3
11.4 Radiation Intensity .................................. 11-5
11.5 Irradiation andRadiosity ............................. 11-9
11.6 Radiation Laws ...................................... 11-14
11.6.1 Kirchhoffs Law ............................... 11-14
11.6.2 Stefan-Boltzmann Law ......................... 11-15
11.6.3 Planck's Distribution Law .................... 11-18
11.6.4 Wien's Displacement Law ...................... 11-23
11.7 Characteristics of Real Surfaces .................... 11-24
11.7.1 Absorptivity and Reflectivity ................ 11-27
11.7.2 Transmissivity ............................... 11-28
11.8 Summary ............................................. 11-31
11.9 Problems ............................................ 11-31
11.9.1 Radiation Spectrum ........................... 11-31
11.9.2 Radiation Intensity .......................... 11-33
11.9.3 Radiation andRadiosity ....................... 11-35
11.9.4 Radiation Laws ............................... 11-35
11.9.5 Characteristics of Real Surfaces ............. 11-36
12 Radiation Heat Transfer between Surfaces
12.1 Introduction ......................................... 12-1
12.2 View Factor .......................................... 12-1
12.2.1 View Factor between Two Differential
Elements ...................................... 12-2
12.2.2 View Factor between Differential Element
and Finite Area ............................... 12-4
12.2.3 View Factors for Two Finite Areas ............. 12-6
12.3 Methods for Evaluating View Factors .................. 12-6
12.3.1 View-Factor Algebra for Pairs of Surfaces ..... 12-7
12.3.2 View-Factor Algebra for Enclosures ........... 12-15
12.3.3 Crossed-String Method ........................ 12-17
12.4 Radiation Heat Transfer within Enclosure of Black
Surfaces ............................................ 12-20
12.5 Radiation Heat Transfer within an Enclosure of
Diffuse-Gray Surfaces ............................... 12-24
12.5.1 Surface Heating and Surface Temperature ...... 12-26
12.5.2 Radiosity and Surface Temperature ............ 12-30
12.5.3 Electrical Analogy ........................... 12-31
12.6 Summary ............................................. 12-36
12.7 Problems ............................................ 12-37
12.7.1 View Factor and Heat Transfer Radiation ...... 12-37
12.7.2 Radiation in Enclosure of Black Surfaces ..... 12-41
12.7.3 Radiation in Enclosure of Diffuse-Gray
Surfaces ..................................... 12-42
12.8 Project Problems .................................... 12-45
Bibliography and Selected References .......................... B-l
Appendixes .................................................... A-l
A.l Prefixes .............................................. A-l
A.2 Conversion Factors Listed by Physical Quantity ........ A-l
A.3 Temperature Conversions ............................... A-3
A.4 Hyperbolic Functions .................................. A-3
A.5 Error Function or Probability Integral ................ A-6
A.6 Symbols and Units ..................................... A-8
B.l Thermal Properties of Selected Metallic Elements
at 293 К (20°C) or 528°R (65°F) ....................... A-9
B.2 Thermal Properties of Selected Alloys at 293 К
(20°C) or 528°R (65°F) ............................... A-10
B.3 Thermal Properties of Selected Building Materials
and Insulations at 293 К (20°C) or 528°R (65°F) ...... A-ll
C.l Properties of Saturated Liquids: Ammonia NH3 ......... A-13
C.2 Properties of Saturated Liquids: Carbon Dioxide
CO2 .................................................. A-14
C.3 Properties of Saturated Liquids:
Dichlorodifluoromethane (Freon-12) CC12F2 ............ A-15
C.4 Properties of Saturated Liquids: Engine Oil
(Unused) ............................................. A-16
C.5 Properties of Saturated Liquids: Ethylene Glycol
C2H4(OH2) ............................................ A-16
C.6 Properties of Saturated Liquids: Eutectic Calcium
Chloride Solution (29.9% CaCl2) ...................... A-17
C.7 Properties of Saturated Liquids: Glycerin
C3H5(OH)3 ............................................ A-17
C.8 Properties of Saturated Liquids: Mercury Hg .......... A-18
C.9 Properties of Saturated Liquids: Methyl Cloride
Ch3Cl ................................................ A-18
C.10 Properties of Saturated Liquids: Sulfur dioxide
SO2 .................................................. A-19
C.ll Properties of Saturated Liquids: Water H2O ........... A-20
D.l Properties of Gases at Atmospheric Pressure
(101.3 kPa = 14.7 psia): Air [Gas constant =
286.8 J/(kg · K) = 53.3 ft · lbf/lbm · °R; γ =
cp/cv = 1.4] ......................................... A-21
D.2 Properties of Gases at Atmospheric Pressure (101.3
kPa = 14.7 psia): Carbon Dioxide [Gas constant =
188.9 J/(kg · K) = 35.11 ft-lbf/lbm · °R; γ =
cp/cv = 1.30] ........................................ A-22
D.3 Properties of Gases at Atmospheric Pressure (101.3
kPa = 14.7 psia): Helium [Gas constant = 2 077
J/(kg · K) = 386 ft · lbf/lbm · °R; γ = cp/cv =
1.66] ................................................ A-22
D.4 Properties of Gases at Atmospheric Pressure
(101.3 kPa = 14.7 psia): Hydrogen [Gas constant =
4 126 J/(kg · K) = 767 ft ¦ lbf/lbm · °R; γ =
cp/cv = 1.405] ....................................... A-23
D.5 Properties of Gases at Atmospheric Pressure (101.3
kPa = 14.7 psia): Nitrogen [Gas constant = 296.8
J/(kg · K) = 55.16 ft · lbf/lbm · °R; γ = cp/cv =
1.40] ................................................ A-24
D.6 Properties of Gases at Atmospheric Pressure (101.3
kPa =14.7 psia): Oxygen [Gas constant = 260
J/(kg · K) = 48.3 ft · lbf/lbm · °R; γ = cp/cv =
1.40] ................................................ A-24
D.7 Properties of Gases at Atmospheric Pressure (101.3
kPa = 14.7 psia): Water Vapor or Steam [Gas
constant = 461.5 J/(kg · K) = 85.78 ft · lbf/lbm
· °R; γ = cp/cv = 1.33] .............................. A-25
E.l Normal Emissivity of Various Metals .................. A-26
E.2 Normal or Total (Hemispherical) Emissivity of
Various Nonmetallic Solids ........................... A-26
F.l Dimensions of Wrought-Steel and Wrought-Iron
Pipe ................................................ A-27
F.2 Dimensions of Seamless Copper Tubing ................ A-29
G.l The Greek Alphabet ................................... A-30
Answers to Selected Odd-Numbered Problems .................... A-31
Index ......................................................... 1-1
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