Introduction to Convective Heat Transfer: A Software-Based Approach Using Maple and MATLAB

Cover
Title Page
Copyright
Contents
Preface
About the Author
About the Companion Website
Chapter 1 Foundations of Convective Heat Transfer
1.1 Fundamental Concepts
1.2 Coordinate Systems
1.3 The Continuum and Thermodynamic Equilibrium Concepts
1.4 Velocity and Acceleration
1.5 Description of a Fluid Motion: Eulerian and Lagrangian Coordinates and Substantial Derivative
1.5.1 Lagrangian Approach
1.5.2 Eulerian Approach
1.6 Substantial Derivative
1.7 Conduction Heat Transfer
1.8 Fluid Flow and Heat Transfer
1.9 External Flow
1.9.1 Velocity Boundary Layer and Newton's Viscosity Relation
1.9.2 Thermal Boundary Layer
1.10 Internal Flow
1.10.1 Mean Velocity
1.10.2 Mean Temperature
1.11 Thermal Radiation Heat Transfer
1.12 The Reynolds Transport Theorem: Time Rate of Change of an Extensive Property of a System Expressed in Terms of a Fixed Finite Control Volume
Problems
References
Chapter 2 Fundamental Equations of Laminar Convective Heat Transfer
2.1 Introduction
2.2 Integral Formulation
2.2.1 Conservation of Mass in Integral Form
2.2.2 Conservation of Linear Momentum in Integral Form
2.2.3 Conservation of Energy in Integral Form
2.3 Differential Formulation of Conservation Equations
2.3.1 Conservation of Mass in Differential Form
2.3.1.1 Cylindrical Coordinates
2.3.1.2 Spherical Coordinates
2.3.2 Conservation of Linear Momentum in Differential Form
2.3.2.1 Equation of Motion for a Newtonian Fluid with Constant Dynamic Viscosity μ and Density ρ
2.3.2.2 Cartesian Coordinates (x, y, z)
2.3.2.3 Cylindrical Coordinates (r, θ, z)
2.3.2.4 Spherical Coordinates (r, θ, ϕ)
2.3.3 Conservation of Energy in Differential Form
2.3.3.1 Mechanical Energy Equation
2.3.3.2 Thermal Energy Equation
2.3.3.3 Thermal Energy Equation in Terms of Internal Energy
2.3.3.4 Thermal Energy Equation in Terms of Enthalpy
2.3.3.5 Temperature T and Constant Volume Specific Heat cv
2.3.3.6 Temperature and Constant Pressure Specific Heat cp
2.3.3.7 Special Cases of the Differential Energy Equation
2.3.3.8 Perfect Gas and the Thermal Energy Equation Involving T and cp
2.3.3.9 Perfect Gas and the Thermal Energy Equation Involving T and cv
2.3.3.10 An Incompressible Pure Substance
2.3.3.11 Rectangular Coordinates
2.3.3.12 Cylindrical Coordinates (r, θ, z)
2.3.3.13 Spherical Coordinates (r, θ, ϕ)
Problems
References
Chapter 3 Equations of Incompressible External Laminar Boundary Layers
3.1 Introduction
3.2 Laminar Momentum Transfer
3.3 The Momentum Boundary Layer Concept
3.3.1 Scaling of Momentum Equation
3.4 The Thermal Boundary Layer Concept
3.4.1 Scaling of Energy Equation
3.5 Summary of Boundary Layer Equations of Steady Laminar Flow
Problems
References
Chapter 4 Integral Methods in Convective Heat Transfer
4.1 Introduction
4.2 Conservation of Mass
4.3 The Momentum Integral Equation
4.3.1 The Displacement Thickness δ1
4.3.2 Momentum Thickness δ2
4.4 Alternative Form of the Momentum Integral Equation
4.5 Momentum Integral Equation for Two‐Dimensional Flow
4.6 Energy Integral Equation
4.6.1 Enthalpy Thickness
4.6.2 Conduction Thickness
4.6.3 Convection Conductance or Heat Transfer Coefficient
4.7 Alternative Form of the Energy Integral Equation
4.8 Energy Integral Equation for Two‐Dimensional Flow
Problems
References
Chapter 5 Dimensional Analysis
5.1 Introduction
5.2 Dimensional Analysis
5.2.1 Dimensional Homogeneity
5.2.2 Buckingham π Theorem
5.2.3 Determination of π Terms
5.3 Nondimensionalization of Basic Differential Equations
5.4 Discussion
5.5 Dimensionless Numbers
5.5.1 Reynolds Number
5.5.2 Peclet Number
5.5.3 Prandtl Number
5.5.4 Nusselt Number
5.5.5 Stanton Number
5.5.6 Skin Friction Coefficient
5.5.7 Graetz Number
5.5.8 Eckert Number
5.5.9 Grashof Number
5.5.10 Rayleigh Number
5.5.11 Brinkman Number
5.6 Correlations of Experimental Data
Problems
References
Chapter 6 One‐Dimensional Solutions in Convective Heat Transfer
6.1 Introduction
6.2 Couette Flow
6.3 Poiseuille Flow
6.4 Rotating Flows
Problems
References
Chapter 7 Laminar External Boundary Layers: Momentum and Heat Transfer
7.1 Introduction
7.2 Velocity Boundary Layer over a Semi‐Infinite Flat Plate: Similarity Solution
7.3 Momentum Transfer over a Wedge (Falkner–Skan Wedge Flow): Similarity Solution
7.4 Application of Integral Methods to Momentum Transfer Problems
7.4.1 Laminar Forced Flow over a Flat Plate with Uniform Velocity
7.4.2 Two‐Dimensional Laminar Flow over a Surface with Pressure Gradient (Variable Free Stream Velocity)
7.4.2.1 The Correlation Method of Thwaites
7.4.2.2 A Thwaites Type Correlation for Axisymmetric Body
7.5 Viscous Incompressible Constant Property Parallel Flow over a Semi‐Infinite Flat Plate: Similarity Solution for Uniform Wall Temperature Boundary Condition
7.6 Low‐Prandtl‐Number Viscous Incompressible Constant Property Parallel Flow over a Semi‐Infinite Flat Plate: Similarity Solutions for Uniform Wall Temperature Boundary Condition
7.7 High‐Prandtl‐Number Viscous Incompressible Constant Property Parallel Flow over a Semi‐Infinite Flat Plate: Similarity Solutions for Uniform Wall Temperature Boundary Condition
7.8 Viscous Incompressible Constant Property Parallel Flow over a Semi‐Infinite Flat Plate: Similarity Solution for Uniform Heat Flux Boundary Condition
7.9 Viscous Incompressible Constant Property Parallel Flow over a Semi‐Infinite Flat Plate: Similarity Solutions for Variable Wall Temperature Boundary Condition
7.9.1 Superposition Principle
7.10 Viscous Incompressible Constant Property Flow over a Wedge (Falkner–Skan Wedge Flow): Similarity Solution for Uniform Wall Temperature Boundary Condition
7.11 Effect of Property Variation
7.12 Application of Integral Methods to Heat Transfer Problems
7.12.1 Viscous Flow with Constant Free Stream Velocity Along a Semi‐Infinite Plate Under Uniform Wall Temperature: With Unheated Starting Length or Adiabatic Segment
7.12.1.1 The Plate Without Unheated Starting Length
7.12.2 Viscous Flow with Constant Free Stream Velocity Along a Semi‐Infinite Plate with Uniform Wall Heat Flux: With Unheated Starting Length (Adiabatic Segment)
7.12.2.1 The Plate with No Unheated Starting Length
7.13 Superposition Principle
7.13.1 Superposition Principle Applied to Slug Flow over a Flat Plate: Arbitrary Variation in Wall Temperature
7.13.1.1 Boundary Condition: Single Step at x = 0
7.13.1.2 Boundary Condition: Two Steps at x = 0 and x = ξ1
7.13.1.3 Boundary Condition: Three Steps at x = 0, x = ξ1, and x = ξ2
7.13.2 Superposition Principle Applied to Slug Flow over a Flat Plate: Arbitrary Variation in Wall Heat Flux
7.13.2.1 Boundary Condition: Single Step at x = 0
7.13.2.2 Boundary Condition: Two Steps at x = 0 and x = ξ1
7.13.2.3 Boundary Condition: Triple Steps at x = 0, x = ξ1, and x = ξ2
7.13.3 Superposition Principle Applied to Viscous Flow over a Flat Plate: Stepwise Variation in Wall Temperature
7.13.3.1 First Problem
7.13.3.2 Second Problem
7.13.3.3 Heat Flux for 0 < x < ξ
7.13.3.4 The Heat Flux for x > ξ1
7.13.4 Superposition Principle Applied to Viscus Flow over a Flat Plate: Stepwise Variation in Surface Heat Flux
7.13.4.1 First Problem
7.13.4.2 Second Problem
7.14 Viscous Flow over a Flat Plate with Arbitrary Surface Temperature Distribution
7.15 Viscous Flow over a Flat Plate with Arbitrarily Specified Heat Flux
7.16 One‐Parameter Integral Method for Incompressible Two‐Dimensional Laminar Flow Heat Transfer: Variable U∞(x) and Constant Tw − T∞ = const
7.17 One‐Parameter Integral Method for Incompressible Laminar Flow Heat Transfer over a Constant Temperature of a Body of Revolution
Problems
References
Chapter 8 Laminar Momentum and Heat Transfer in Channels
8.1 Introduction
8.2 Momentum Transfer
8.2.1 Hydrodynamic Considerations in Ducts
8.2.2 Fully Developed Laminar Flow in Circular Tube
8.2.3 Fully Developed Flow Between Two Infinite Parallel Plates
8.3 Thermal Considerations in Ducts
8.4 Heat Transfer in the Entrance Region of Ducts
8.4.1 Circular Pipe: Slug Flow Heat Transfer in the Entrance Region
8.4.1.1 Heat Transfer for Low‐Prandtl‐Number Fluid Flow (Slug Flow) in the Entrance Region of Circular Tube Subjected to Constant Wall Temperature
8.4.1.2 Heat Transfer to Low‐Prandtl‐Number Fluid Flow (Slug Flow) in the Entrance Region of the Circular Tube Subjected to Constant Heat Flux
8.4.1.3 Empirical and Theoretical Correlations for Viscous Flow Heat Transfer in the Entrance Region of the Circular Tube
8.4.2 Parallel Plates: Slug Flow Heat Transfer in the Entrance Region
8.4.2.1 Heat Transfer to a Low‐Prandtl‐Number Fluid (Slug Flow) in the Entrance Region of Parallel Plates: Both Plates Are Subjected to Constant Wall Temperatures
8.4.2.2 Heat Transfer for Low‐Prandtl‐Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Both Plates Are Subjected to UHF
8.4.2.3 Heat Transfer for Low‐Prandtl‐Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Upper Plate Is Insulated While the Lower Plate Is Subjected to Constant Wall Temperature
8.4.2.4 Heat Transfer for Low‐Prandtl‐Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Upper Plate Is Insulated While the Lower Plate Is Subjected to Constant Heat Flux
8.4.2.5 Empirical and Theoretical Correlations for Viscous Flow Heat Transfer in the Entrance Region of Parallel Plates
8.5 Fully Developed Heat Transfer
8.5.1 Circular Tube
8.5.1.1 HFD and TFD Laminar Forced Convection Heat Transfer for Slug Flow in a Circular Pipe Subjected to Constant Wall Heat Flux
8.5.1.2 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow in a Circular Tube Subjected to Constant Wall Heat Flux
8.5.1.3 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow in a Circular Tube Subjected to Constant Wall Temperature
8.5.2 Infinite Parallel Plates
8.5.2.1 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow Between a Parallel Plate Channel. Both Plates Are Subjected to Constant Wall Heat Flux Boundary Condition
8.6 Heat Transfer in the Thermal Entrance Region
8.6.1 Circular Tube
8.6.1.1 Graetz Problem: HFD and Thermally Developing Flow in a Circular Tube under Constant Wall Temperature Boundary Condition
8.6.1.2 The Leveque Solution: UWT Boundary Condition
8.6.1.3 Graetz Problem: HFD and Thermally Developing Flow for Viscous Flow in Circular Tube Under Uniform Wall Heat Flux Boundary Condition
8.6.1.4 Empirical and Theoretical Correlations for Viscous Flow in the Thermal Entrance Region of the Pipe
8.6.2 Two Infinite Parallel Plates
8.6.2.1 Graetz Problem: HFD and Thermally Developing Flow Between Parallel Plates Subjected to Constant Wall Temperature
8.6.2.2 Graetz Problem: HFD and Thermally Developing Flow Between Parallel Plates Subjected to Constant Wall Heat Flux
8.6.2.3 Empirical and Theoretical Correlations for Viscous Flow in Thermal Entrance Region of Parallel Plates
8.7 Circular Pipe with Variable Surface Temperature Distribution in the Axial Direction
8.8 Circular Pipe with Variable Surface Heat Flux Distribution in the Axial Direction
8.9 Short Tubes
8.10 Effect of Property Variation
8.11 Regular Sturm‐Liouville Systems
Problems
References
Chapter 9 Foundations of Turbulent Flow
9.1 Introduction
9.2 The Reynolds Experiment
9.3 Nature of Turbulence
9.4 Time Averaging and Fluctuations
9.5 Isotropic Homogeneous Turbulence
9.6 Reynolds Averaging
9.7 Governing Equations of Incompressible Steady Mean Turbulent Flow
9.8 Turbulent Momentum Boundary Layer Equation
9.9 Turbulent Energy Equation
9.10 Turbulent Boundary Layer Energy Equation
9.11 Closure Problem of Turbulence
9.12 Eddy Diffusivity of Momentum
9.13 Eddy Diffusivity of Heat
9.14 Transport Equations in the Cylindrical Coordinate System
9.15 Experimental Work on the Turbulent Mean Flow
9.15.1 Turbulent Flow in Pipe: Velocity Profiles
9.15.2 Turbulent Flow over a Flat Plate: Velocity Profiles
9.16 Transition to Turbulent Flow
Problems
References
Chapter 10 Turbulent External Boundary Layers: Momentum and Heat Transfer
10.1 Introduction
10.2 Turbulent Momentum Boundary Layer
10.3 Turbulence Models
10.3.1 Zero‐Equation Models
10.3.1.1 Boussinesq Model
10.3.1.2 Prandtl's Mixing‐Length Model
10.3.1.3 Van Driest Model
10.4 Turbulent Flow over a Flat Plate with Constant Free‐Stream Velocity: Couette Flow Approximation
10.4.1 Inner Region
10.5 The Universal Velocity Profile
10.5.1 Three‐Layer (von Karman) Model for the Velocity Profile
10.5.2 Other Velocity Models
10.6 Approximate Solution by the Integral Method for the Turbulent Momentum Boundary Layer over a Flat Plate
10.7 Laminar and Turbulent Boundary Layer
10.8 Other Eddy Diffusivity Momentum Models
10.9 Turbulent Heat Transfer
10.10 Analogy Between Momentum and Heat Transfer
10.10.1 Reynold's Analogy
10.10.2 Chilton–Colburn Analogy
10.10.3 Prandtl–Taylor Analogy
10.10.4 Von Karman Analogy
10.11 Some Other Correlations for Turbulent Flow over a Flat Plate
10.12 Turbulent Flow Along a Semi‐infinite Plate with Unheated Starting Length: Constant Temperature Solution
10.13 Flat Plate with Arbitrarily Specified Surface Temperature
10.14 Constant Free‐Stream Velocity Flow Along a Flat Plate with Uniform Heat Flux
10.15 Turbulent Flow Along a Semi‐Infinite Plate with Arbitrary Heat Flux Distribution
10.16 Turbulent Transition and Overall Heat Transfer
10.17 Property Variation
Problems
References
Chapter 11 Turbulent Internal Flow: Momentum and Heat Transfer
11.1 Introduction
11.2 Momentum Transfer
11.2.1 Momentum Transfer in Infinite Two Parallel Plates
11.2.1.1 The Entrance Region
11.2.1.2 The HFD Region
11.2.1.3 Prandtl's Mixing‐Length Model
11.2.1.4 Buffer Region
11.2.1.5 The Mean Velocity
11.2.1.6 Skin Friction Coefficient or Fanning Friction Factor cf
11.2.2 Momentum Transfer in Circular Pipe Flow
11.2.2.1 Entrance Region
11.2.2.2 The HFD Region
11.2.2.3 Average Velocity V
11.2.2.4 Skin Friction Factor cf
11.2.2.5 Moody Friction Factor f
11.2.2.6 Prandtl Mixing‐Length Model
11.2.2.7 Laminar Sublayer
11.2.2.8 Buffer Region
11.2.2.9 Turbulent Region
11.2.2.10 Moody Friction Factor
11.2.2.11 Fanning Friction Factor
11.2.2.12 The Power Law Velocity Distribution
11.3 Fully Developed Turbulent Heat Transfer
11.3.1 TFD and HFD Turbulent Flow Between Parallel Plates Subjected to UHF
11.3.1.1 Mean Stream Temperature
11.3.2 TFD and HFD Turbulent Flow in a Pipe Subjected to UHF
11.3.2.1 Laminar Viscous Sublayer: 0 < y+ < 5
11.3.2.2 Buffer Layer: 5 < y+ < 30
11.3.2.3 Turbulent Region: y+ > 30
11.4 HFD Thermally Developing Turbulent Heat Transfer
11.4.1 Circular Duct with UWT
11.4.2 Circular Duct with Uniform Wall Heat Flux
11.4.2.1 Solution for Fully Developed Temperature Distribution θ1
11.4.2.2 Solution for the Entry Region Temperature Distribution θ2
11.5 Analogies for Internal Flow
11.5.1 Reynolds Analogy
11.5.2 Colburn Analogy
11.5.3 Prandtl–Taylor Analogy
11.5.3.1 Laminar Sublayer
11.5.3.2 Turbulent Core
11.5.4 von Karman Analogy
11.5.4.1 Laminar Sublayer: 0 ≤ y+ ≪ 5
11.5.4.2 Buffer Layer: 5 ≤ y+ ≪ 30
11.5.4.3 Turbulent Core: y+ ≥ 30
11.5.5 The Analogy of Kadar and Yaglom
11.5.6 The Analogy of Yu et al.
11.5.7 Martinelli Analogy
11.6 Combined Entrance Region
11.7 Empirical and Theoretical Correlations for Turbulent Flow in Channels
11.8 Heat Transfer in Transitional Flow
11.8.1 Friction Factor in the Transitional Flow
11.8.2 Heat Transfer in the Transition Region
11.8.2.1 Tam and Ghajar Approach
11.8.2.2 Churchill Approach
11.8.2.3 Gnielinski Approach
11.8.2 UWT Boundary Condition
11.8.2 UHF Boundary Condition
11.8.2.4 Abraham et al. Approach
11.8.2 UHF Boundary Condition
11.8.2 UWT Boundary Condition
11.9 Effect of Property Variation
Problems
References
Chapter 12 Free Convection Heat Transfer
12.1 Introduction
12.2 Fundamental Equations and Dimensionless Parameters of Free Convection
12.3 Scaling in Natural Convection
12.4 Similarity Solution for Laminar Boundary Layer over a Semi‐Infinite Vertical Flat Plate
12.4.1 Constant Wall Temperature
12.4.2 Uniform Heat Flux
12.5 Integral Method (von Karman–Pohlhausen Method): An Approximate Analysis of Laminar Free Convection on a Vertical Plate
12.5.1 Constant Wall Temperature
12.5.2 Uniform Heat Flux
12.6 Turbulent Free Convection Heat Transfer on a Vertical Plate
12.7 Empirical Correlations for Free Convection
12.7.1 Vertical Plate
12.7.2 Horizontal Plate
12.7.3 Inclined Plates
12.7.4 Vertical Cylinders
12.7.5 Horizontal Cylinder
12.7.6 Inclined Cylinder
12.7.7 Free Convection from Vertical Cylinders of Small Diameter
12.8 Free Convection Within Parallel Plate Channels
12.8.1 Vertical Parallel Plate Channel
12.8.2 Horizontal Parallel Plate Channel
12.8.3 Inclined Parallel Plate Channel
12.9 Rectangular Enclosures
12.9.1 Horizontal Rectangular Enclosure (θ = 0)
12.9.2 Vertical Rectangular Enclosure
12.9.3 Inclined Rectangular Enclosure
12.10 Horizontal Concentric Cylinders
12.11 Concentric Spheres
12.12 Spheres
Problems
References
Index
EULA