Inverse Heat Conduction Ill Posed Problems 2nd Edition by Hamidreza Najafi, Keith A Woodbury, Filippo De Monte, James V Beck ISBN 9781119840190 1119840198

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ISBN 10: 1119840198
ISBN 13: 9781119840190
Author: Hamidreza Najafi, Keith A Woodbury, Filippo De Monte, James V Beck

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

Inverse Heat Conduction Ill Posed Problems 2nd Edition Table of contents:

1 Inverse Heat Conduction Problems

1.1 Introduction

1.2 Basic Mathematical Description

1.3 Classification of Methods

1.4 Function Estimation Versus Parameter Estimation

1.5 Other Inverse Function Estimation Problems

1.6 Early Works on IHCPs

1.7 Applications of IHCPs: A Modern Look

1.8 Measurements

1.9 Criteria for Evaluation of IHCP Methods

1.10 Scope of Book

1.11 Chapter Summary

References

2 Analytical Solutions of Direct Heat Conduction Problems

2.1 Introduction

2.2 Numbering System

2.3 One‐Dimensional Temperature Solutions

2.4 Two‐Dimensional Temperature Solutions

2.5 Chapter Summary

Problems

References

3 Approximate Methods for Direct Heat Conduction Problems

3.1 Introduction

3.2 Superposition Principles

3.3 One‐Dimensional Problem with Time‐Dependent Surface Temperature

3.4 One‐Dimensional Problem with Time‐Dependent Surface Heat Flux

3.5 Two‐Dimensional Problem with Space‐Dependent and Constant Surface Heat Flux

3.6 Two‐Dimensional Problem with Space‐ and Time‐Dependent Surface Heat Flux

3.7 Chapter Summary

Problems

References

4 Inverse Heat Conduction Estimation Procedures

4.1 Introduction

4.2 Why is the IHCP Difficult?

4.3 Ill‐Posed Problems

4.4 IHCP Solution Methodology

4.5 Sensitivity Coefficients

4.6 Stolz Method: Single Future Time Step Method

4.7 Function Specification Method

4.8 Tikhonov Regularization Method

4.9 Gradient Methods

4.10 Truncated Singular Value Decomposition Method

4.11 Kalman Filter

4.12 Chapter Summary

Problems

References

5 Filter Form of IHCP Solution

5.1 Introduction

5.2 Temperature Perturbation Approach

5.3 Filter Matrix Perspective

5.4 Sequential Filter Form

5.5 Using Second Temperature Sensor as Boundary Condition

5.6 Filter Coefficients for Multi‐Layer Domain

5.7 Filter Coefficients for Non‐Linear IHCP: Application for Heat Flux Measurement Using Directional Flame Thermometer

5.8 Chapter Summary

Problems

References

6 Optimal Regularization

6.1 Preliminaries

6.2 Two Conflicting Objectives

6.3 Mean Squared Error

6.4 Minimize Mean Squared Error in Heat Flux

6.5 Mean Squared Error in Temperature

6.6 The L‐Curve

6.7 Generalized Cross Validation

6.8 Chapter Summary

Problems

References

7 Evaluation of IHCP Solution Procedures

7.1 Introduction

7.2 Test Cases

7.3 Function Specification Method

7.4 Tikhonov Regularization

7.5 Conjugate Gradient Method

7.6 Truncated Singular Value Decomposition

7.7 Kalman Filter

7.8 Chapter Summary

Problems

References

8 Multiple Heat Flux Estimation

8.1 Introduction

8.2 The Forward and the Inverse Problems

8.3 Examples

8.4 Chapter Summary

Problems

References

9 Heat Transfer Coefficient Estimation

9.1 Introduction

9.2 Sensitivity Coefficients

9.3 Lumped Body Analyses

9.4 Bodies with Internal Temperature Gradients

9.5 Chapter Summary

Problems

References

10 Temperature Measurement

10.1 Introduction

10.2 Correction Kernel Concept

10.3 Unsteady Surface Element Method

10.4 Chapter Summary

Problems

References

Appendix A: Numbering System

A.1 Dimensionality, Coordinate System, and Types of Boundary Conditions

A.2 Boundary Condition Information

A.3 Initial Temperature Distribution

References

Appendix B: Exact Solution X22B(y1pt1)0Y22B00T0

B.1 Exact Analytical Solution: Short‐Time Form

B.2 Exact Analytical Solution. Large‐Time Form

References

Appendix C: Green’s Functions Solution Equation

C.1 Introduction

C.2 One‐Dimensional Problem with Time‐Dependent Surface Temperature

C.3 One‐Dimensional Problem with Time‐Dependent Surface Heat Flux

C.4 Two‐Dimensional Problem with Space‐ and Time‐Dependent Surface Heat Flux

Reference

Index

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