01891nam 2200409 n 450 99638804920331620200824120829.0(CKB)1000000000623944(EEBO)2240913365(UnM)99850957e(UnM)99850957(EXLCZ)99100000000062394419920318d1614 uy |engurbn||||a|bb|A treatise of the vnvvritten Word of God, commonly called traditions. Written in Latin, by the R. Father Iames Gordon Huntley of Scotland, Doctour of Diuinity, of the Society of Iesus. And translated into English by I. L. of the same Society. The second part of the first controuersy[electronic resource][Saint-Omer Printed at the English College Press]M.DC.XIV [1614]61, [3] pI.L. = William Wright.A translation of the second part of the first controversy in: Gordon, James. Controversiarum epitomes.Place of publication and name of press from STC.Last leaf blank?.Reproduction of the original in the British Library.Preceding date in imprint: Permissu superiorum.eebo-0018Tradition (Theology)Early works to 1800Tradition (Theology)Gordon James1541-1620.1004861Wright William1563-1639.1003408Cu-RivESCu-RivESCStRLINWaOLNBOOK996388049203316A treatise of the vnvvritten Word of God, commonly called traditions. Written in Latin, by the R. Father Iames Gordon Huntley of Scotland, Doctour of Diuinity, of the Society of Iesus. And translated into English by I. L. of the same Society. The second part of the first controuersy2398863UNISA10856nam 2200505 450 991083022680332120230520224631.01-119-84022-81-119-84020-1(MiAaPQ)EBC7205778(Au-PeEL)EBL7205778(CKB)26170441700041(EXLCZ)992617044170004120230520d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierInverse Heat Conduction Ill-Posed Problems /Hamidreza Najafi [and three others]Second edition.Hoboken, New Jersey :John Wiley & Sons, Inc.,[2023]©20231 online resource (355 pages)Print version: Najafi, Hamidreza Inverse Heat Conduction Newark : John Wiley & Sons, Incorporated,c2023 9781119840190 Includes bibliographical references and index.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.HeatConductionNumerical analysisImproperly posed problems. HeatConduction.Numerical analysisImproperly posed problems. .536.23Najafi Hamidreza1663712MiAaPQMiAaPQMiAaPQBOOK9910830226803321Inverse Heat Conduction4021232UNINA