Inverse Heat Conduction
Ill-Posed Problems
2. Edition April 2023
352 Pages, Hardcover
Wiley & Sons Ltd
Further versions
Inverse Heat Conduction
A comprehensive reference on the field of inverse heat conduction problems (IHCPs), now including advanced topics, numerous practical examples, and downloadable MATLAB codes.
The First Edition of the classic book Inverse Heat Conduction: III-Posed Problems, published in 1985, has been used as one of the primary references for researchers and professionals working on IHCPs due to its comprehensive scope and dedication to the topic. The Second Edition of the book is a largely revised version of the First Edition with several all-new chapters and significant enhancement of the previous material. Over the past 30 years, the authors of this Second Edition have collaborated on research projects that form the basis for this book, which can serve as an effective textbook for graduate students and as a reliable reference book for professionals. Examples and problems throughout the text reinforce concepts presented.
The Second Edition continues emphasis from the First Edition on linear heat conduction problems with revised presentation of Stolz, Function Specification, and Tikhonov Regularization methods, and expands coverage to include Conjugate Gradient Methods and the Singular Value Decomposition method. The Filter Matrix concept is explained and embraced throughout the presentation and allows any of these solution techniques to be represented in a simple explicit linear form. Two direct approaches suitable for non-linear problems, the Adjoint Method and Kalman Filtering, are presented, as well as an adaptation of the Filter Matrix approach applicable to non-linear heat conduction problems.
In the Second Edition of Inverse Heat Conduction: III-Posed Problems, readers will find:
* A comprehensive literature review of IHCP applications in various fields of engineering
* Exact solutions to several fundamental problems for direct heat conduction problems, the concept of the computational analytical solution, and approximate solution methods for discrete time steps using superposition of exact solutions which form the basis for the IHCP solutions in the text
* IHCP solution methods and comparison of many of these approaches through a common suite of test problems
* Filter matrix form of IHCP solution methods and discussion of using filter-form Tikhonov regularization for solving complex IHCPs in multi-layer domain with temperature-dependent material properties
* Methods and criteria for selection of the optimal degree of regularization in solution of IHCPs
* Application of the filter concept for solving two-dimensional transient IHCP problems with multiple unknown heat fluxes
* Estimating the heat transfer coefficient, h, for lumped capacitance body and bodies with temperature gradients
* Bias in temperature measurements in the IHCP and correcting for temperature measurement bias
Inverse Heat Conduction is a must-have resource on the topic for mechanical, aerospace, chemical, biomedical, or metallurgical engineers who are active in the design and analysis of thermal systems within the fields of manufacturing, aerospace, medical, defense, and instrumentation, as well as researchers in the areas of thermal science and computational heat transfer.
Preface Second Edition
Nomenclature
1 Inverse Heat Conduction Problems: An Overview 1-1
1.1 Introduction 1-1
1.2 Basic Mathematical Description 1-3
1.3 Classification of Methods 1-5
1.4 Function Estimation Versus Parameter Estimation 1-7
1.5 Other Inverse Function Estimation Problems 1-7
1.6 Early Works on IHCPs 1-9
1.7 Applications of IHCPS: A Modern Look 1-10
1.8 Measurements 1-20
1.9 Criteria for Evaluation of IHCP Methods 1-23
1.10 Scope of Book 1-24
1.11 Chapter Summary 1-24
1.12 References 1-25
1.13 List of Figures 1-33
1.14 List of Tables 1-34
2 Analytical Solutions of Direct Heat Conduction Problems 2.1
2.1 Introduction 2.1
2.2 Numbering System 2.2
2.3 One-Dimensional Temperature Solutions 2.3
2.4 Two-Dimensional Temperature Solutions 2.27
2.5 Chapter Summary 2.48
2.6 References 2.50
2.7 Problems 2.52
2.8 List of Figures 2.55
2.9 List of Tables 2.56
3 Approximate Methods for Direct Heat Conduction Problems 3-1
3.1 Introduction 3-1
3.2 Superposition Principles 3-2
3.3 One-Dimensional Problem with Time-Dependent Surface Temperature 3-4
3.4 One-Dimensional Problem with Time-Dependent Surface Heat Flux 3-21
3.5 Two-Dimensional Problem with Space-Dependent and Constant Surface Heat Flux 3-34
3.6 Two-Dimensional Problem with Space- and Time-Dependent Surface Heat Flux 3-41
3.7 Chapter Summary 3-52
3.8 References 3-53
3.9 Problems 3-53
3.10 List of Figures 3-59
3.11 List of Tables 3-60
4 Inverse Heat Conduction Estimation Procedures 4.1
4.1 Introduction 4.1
4.2 Why is the IHCP Difficult? 4.2
4.3 Ill-Posed Problems 4.4
4.4 IHCP Solution Methodology 4.8
4.5 Sensitivity Coefficients 4.9
4.6 Stolz Method: Single Future Time Step Method 4.19
4.7 Function Specification Method 4.23
4.8 Tikhonov Regularization Method 4.35
4.9 Gradient Methods 4.44
4.10 Truncated Singular Value Decomposition Method 4.55
4.11 Kalman Filter 4.58
4.12 Chapter Summary 4.66
4.13 References 4.67
4.14 Problems 4.71
4.15 List of Figures 4.74
4.16 List of Tables 4.75
5 Filter Form of IHCP Solution 5-1
5.1 Introduction 5-1
5.2 Temperature Perturbation Approach 5-1
5.3 Filter Matrix Perspective 5-3
5.4 Sequential Filter Form 5-15
5.5 Using Second Temperature Sensor as Boundary Condition 5-18
5.6 Filter Coefficients for Multi-Layer Domain 5-26
5.7 Filter Coefficients for Non-Linear IHCP: Application for Heat Flux Measurement Using Directional Flame Thermometer 5-33
5.8 Chapter Summary 5-46
5.9 Problems 5-46
5.10 References 5-47
5.11 List of Figures 5-49
5.12 List of Tables 5-51
6 Optimal Regularization 6.1
6.1 Preliminaries 6.1
6.2 Two Conflicting Objectives 6.2
6.3 Mean Squared Error 6.4
6.4 Minimize Mean Squared Error in Heat Flux 6.5
6.5 Minimize Mean Squared Error in Temperature 6.13
6.6 The L-curve 6.17
6.7 Generalized Cross Validation 6.20
6.8 Chapter Summary 6.24
6.9 References 6.26
6.10 Problems 6.27
6.11 List of Figures 6.28
6.12 List of Tables 6.29
7 Evaluation of IHCP Solution Procedures 7.1
7.1 Introduction 7.1
7.2 Test Cases 7.3
7.3 Function Specification Method 7.13
7.4 Tikhonov Regularization 7.22
7.5 Conjugate Gradient Method 7.29
7.6 Truncated Singular Value Decomposition 7.37
7.7 Kalman Filter 7.44
7.8 Chapter Summary 7.51
7.9 References 7.55
7.10 Problems 7.55
7.11 List of Figures 7.57
7.12 List of Tables 7.61
8 Multiple Heat Flux Estimation 8-1
8.1 Introduction 8-1
8.2 The forward and the inverse problems 8-1
8.3 Examples 8-7
8.4 Chapter Summary 8-15
8.5 References 8-16
8.6 Problems 8-16
8.7 List of Figures 8-17
8.8 List of Tables 8-19
9 Heat Transfer Coefficient Estimation 9-1
9.1 Introduction 9-1
9.2 Sensitivity Coefficients 9-4
9.3 Lumped Body Analyses 9-8
9.4 Bodies with Internal Temperature Gradients 9-15
9.5 Chapter Summary 9-18
9.6 References 9-18
9.7 Problems 9-20
9.8 Figures 9-21
9.9 Tables 9-22
10 Temperature Measurement 10.1
10.1 Introduction 10.1
10.2 Correction Kernel Concept 10.3
10.3 Unsteady surface element method 10.16
10.4 Chapter Summary 10.22
10.5 References 10.23
10.6 Problems 10.25
10.7 Figures 10.27
10.8 Tables 10.27
Appendices
A Numbering System A.1
A.1 Dimensionality, coordinate system, and types of boundary condition A.1
A.2 Boundary condition information A.2
A.3 Initial temperature distribution A.5
A.4 REFERENCES A.6
B Exact Solution X22B(y1pt1)0Y22B00T0 B.1
B.1 Exact analytical solution. Short-time form B.1
B.2 Exact analytical solution. Large-time form B.4
B.3 References B.8
C Green's functions Solution Equation C-1
C.1 Introduction C-1
C.2 One-Dimensional Problem with Time-Dependent Surface Temperature C-1
C.3 One-Dimensional Problem with Time-Dependent Surface Heat Flux C-9
C.4 Two-Dimensional Problem With Space- And Time-Dependent Surface Heat Flux C-14
C.5 References C-16
C.6 List of Figures C-16
Hamidreza Najafi is Associate Professor of Mechanical Engineering and Director of the Heat Transfer Lab at Florida Institute of Technology. He has authored and co-authored numerous articles in the areas of inverse heat conduction problems, computational heat transfer, and design and optimization of energy/thermal systems. Dr. Najafi is an active member of ASME and ASHRAE and has served in various leadership roles in multiple technical committees.
Filippo de Monte is Professor of Mechanical Engineering at the University L'Aquila, Italy. He served as a full-time Visiting Ph.D. student at the Department of Engineering, University of Cambridge, UK, in 1992, and a seasonal Visiting Associate Professor at the Department of Mechanical Engineering, Michigan State University, USA, from 2007 to 2014. He is a Member of the American Society of Mechanical Engineers (ASME) and holds editorial positions at the Journal of Verification, Validation and Uncertainty Quantification (ASME) and Heat Transfer Engineering. He was the Chairman of the 10th International Conference on Inverse Problems in Engineering (ICIPE 22), May 15-19, 2022, Francavilla al Mare (Chieti), Italy, and is co-editor of the book Modeling of Mass Transport Processes in Biological Media (July 2022).
James V. Beck (1930-2022) was Professor Emeritus of Mechanical Engineering at Michigan State University (MSU), a Fellow of ASME, and one of the pioneers of the fields of inverse problems and parameter estimation. Dr. Beck was honored with the MSU Distinguished Faculty Award (1987) and the ASME Heat Transfer Memorial Award (1998). He was the originator of the Inverse Problems Symposium and was the inventor, with Professor Litkouhi, of the numbering system for heat conduction solutions. Professor Beck made outstanding pioneering contributions to the field of heat transfer with numerous refereed journal articles and books.
