1R49. Inverse Heat Transfer: Fundamentals and Applications. - MN Ozisik (Dept of Mech and Aerospace Eng, N Carolina State Univ, Raleigh NC) and HRB Orlande (Dept of Mech Eng, EE-COPPE, Fed Univ, Rio de Janeiro, Brazil). Taylor & Francis Publ, New York NY. 2000. 330 pp. ISBN 1-56032-838-X. $95.00.
Reviewed by AJ Kassab (Dept of Mech, Mat, and Aerospace Eng, Col of Eng, Univ of Central Florida, Orlando FL 32816-2450).
This is a book specifically focused on the solution of inverse heat transfer problems, that is problems that, for instance, address the reconstruction of unknown heat fluxes, the determination of unknown thermophysical properties such as thermal conductivities and diffusivities, or the determination of unknown energy generation (source term) in the governing heat conduction equation. The authors focus on the Levenberg-Marquardt method and Alifanov’s method of iterative regularization for both parameter and function estimation. In the latter approach, the authors adopt the conjugate gradient method and use the adjoint method.
The book is divided into two parts. The first part consists of Chapters 1 and 2 which cover fundamentals, and the second part consists of Chapters 3–6 which cover applications of the fundamentals to various 1D and 2D inverse problems. The first chapter provides a detailed literature review on inverse problems and develops basic concepts of inverse problems in heat transfer. The notes at the end of the chapter introduce elementary concepts in statistics. The second chapter details the Levenberg–Marquardt (LM) and conjugate gradient (CG) methods for solution of parameter estimation and function estimation problems. The LM method is derived in detail for linear and nonlinear problems, and criteria selection for stopping the iteration is provided. Three methods are identified to find the requisite sensitivity coefficients. Next, the authors develop the details of the conjugate gradient method along with the adjoint problem as a means of solving inverse problems. Stopping criteria are enumerated, and best practices are discussed. For each method, the authors provide step-by-step derivations and procedures. The chapter concludes with an example problem of reconstruction of the source term in the heat conduction equation and is supplemented by seven notes covering topics ranging from statistical analysis for parameter estimation, design of experiments, to issues involved in various approaches to stopping criteria.
The second part of the book addresses applications of inverse problems to various heat conduction, convection, and radiation problems. Chapter 3 applies the methods of the first part to inverse conduction problems of retrieving the initial condition, identifying unknown thermal conductivity of an othotropic medium, determining space wise and temporal variations of sources terms, estimating thermal diffusivities in the hyperbolic heat conduction equations, and estimating contact conductances. The formulation and solution procedure for each problem is detailed and solutions are presented in much detail in chart and tabular formats. This style is maintained throughout the book, where in the next chapters’ various inverse problems in convection and radiation are treated. For instance, the problems of estimation of inlet temperature profiles and variation of wall fluxes in laminar and turbulent flows are considered in Chapter 4. While in Chapter 5, a very brief review of solutions methods for direct or forward radiation problems is followed by inverse problem applications in identifying the unknown radiative source term and identifying the unknown surface reflectivity. Both the LM and CG methods are used, and results are compared. The book concludes with Chapter 6 which addresses multi-dimensional solutions of the direct problem using body-fitted coordinates. This is followed by a generalized approach to inverse problems which is illustrated in an inverse problem addressing the cooling of electronic components.
There are ample examples supported by a copious number of tables, plots, and illustrations. The book has a detailed table of contents and an index. There are several problems at the end of each chapter, and each of the topics presented is presented in a detailed manner rendering the book quite suitable for teaching. Each chapter features a rather complete reference list. Moreover, most chapters are appended with notes exploring certain concepts and providing the mathematical details of derivations which are drawn-upon in the chapter.
Inverse Heat Transfer: Fundamentals and Applications is an excellent reference for researchers involved in inverse problems. The book should certainly be acquired by university and research laboratory libraries as a solid reference on the increasingly important subject of inverse problems. It should also be considered by instructors as a text for a course dedicated to inverse heat transfer problems or as a reference to supplement graduate heat transfer courses in heat conduction or intermediate heat transfer.
