John Wiley & Sons Ltd, 2004. 341 р.
1 Introduction
Importance of Heat Transfer
Heat TransferModes
The Laws of Heat Transfer
Formulation of Heat Transfer Problems
Heat transfer from a plate exposed to solar heat flux
Incandescent lamp
Systems with a relative motion and inteal heat generation
Heat Conduction Equation
Boundary and Initial Conditions
Solution Methodology
Summary
Exercise
2 Some Basic Discrete Systems
Introduction
Steady State Problems
Heat flow in a composite slab
Fluid flow network
Heat transfer in heat sinks (combined conduction–convection)
Analysis of a heat exchanger
Transient Heat Transfer Problem (Propagation Problem)
The Finite Element Method
Introduction
Elements and Shape Functions
One-dimensional linear element
One-dimensional quadratic element
Two-dimensional linear triangular elements
Area coordinates
Quadratic triangular elements
Two-dimensional quadrilateral elements
Isoparametric elements
Three-dimensional elements
Formulation (Element Characteristics)
Ritz method (Heat balance integral method—Goodman’s method)
The method of weighted residuals
Galerkin finite element method
Formulation for the Heat Conduction Equation
Variational approach
The Galerkin method
Requirements for Interpolation Functions
4 Steady State Heat Conduction in One Dimension
Introduction
PlaneWalls
Homogeneous wall
Composite wall
Finite element discretization
Wall with varying cross-sectional area
Plane wall with a heat source: solution by linear elements
Plane wall with a heat source: solution by quadratic elements
Plane wall with a heat source: solution by modified quadratic equations (static condensation)
Radial Heat Flow in a Cylinder
Cylinder with heat source
Conduction–Convection Systems
5 Steady State Heat Conduction in Multi-dimensions
Introduction
Two-dimensional Plane Problems
Triangular elements
Rectangular Elements
Plate with Variable Thickness
Three-dimensional Problems
Axisymmetric Problems
Galerkin’s method for linear triangular axisymmetric elements
6 Transient Heat Conduction Analysis
Introduction
Lumped Heat Capacity System
Numerical Solution
Transient goveing equations and boundary and initial conditions .
The Galerkin method
One-dimensional Transient State Problem
Time discretization using the Finite Difference Method (FDM)
Time discretization using the Finite Element Method (FEM)
Stability
Multi-dimensional Transient Heat Conduction
Phase Change Problems—Solidification and Melting
The goveing equations
Enthalpy formulation
Inverse Heat Conduction Problems
One-dimensional heat conduction
7 Convection Heat Transfer
Introduction
Types of fluid-motion-assisted heat transport
Navier–Stokes Equations
Conservation of mass or continuity equation
Conservation of momentum
Energy equation
Non-dimensional Form of the Goveing Equations
Forced convection
Natural convection (Buoyancy-driven convection)
Mixed convection
The Transient Convection–diffusion Problem
Finite element solution to convection–diffusion equation
Extension to multi-dimensions
Stability Conditions
Characteristic-based Split (CBS) Scheme
Spatial discretization
Time-step calculation
Boundary and initial conditions
Steady and transient solution methods
Artificial Compressibility Scheme
Nusselt Number, Drag and Stream Function
Nusselt number
Drag calculation
Stream function
Mesh Convergence
Laminar Isothermal Flow
Geometry, boundary and initial conditions
Solution
Laminar Non-isothermal Flow
Forced convection heat transfer
Buoyancy-driven convection heat transfer
Mixed convection heat transfer
Introduction to Turbulent Flow
Solution procedure and result
Extension to Axisymmetric Problems
8 Convection in Porous Media 240
Introduction
Generalized Porous Medium Flow Approach
Non-dimensional scales
Limiting cases
Discretization Procedure
Temporal discretization
Spatial discretization
Semi- and quasi-implicit forms
Non-isothermal Flows
Forced Convection
Natural Convection
Constant porosity medium
9 Some Examples of Fluid Flow and Heat Transfer Problems
Introduction
Isothermal Flow Problems
Steady state problems
Transient flow
Non-isothermal Benchmark Flow Problem
Backward-facing step
Thermal Conduction in an Electronic Package
Forced Convection Heat Transfer From Heat Sources
10 Implementation of Computer Code
Introduction
Preprocessing
Mesh generation
Linear triangular element data
Element size calculation
Shape functions and their derivatives
Boundary normal calculation
Mass matrix and mass lumping
Implicit pressure or heat conduction matrix
Main Unit
Time-step calculation
Element loop and assembly
Updating solution
Boundary conditions
Monitoring steady state
Postprocessing
Interpolation of data
A Green’s Lemma
B Integration Formulae
B.1 Linear Triangles
B.2 Linear Tetrahedron
C Finite Element Assembly Procedure
D Simplified Form of the Navier–Stokes Equations
Index
1 Introduction
Importance of Heat Transfer
Heat TransferModes
The Laws of Heat Transfer
Formulation of Heat Transfer Problems
Heat transfer from a plate exposed to solar heat flux
Incandescent lamp
Systems with a relative motion and inteal heat generation
Heat Conduction Equation
Boundary and Initial Conditions
Solution Methodology
Summary
Exercise
2 Some Basic Discrete Systems
Introduction
Steady State Problems
Heat flow in a composite slab
Fluid flow network
Heat transfer in heat sinks (combined conduction–convection)
Analysis of a heat exchanger
Transient Heat Transfer Problem (Propagation Problem)
The Finite Element Method
Introduction
Elements and Shape Functions
One-dimensional linear element
One-dimensional quadratic element
Two-dimensional linear triangular elements
Area coordinates
Quadratic triangular elements
Two-dimensional quadrilateral elements
Isoparametric elements
Three-dimensional elements
Formulation (Element Characteristics)
Ritz method (Heat balance integral method—Goodman’s method)
The method of weighted residuals
Galerkin finite element method
Formulation for the Heat Conduction Equation
Variational approach
The Galerkin method
Requirements for Interpolation Functions
4 Steady State Heat Conduction in One Dimension
Introduction
PlaneWalls
Homogeneous wall
Composite wall
Finite element discretization
Wall with varying cross-sectional area
Plane wall with a heat source: solution by linear elements
Plane wall with a heat source: solution by quadratic elements
Plane wall with a heat source: solution by modified quadratic equations (static condensation)
Radial Heat Flow in a Cylinder
Cylinder with heat source
Conduction–Convection Systems
5 Steady State Heat Conduction in Multi-dimensions
Introduction
Two-dimensional Plane Problems
Triangular elements
Rectangular Elements
Plate with Variable Thickness
Three-dimensional Problems
Axisymmetric Problems
Galerkin’s method for linear triangular axisymmetric elements
6 Transient Heat Conduction Analysis
Introduction
Lumped Heat Capacity System
Numerical Solution
Transient goveing equations and boundary and initial conditions .
The Galerkin method
One-dimensional Transient State Problem
Time discretization using the Finite Difference Method (FDM)
Time discretization using the Finite Element Method (FEM)
Stability
Multi-dimensional Transient Heat Conduction
Phase Change Problems—Solidification and Melting
The goveing equations
Enthalpy formulation
Inverse Heat Conduction Problems
One-dimensional heat conduction
7 Convection Heat Transfer
Introduction
Types of fluid-motion-assisted heat transport
Navier–Stokes Equations
Conservation of mass or continuity equation
Conservation of momentum
Energy equation
Non-dimensional Form of the Goveing Equations
Forced convection
Natural convection (Buoyancy-driven convection)
Mixed convection
The Transient Convection–diffusion Problem
Finite element solution to convection–diffusion equation
Extension to multi-dimensions
Stability Conditions
Characteristic-based Split (CBS) Scheme
Spatial discretization
Time-step calculation
Boundary and initial conditions
Steady and transient solution methods
Artificial Compressibility Scheme
Nusselt Number, Drag and Stream Function
Nusselt number
Drag calculation
Stream function
Mesh Convergence
Laminar Isothermal Flow
Geometry, boundary and initial conditions
Solution
Laminar Non-isothermal Flow
Forced convection heat transfer
Buoyancy-driven convection heat transfer
Mixed convection heat transfer
Introduction to Turbulent Flow
Solution procedure and result
Extension to Axisymmetric Problems
8 Convection in Porous Media 240
Introduction
Generalized Porous Medium Flow Approach
Non-dimensional scales
Limiting cases
Discretization Procedure
Temporal discretization
Spatial discretization
Semi- and quasi-implicit forms
Non-isothermal Flows
Forced Convection
Natural Convection
Constant porosity medium
9 Some Examples of Fluid Flow and Heat Transfer Problems
Introduction
Isothermal Flow Problems
Steady state problems
Transient flow
Non-isothermal Benchmark Flow Problem
Backward-facing step
Thermal Conduction in an Electronic Package
Forced Convection Heat Transfer From Heat Sources
10 Implementation of Computer Code
Introduction
Preprocessing
Mesh generation
Linear triangular element data
Element size calculation
Shape functions and their derivatives
Boundary normal calculation
Mass matrix and mass lumping
Implicit pressure or heat conduction matrix
Main Unit
Time-step calculation
Element loop and assembly
Updating solution
Boundary conditions
Monitoring steady state
Postprocessing
Interpolation of data
A Green’s Lemma
B Integration Formulae
B.1 Linear Triangles
B.2 Linear Tetrahedron
C Finite Element Assembly Procedure
D Simplified Form of the Navier–Stokes Equations
Index