Jan Taler & Piotr Duda 
Solving Direct and Inverse Heat Conduction Problems 

This book is devoted to the concept of simple and inverse heat conduction problems. The process of solving direct problems is based on the tempera­ ture determination when initial and boundary conditions are known, while the solving of inverse problems is based on the search for boundary condi­ tions when temperature properties are known, provided that temperature is the function of time, at the selected inner points of a body. In the first part of the book (Chaps. 1-5), we have discussed theoretical basis for thermal conduction in solids, motionless liquids and liquids that move in time. In the second part of the book, (Chapters 6-26), we have discussed at great length different engineering problems, which we have presented together with the proposed solutions in the form of theoretical and mathematical examples. It was our intention to acquaint the reader in a step-by-step fashion with all the mathematical derivations and solutions to some of the more significant transient and steady-state heat conduction problems with respect to both, the movable and immovable heat sources and the phenomena of melting and freezing. Lots of attention was paid to non-linear problems. The methods for solving heat conduction problems, i. e. the exact and approximate analytical methods and numerical methods, such as the finite difference method, the finite volume method, the finite element method and the boundary element method are discussed in great detail. Aside from algorithms, applicable computational programs, written in a FORTRAN language, were given.

Table of Content

Heat Conduction Fundamentals.- Fourier Law.- Mass and Energy Balance Equations.- The Reduction of Transient Heat Conduction Equations and Boundary Conditions.- Substituting Heat Conduction Equation by Two-Equations System.- Variable Change.- Exercises. Solving Heat Conduction Problems.- Heat Transfer Fundamentals.- Two-Dimensional Steady-State Heat Conduction. Analytical Solutions.- Analytical Approximation Methods. Integral Heat Balance Method.- Two-Dimensional Steady-State Heat Conduction. Graphical Method.- Two-Dimensional Steady-State Problems. The Shape Coefficient.- Solving Steady-State Heat Conduction Problems by Means of Numerical Methods.- Finite Element Balance Method and Boundary Element Method.- Transient Heat Exchange between a Body with Lumped Thermal Capacity and Its Surroundings.- Transient Heat Conduction in Half-Space.- Transient Heat Conduction in Simple-Shape Elements.- Superposition Method in One-Dimensional Transient Heat Conduction Problems.- Transient Heat Conduction in a Semi-Infinite Body. The Inverse Problem.- Inverse Transient Heat Conduction Problems.- Multidimensional Problems. The Superposition Method.- Approximate Analytical Methods for Solving Transient Heat Conduction Problems.- Finite Difference Method.- Solving Transient Heat Conduction Problems by Means of Finite Element Method (FEM).- Numerical-Analytical Methods.- Solving Inverse Heat Conduction Problems by Means of Numerical Methods.- Heat Sources.- Melting and Solidification (Freezing).

About the author

Professor Jan Taler is a director of the Department of Process and Power Engineering at the Faculty of Mechanical Engineering, Krakow University of Technology. He has lectures on heat transfer processes and thermal power plants at the Faculty of Mechanical Engineering and the Faculty of Computer and Electrical Engineering. His research interests mainly lie in heat transfer, inverse heat conduction problems and monitoring of thermal stresses, which arise during the operations of energy installations and machinery. The results of his research on heat transfer, thermal stresses, optimum heating and cooling of solids and measuring of heat flux were published in well-known international journals, such as Transactions of the ASME, International Journal of Heat and Mass Transfer, Heat and Mass Transfer, Forschung im Ingenieurwessen, Brennstoff-Warme-Kraft, VGB Kraftwerkstechnik and VGB Power Tech.
Professor Taler was a research fellow of DAAD in Germany and of Alexander von Humboldt Foundation at the University of Stuttgart. He is also a member of the Committee of Combustion and Thermodynamics at the Polish Academy of Sciences. He is also the author of over 200 publications and 5 monographies, including three in German language. He has received Siemens Award for his achievements in scientific research, the Award of the Minister of Education and the Award of the Rector of the Krakow University of Technology.

Dr. Piotr Duda is an associate professor at the Department of Process and Power Engineering of the Faculty of Mechanical Engineering, Krakow University of Technology. Between 1997-1998, he was a research fellow at the Swiss Federal Institute of Technology in Lausanne (EPFL). Between 2002-2003, he was a research fellow of the Alexander von Humboldt Foundation at the University of Stuttgart, Germany. He has published over 50 articles on heat transfer problems, thermal stresses and numerical methods both at homeand abroad.