Inverse Heat Conduction : Ill-Posed Problems / / Hamidreza Najafi [and three others]

• Autore: Najafi Hamidreza
• Pubblicazione: Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2023]; ©2023
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (355 pages)
• Disciplina: 536.23
• Soggetto topico: Heat - Conduction; Numerical analysis - Improperly posed problems
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Title Page -- Copyright Page -- Contents -- List of Figures -- Nomenclature -- Preface to First Edition -- Preface to Second Edition -- Chapter 1 Inverse Heat Conduction Problems: An Overview -- 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 -- 1.7.1 Manufacturing Processes -- 1.7.1.1 Machining Processes -- 1.7.1.2 Milling and Hot Forming -- 1.7.1.3 Quenching and Spray Cooling -- 1.7.1.4 Jet Impingement -- 1.7.1.5 Other Manufacturing Applications -- 1.7.2 Aerospace Applications -- 1.7.3 Biomedical Applications -- 1.7.4 Electronics Cooling -- 1.7.5 Instrumentation, Measurement, and Non-Destructive Testing -- 1.7.6 Other Applications -- 1.8 Measurements -- 1.8.1 Description of Measurement Errors -- 1.8.2 Statistical Description of Errors -- 1.9 Criteria for Evaluation of IHCP Methods -- 1.10 Scope of Book -- 1.11 Chapter Summary -- References -- Chapter 2 Analytical Solutions of Direct Heat Conduction Problems -- 2.1 Introduction -- 2.2 Numbering System -- 2.3 One-Dimensional Temperature Solutions -- 2.3.1 Generalized One-Dimensional Heat Transfer Problem -- 2.3.2 Cases of Interest -- 2.3.3 Dimensionless Variables -- 2.3.4 Exact Analytical Solution -- 2.3.5 The Concept of Computational Analytical Solution -- 2.3.5.1 Absolute and Relative Errors -- 2.3.5.2 Deviation Time -- 2.3.5.3 Second Deviation Time -- 2.3.5.4 Quasi-Steady, Steady-State and Unsteady Times -- 2.3.5.5 Solution for Large Times -- 2.3.5.6 Intrinsic Verification -- 2.3.6 X12B10T0 Case -- 2.3.6.1 Computational Analytical Solution -- 2.3.6.2 Computer Code and Plots -- 2.3.7 X12B20T0 Case -- 2.3.7.1 Computational Analytical Solution. ; 2.3.7.2 Computer Code and Plots -- 2.3.8 X22B10T0 Case -- 2.3.8.1 Computational Analytical Solution -- 2.3.8.2 Computer Code and Plots -- 2.3.9 X22B20T0 Case -- 2.3.9.1 Computational Analytical Solution -- 2.3.9.2 Computer Code and Plots -- 2.4 Two-Dimensional Temperature Solutions -- 2.4.1 Dimensionless Variables -- 2.4.2 Exact Analytical Solution -- 2.4.3 Computational Analytical Solution -- 2.4.3.1 Absolute and Relative Errors -- 2.4.3.2 One- and Two-Dimensional Deviation Times -- 2.4.3.3 Quasi-Steady Time -- 2.4.3.4 Number of Terms in the Quasi-Steady Solution with Eigenvalues in the Homogeneous Direction -- 2.4.3.5 Number of Terms in the Quasi-Steady Solution with Eigenvalues in the Nonhomogeneous Direction -- 2.4.3.6 Deviation Distance Alongx -- 2.4.3.7 Deviation Distance Alongy -- 2.4.3.8 Number of Terms in the Complementary Transient Solution -- 2.4.3.9 Computer Code and Plots -- 2.5 Chapter Summary -- Problems -- References -- Chapter 3 Approximate Methods for Direct Heat Conduction Problems -- 3.1 Introduction -- 3.1.1 Various Numerical Approaches -- 3.1.2 Scope of Chapter -- 3.2 Superposition Principles -- 3.2.1 Green's Function Solution Interpretation -- 3.2.2 Superposition Example - Step Pulse Heating -- 3.3 One-Dimensional Problem with Time-Dependent Surface Temperature -- 3.3.1 Piecewise-Constant Approximation -- 3.3.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.3.1.2 Sequential-in-time Nature and Sensitivity Coefficients -- 3.3.1.3 Basic "Building Block" Solution -- 3.3.1.4 Computer Code and Example -- 3.3.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.3.2 Piecewise-Linear Approximation -- 3.3.2.1 Superposition-Based Numerical Approximation of the Solution -- 3.3.2.2 Sequential-in-time Nature and Sensitivity Coefficients -- 3.3.2.3 Basic "Building Block" Solutions. ; 3.3.2.4 Computer Code and Examples -- 3.3.2.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.4 One-Dimensional Problem with Time-Dependent Surface Heat Flux -- 3.4.1 Piecewise-Constant Approximation -- 3.4.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.4.1.2 Heat Flux-Based Sensitivity Coefficients -- 3.4.1.3 Basic "Building Block" Solution -- 3.4.1.4 Computer Code and Example -- 3.4.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.4.2 Piecewise-Linear Approximation -- 3.4.2.1 Superposition-Based Numerical Approximation of the Solution -- 3.4.2.2 Heat Flux-Based Sensitivity Coefficients -- 3.4.2.3 Basic "Building Block" Solutions -- 3.4.2.4 Computer Code and Examples -- 3.4.2.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.5 Two-Dimensional Problem with Space-Dependent and Constant Surface Heat Flux -- 3.5.1 Piecewise-Uniform Approximation -- 3.5.1.1 Superposition-Based Numerical Approximation of the Solution -- 3.5.1.2 Heat Flux-Based Sensitivity Coefficients -- 3.5.1.3 Basic "Building Block" Solution -- 3.5.1.4 Computer Code and Examples -- 3.5.1.5 Matrix Form of the Superposition-Based Numerical Approximation -- 3.6 Two-Dimensional Problem with Space- and Time-Dependent Surface Heat Flux -- 3.6.1 Piecewise-Uniform Approximation -- 3.6.1.1 Numerical Approximation in Space -- 3.6.2 Piecewise-Constant Approximation -- 3.6.2.1 Numerical Approximation in Time -- 3.6.3 Superposition-Based Numerical Approximation of the Solution -- 3.6.3.1 Sequential-in-time Nature and Sensitivity Coefficients -- 3.6.3.2 Basic "Building Block" Solution -- 3.6.3.3 Computer Code and Example -- 3.6.3.4 Matrix Form of the Superposition-Based Numerical Approximation -- 3.7 Chapter Summary -- Problems -- References -- Chapter 4 Inverse Heat Conduction Estimation Procedures. ; 4.1 Introduction -- 4.2 Why is the IHCP Difficult? -- 4.2.1 Sensitivity to Errors -- 4.2.2 Damping and Lagging -- 4.2.2.1 Penetration Time -- 4.2.2.2 Importance of the Penetration Time -- 4.3 Ill-Posed Problems -- 4.3.1 An Exact Solution -- 4.3.2 Discrete System of Equations -- 4.3.3 The Need for Regularization -- 4.4 IHCP Solution Methodology -- 4.5 Sensitivity Coefficients -- 4.5.1 Definition of Sensitivity Coefficients and Linearity -- 4.5.2 One-Dimensional Sensitivity Coefficient Examples -- 4.5.2.1 X22 Plate Insulated on One Side -- 4.5.2.2 X12 Plate Insulated on One Side, Fixed Boundary Temperature -- 4.5.2.3 X32 Plate Insulated on One Side, Fixed Heat Transfer Coefficient -- 4.5.3 Two-Dimensional Sensitivity Coefficient Example -- 4.6 Stolz Method: Single Future Time Step Method -- 4.6.1 Introduction -- 4.6.2 Exact Matching of Measured Temperatures -- 4.7 Function Specification Method -- 4.7.1 Introduction -- 4.7.2 Sequential Function Specification Method -- 4.7.2.1 Piecewise Constant Functional Form -- 4.7.2.2 Piecewise Linear Functional Form -- 4.7.3 General Remarks About Function Specification Method -- 4.8 Tikhonov Regularization Method -- 4.8.1 Introduction -- 4.8.2 Physical Significance of Regularization Terms -- 4.8.2.1 Continuous Formulation -- 4.8.2.2 Discrete Formulation -- 4.8.3 Whole Domain TR Method -- 4.8.3.1 Matrix Formulation -- 4.8.4 Sequential TR Method -- 4.8.5 General Comments About Tikhonov Regularization -- 4.9 Gradient Methods -- 4.9.1 Conjugate Gradient Method -- 4.9.1.1 Fletcher-Reeves CGM -- 4.9.1.2 Polak-Ribiere CGM -- 4.9.2 Adjoint Method (Nonlinear Problems) -- 4.9.2.1 Some Necessary Mathematics -- 4.9.2.2 The Continuous Form of IHCP -- 4.9.2.3 The Sensitivity Problem -- 4.9.2.4 The Lagrangian and the Adjoint Problem -- 4.9.2.5 The Gradient Equation -- 4.9.2.6 Summary of IHCP solution by Adjoint Method. ; 4.9.2.7 Comments About Adjoint Method -- 4.9.3 General Comments about CGM -- 4.10 Truncated Singular Value Decomposition Method -- 4.10.1 SVD Concepts -- 4.10.2 TSVD in the IHCP -- 4.10.3 General Remarks About TSVD -- 4.11 Kalman Filter -- 4.11.1 Discrete Kalman Filter -- 4.11.2 Two Concepts for Applying Kalman Filter to IHCP -- 4.11.3 Scarpa and Milano Approach -- 4.11.3.1 Kalman Filter -- 4.11.3.2 Smoother -- 4.11.4 General Remarks About Kalman Filtering -- 4.12 Chapter Summary -- Problems -- References -- Chapter 5 Filter Form of IHCP Solution -- 5.1 Introduction -- 5.2 Temperature Perturbation Approach -- 5.3 Filter Matrix Perspective -- 5.3.1 Function Specification Method -- 5.3.2 Tikhonov Regularization -- 5.3.3 Singular Value Decomposition -- 5.3.4 Conjugate Gradient -- 5.4 Sequential Filter Form -- 5.5 Using Second Temperature Sensor as Boundary Condition -- 5.5.1 Exact Solution for the Direct Problem -- 5.5.2 Tikhonov Regularization Method as IHCP Solution -- 5.5.3 Filter Form of IHCP Solution -- 5.6 Filter Coefficients for Multi-Layer Domain -- 5.6.1 Solution Strategy for IHCP in Multi-Layer Domain -- 5.6.1.1 Inner Layer -- 5.6.1.2 Outer Layer -- 5.6.1.3 Combined Solution -- 5.6.2 Filter Form of the Solution -- 5.7 Filter Coefficients for Non-Linear IHCP: Application for Heat Flux Measurement Using Directional Flame Thermometer -- 5.7.1 Solution for the IHCP -- 5.7.1.1 Back Layer (Insulation) -- 5.7.1.2 Front Layer (Inconel plate) -- 5.7.1.3 Combined Solution -- 5.7.2 Filter form of the solution -- 5.7.3 Accounting for Temperature-Dependent Material Properties -- 5.7.4 Examples -- 5.8 Chapter Summary -- Problems -- References -- Chapter 6 Optimal Regularization -- 6.1 Preliminaries -- 6.1.1 Some Mathematics -- 6.1.2 Design vs. Experimental Setting -- 6.2 Two Conflicting Objectives -- 6.2.1 Minimum Deterministic Bias. ; 6.2.2 Minimum Sensitivity to Random Errors.
• Titolo autorizzato: Inverse Heat Conduction
• ISBN: 1-119-84022-8; 1-119-84020-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910830226803321
• Lo trovi qui: Univ. Federico II