Inverse Heat Transfer: Fundamentals and Applications

Description

This book introduces the fundamental concepts of inverse heat transfer solutions and their applications for solving problems in convective, conductive, radiative, and multi-physics problems. Inverse Heat Transfer: Fundamentals and Applications, Second Edition includes techniques within the Bayesian framework of statistics for the solution of inverse problems. By modernizing the classic work of the late Professor M. Necati Özisik and adding new examples and problems, this new edition provides a powerful tool for instructors, researchers, and graduate students studying thermal-fluid systems and heat transfer. FEATURES Introduces the fundamental concepts of inverse heat transfer Presents in systematic fashion the basic steps of powerful inverse solution techniques Develops inverse techniques of parameter estimation, function estimation, and state estimation Applies these inverse techniques to the solution of practical inverse heat transfer problems Shows inverse techniques for conduction, convection, radiation, and multi-physics phenomena M. Necati Özisik (1923–2008) retired in 1998 as Professor Emeritus of North Carolina State University’s Mechanical and Aerospace Engineering Department. Helcio R. B. Orlande is a Professor of Mechanical Engineering at the Federal University of Rio de Janeiro (UFRJ), where he was the Department Head from 2006 to 2007. Cover Half Title Series Page Title Page Copyright Page Dedication Table of Contents Preface Preface of the First Edition Authors PART I: Introduction and Parameter Estimation Chapter 1 Basic Concepts 1.1 Inverse Heat Transfer Problem Concept 1.2 Classification of IHTPs 1.3 Difficulties in the Solution of Inverse Heat Transfer Problems 1.4 An Overview of Solution Techniques for Inverse Heat Transfer Problems 1.5 Basic Steps for the Solution of Inverse Heat Transfer Problems Problems Note 1: Statistical Concepts Random Variable Probability Distribution Expected Value of X Expected Value of a Function g(X) Variance of a Random Variable X Covariance of Two Random Variables X and Y Gaussian Distribution Uniform Distribution Rayleigh Distribution Gamma Distribution Beta Distribution Chi-Square Distribution Covariance Matrix Multivariate Gaussian Distribution Chapter 2 Parameter Estimation: Minimization of an Objective Function without Prior Information about the Unknown Parameters 2.1 Objective Function 2.2 Technique I: The Levenberg-Marquardt Method The Direct Problem The Inverse Problem The Iterative Procedure for Technique I The Stopping Criteria for Technique I The Computational Algorithm for Technique I 2.3 Technique II: The Conjugate Gradient Method for Parameter Estimation The Direct Problem The Inverse Problem The Iterative Procedure for Technique II The Stopping Criterion for Technique II The Computational Algorithm for Technique II 2.4 Sensitivity Coefficients Methods of Determining the Sensitivity Coefficients Direct Analytic Solution for Determining Sensitivity Coefficients The Boundary Value Problem Approach for Determining the Sensitivity Coefficients Finite Difference Approximation for Determining Sensitivity Coefficients 2.5 Design of Optimum Experiments 2.6 The Use of Multiple Sensors 2.7 Statistical Analysis 2.8 Estimation of Thermal Conductivity Components of an Orthotropic Heat Conducting Medium The Direct Problem The Inverse Problem Analysis of the Sensitivity Coefficients and Design of Optimum Experiments Parameter Estimation and Statistical Analysis 2.9 Technique III: The Conjugate Gradient Method with Adjoint Problem for Parameter Estimation The Direct Problem The Inverse Problem The Sensitivity Problem The Adjoint Problem The Gradient Equation The Iterative Procedure for Technique III The Stopping Criterion for Technique III The Computational Algorithm for Technique III The Use of Multiple Sensors 2.10 Estimation of a Heat Source Term in a Heat Conduction Problem Problems Note 1: Search Step-Size for Technique II Note 2: Search Step-Size for Technique III Chapter 3 Parameter Estimation: Minimization of an Objective Function with Prior Information about the Unknown Parameters 3.1 Objective Function Maximum a Posteriori Objective Function with a Uniform Prior Maximum a Posteriori Objective Function with a Gaussian Prior Maximum a Posteriori Objective Function with a Truncated Gaussian Prior 3.2 Minimization of the Objective Function 3.3 Identification of the Thermophysical Properties of Semi-Transparent Materials The Direct Problem The Inverse Problem Analysis of the Sensitivity Coefficients and Design of Optimum Experiments Parameter Estimation and Statistical Analysis Problems Chapter 4 Parameter Estimation: Stochastic Simulation with Prior Information about the Unknown Parameters 4.1 Markov Chains 4.2 Technique IV: Markov Chain Monte Carlo (MCMC) Method Proposal Distribution Random Walk Independent Move 4.3 MCMC Estimation of Thermal Conductivity Components of an Orthotropic Heat Conducting Medium The Direct Problem The Inverse Problem Stochastic Simulation 4.4 MCMC Estimation of Thermal Conductivity and Volumetric Heat Capacity of Viscous Liquids with the Line Heat Source Probe The Direct Problem The Inverse Problem Analysis of the Sensitivity Coefficients and Design of Optimum Experiments Stochastic Simulation 4.5 MCMC Estimation of Thermophysical Parameters of Thin Metal Films Heated by Fast Laser Pulses The Direct Problem The Inverse Problem Analysis of the Sensitivity Coefficients and Design of Optimum Experiments Stochastic Simulation 4.6 Analysis of Markov Chains Statistics Convergence of the Markov Chain Proposal Distribution 4.7 Reduction of the Computational Time for Solving Inverse Problems with Technique IV Delayed Acceptance Metropolis-Hastings (DAMH) Algorithm Approximation Error Model (AEM) Approach 4.8 Approximation Error Model to Account for Convective Effects in the Line Heat Source Probe Method Problems Note 1: Metropolis-Hastings Algorithm with Sampling by Blocks of Parameters PART II: Function Estimation Chapter 5 Function Estimation: Minimization of an Objective Functional without Prior Information about the Unknown Functions 5.1 Technique V: The Conjugate Gradient Method with Adjoint Problem for Function Estimation The Direct Problem The Inverse Problem The Sensitivity Problem The Adjoint Problem The Gradient Equation The Iterative Procedure for Technique V The Stopping Criterion for Technique V The Computational Algorithm for Technique V 5.2 Estimation of the Spacewise and Timewise Variations of the Wall Heat Flux in Laminar Flow Direct Problem Inverse Problem Sensitivity Problem Adjoint Problem Gradient Equation Iterative Procedure Results 5.3 Simultaneous Estimation of Spatially Dependent Diffusion Coefficient and Source Term in a Diffusion Problem Direct Problem Inverse Problem Sensitivity Problems Adjoint Problem Gradient Equations Iterative Procedure Results 5.4 Simultaneous Estimation of the Spacewise and Timewise Variations of Mass and Heat Transfer Coefficients in Drying Direct Problem Inverse Problem Sensitivity Problems Adjoint Problem Gradient Equations Iterative Procedure Results Problems Note 1: Hilbert Spaces Note 2: Conjugate Gradient Method of Function Estimation Note 3: Additional Measurement for Selecting the Stopping Criterion of the Conjugate Gradient Method Chapter 6 Function Estimation: Solution within the Bayesian Framework of Statistics with Prior Information about the Unknown Functions 6.1 Prior Distributions Hierarchical Models 6.2 Estimation of the Kidney Metabolic Heat Generation Rate Direct Problem Inverse Problem Results 6.3 Temperature Estimation of Inflamed Bowel Direct Problem Inverse Problem Results 6.4 Detection of Contact Failures by Using Integral Transformed Measurements Direct Problem Inverse Problem Results 6.5 Accelerated Bayesian Inference for the Estimation of Spatially Varying Heat Flux Direct Problem Inverse Problem Results Problems PART III: State Estimation Chapter 7 State Estimation: Kalman Filter 7.1 State Estimation Problem 7.2 Technique VI: The Kalman Filter 7.3 Estimation of a Transient Boundary Heat Flux That Varies over the Surface 7.4 The Steady-State Kalman Filter Problems Chapter 8 State Estimation: Particle Filter 8.1 Technique VII: The Sampling Importance Resampling (SIR) Algorithm 8.2 Technique VII: The Auxiliary Sampling Importance Resampling (ASIR) Algorithm 8.3 Technique VII: The Algorithm of Liu and West 8.4 Estimation of the Fire Front in Regional Scale Wildfire Spread 8.5 A Comparison of Particle Filter Algorithms in Bioheat Transfer Problems Appendix: Approximate Bayesian Computation References Index