This book demonstrates the analytical solution of fundamental problems in heat transfer which covers conduction, convection, and radiation heat transfer. The analytical solution of heat transfer problems is described in a simple way which is easy to understand. This book also provides competence of solving fundamental heat transfer problems by analytical method which is particularly important to gain a strong background on heat transfer.
The book is an interdisciplinary heat transfer book which is useful for all academicians and students from different disciplines with different levels of mathematical knowledge. The book can be used as a core or supplementary textbook in undergraduate and graduate bridge courses. Furthermore, it is suitable for professional and vocational coursework for technology and engineering professionals.
Author(s): Moghtada Mobedi, Gamze Gediz Ilis
Publisher: Springer
Year: 2023
Language: English
Pages: 208
City: Singapore
Preface I
Preface II
Contents
Nomenclature
Greek Letters
Subscripts
1 Mathematics for Heat Transfer
1.1 Importance of Mathematics in Heat Transfer
1.2 Vector and Scalar Quantities
1.3 Multiplication of Vectors
1.4 Definition of Derivative
1.5 Ordinary Differential Equations
1.6 Partial Differential Equations
1.7 Linear and Nonlinear Differential Equations
1.8 Coordinate Systems
1.9 Gradient Operator
1.10 Divergence Operator
1.11 Vector Form Expression of Governing Equations
1.12 Example
1.13 Review Questions
1.14 Problems
2 Basics of Heat Transfer
2.1 Introduction
2.2 Heat Transfer Classification
2.2.1 Newtonian and Non-Newtonian Fluids
2.2.2 Compressible and Incompressible Flow
2.2.3 Steady and Unsteady Heat Transfer
2.2.4 Laminar and Turbulent Flow
2.2.5 Internal and External Flows
2.2.6 One-, Two- and Three-Dimensional Heat Transfer
2.3 Thermodynamics Laws
2.3.1 First Law of Thermodynamics
2.3.2 Second Law of Thermodynamics
2.4 The Modes of Heat Transfer
2.4.1 Conduction Heat Transfer
2.4.2 Convection Heat Transfer
2.4.3 Radiation Heat Transfer
2.5 Important Laws in Heat and Fluid Flow
2.5.1 Newton's Second Law
2.5.2 Fourier's Law
2.5.3 Newton's Cooling Law
2.5.4 Stefan–Boltzmann Law
2.5.5 Newton's Viscous Law
2.6 Common Boundary Conditions in Heat Transfer
2.6.1 Boundary Conditions for Temperature
2.6.2 Boundary Conditions for Velocity
2.7 Dimensionless Numbers in Heat Transfer
2.8 More Terminologies in Heat Transfer
2.8.1 Thermophysical Properties
2.8.2 Flow with Viscous Heat Dissipation
2.8.3 Heat Transfer Rate and Heat Flux
2.8.4 Volumetric Flow Rate and Mass Flow Rate
2.8.5 Pressure Drop
2.8.6 Example
2.9 Review Questions
2.10 Problems
3 One-Dimensional Unsteady Heat Conduction in a Cartesian Coordinate System
3.1 Introduction
3.2 Problem Definition
3.3 Assumptions
3.4 Implementation of Assumptions
3.5 Analytical Solution
3.6 Example
3.7 Review Questions
3.8 Problems
4 Two-Dimensional Steady Heat Conduction in Cartesian Coordinate System
4.1 Introduction
4.2 Problem Definition
4.3 Assumptions
4.4 Implementation of Assumptions
4.5 Analytical Solution
4.6 Example
4.7 Review Questions
4.8 Problems
5 One-Dimensional Unsteady State Heat Conduction in a Cylindrical Coordinate System
5.1 Introduction
5.2 Bessel Function
5.3 Problem Definition
5.4 Assumptions
5.5 Implementation of Assumptions
5.6 Analytical Solution
5.7 Example
5.8 Review Questions
5.9 Problems
6 One-Dimensional Unsteady State Heat Conduction in a Spherical Coordinate System
6.1 Introduction
6.2 Problem Definition
6.3 Assumptions
6.4 Implementation of Assumptions
6.5 Analytical Solution
6.6 Example
6.7 Review Questions
6.8 Problems
7 Basics of Single Phase Convection Heat Transfer and Governing Equations
7.1 Introduction
7.2 Single and Multi-phase Convection Heat Transfer
7.3 Single Phase Forced, Natural, and Mixed Convection Heat Transfer
7.4 Governing Equations for Convection Heat Transfer
7.5 Difficulties in Solving Continuity, Momentum, and Energy Equations
7.6 Example
7.7 Review Questions
7.8 Problems
8 External Flow: Heat and Fluid Flow Over a Flat Plate
8.1 Introduction
8.2 Fluid Flow over a Flat Plate (Isothermal Flow)
8.2.1 Definition of the Problem
8.2.2 Assumptions
8.2.3 Similarity Solution
8.2.4 Solution of ODE
8.2.5 Boundary Layer Thickness
8.3 Heat and Fluid Flow over a Flat Plate
8.3.1 Definition of the Problem
8.3.2 Energy Equation and Assumptions
8.3.3 Simplification of the Energy Equation
8.3.4 Similarity Solution
8.3.5 Solution of ODE
8.3.6 Thermal Boundary Layer Thickness
8.4 Comparison of Velocity and Thermal Boundary Layer Thickness
8.5 Example
8.6 Review Questions
8.7 Problems
9 Internal Flow: Heat and Fluid Flow in a Channel
9.1 Introduction
9.2 Isothermal Flow in a Channel
9.2.1 Definition of the Problem
9.2.2 Entrance and Fully Developed Regions
9.2.3 Governing Equations and Implementation of Assumptions
9.2.4 Solution of ODE
9.3 Non-isothermal Flow in a Channel
9.3.1 Definition of the Problem
9.3.2 Thermally Entrance and Fully Developed Regions
9.3.3 Governing Equation and Implementation of Assumptions
9.3.4 Five Important Points
9.3.5 Reduction of PDE to ODE
9.3.6 Solution of ODE
9.3.7 Determination of the Nusselt Value
9.4 Example
9.5 Review Questions
9.6 Problems
10 Natural Convection Over a Vertical Flat Plate
10.1 Introduction
10.2 Considered Problem
10.3 Assumptions
10.4 Occurrence of Natural Convection
10.5 Governing Equations for Natural Convection Heat Transfer
10.5.1 State Equation for Density
10.5.2 Boussinesq Approximation
10.6 Boundary Layer Concept and Boundary Layer Equations
10.7 Boundary Layer Assumptions and Governing Equations
10.8 Similarity Solution
10.9 Solution of ODE Momentum and Energy Equations
10.10 Example
10.11 Review Questions
10.12 Problems
11 Radiation Heat Transfer
11.1 Introduction
11.2 Emission
11.3 Blackbody Emission
11.4 Real Surface Emission
11.5 Irradiation
11.6 Surface Radiative Properties
11.7 Opaque Surface, Gray Surface and Radiosity
11.8 View Factor
11.9 Radiation Heat Transfer Between Two Black Surfaces
11.10 Radiation Heat Transfer Between Two Gray Surfaces
11.11 Example
11.12 Review Questions
11.13 Problems
Appendix A Finding Roots of Bessel Functions
Appendix B Dimensionless Velocity Values in a Boundary Layer
Appendix C Compatibility Relation
Appendix References
