Inverse Heat Transfer
Fundamentals and Applications
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This book introduces the fundamental concepts of inverse heat transfer solutions and their application for solving problems in convective, conductive, radiative, and multi-physics problems. The textbook includes formulation based on generalized coordinates for the solution of inverse heat conduction problems in two-dimensional regions, involving the introduction of techniques within the Bayesian framework of statistics for solution of inverse problems. By modernizing the classic work of the late Dr. Ozisik, 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.
Table of Contents
PREFACE PART I INTRODUCTION AND PARAMETER ESTIMATION Chapter 1 BASIC CONCEPTS 1.1 Inverse Heat Transfer Problem Concept 1.2 Classification of Inverse Heat Transfer Problems 1.3 Difficulties in the Solution of Inverse Heat Transfer Problems 1.4 An Overview of Solution Techniques for Inverse Heat Transfer Problems Problems Note 1 Statistical Concepts 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 2.3 Technique II: The Conjugate Gradient Method for Parameter Estimation 2.4 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 2.9 Technique III: The Conjugate Gradient Method with Adjoint Problem for Parameter Estimation 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 3.2 Minimization of the Objective Function 3.3 Identification of the Thermophysical Properties of Semi-Transparent Materials 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 4.3 MCMC Estimation of Thermal Conductivity Components of an Orthotropic Heat Conducting Medium 4.4 MCMC Estimation of Thermal Conductivity and Volumetric Heat Capacity of Viscous Liquids with the Line Heat Source Probe 4.5 MCMC Estimation of Thermophysical Parameters of Thin Metal Films Heated by Fast Laser Pulses 4.6 Analysis of Markov Chains 4.7 Reduction of the Computational Time for Solving Inverse Problems with Technique IV 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 Function Without Prior Information About the Unknown Functions 5.1 Technique V: The Conjugate Gradient Method with Adjoint Problem for Function Estimation 5.2 Estimation of the Spacewise and Timewise Variations of the Wall Heat Flux in Laminar Flow 5.3 Simultaneous Estimation of Spatially Dependent Diffusion Coefficient and Source Term in a Diffusion Problem 5.4 Simultaneous Estimation of the Spacewise and Timewise Variations of Mass and Heat Transfer Coefficients in Drying 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 6.2 Estimation of the Kidney Metabolic Heat Generation Term 6.3 Temperature Estimation of Inflamed Bowel 6.4 Detection of Contact Failures by Using Integral Transformed Measurements 6.5 Accelerated Bayesian Inference for the Estimation of Spatially Varying Heat Flux Problems PART III STATE ESTIMATION Chapter 7 STATE ESTIMATION: Kalman Filter 7.1 State Estimation Problem 7.2 The Kalman Filter 7.3 Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux 7.4 The Steady-State Kalman Filter Problems Chapter 8 STATE ESTIMATION: Particle Filter 8.1 Sampling Importance Resampling (SIR) Algorithm 8.2 Auxiliary Sampling Importance Resampling (ASIR) Algorithm 8.3 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 REFERENCES Appendix APPROXIMATE BAYESIAN COMPUTATION A.1 Simultaneous Model Selection and Model Calibration with Approximate Bayesian Computation A.2 An Application of Approximate Bayesian Computation in Bioheat Transfer References
Helcio Rangel Barreto Orlande obtained his B.S. in Mechanical Engineering from the Federal University of Rio de Janeiro (UFRJ) in 1987 and his M.S. in Mechanical Engineering from the same University in 1989. After obtaining his Ph.D. in Mechanical Engineering in 1993 from North Carolina State University, he joined the Department of Mechanical Engineering of UFRJ, where he was the department head during 2006 and 2007. His research areas of interest include the solution of inverse heat and mass transfer problems, as well as the use of numerical, analytical and hybrid numerical-analytical methods of solution of direct heat and mass transfer problems. He is the co-author of 4 books and more than 280 papers in major journals and conferences. He is a member of the Scientific Council of the International Centre for Heat and Mass Transfer and a Delegate in the Assembly for International Heat Transfer Conferences. He serves as an Associate Editor for the journals Heat Transfer Engineering, Inverse Problems in Science and Engineering and High Temperatures – High Pressures.