Solving Direct and Inverse Heat Conduction Problems

1. Front Matter

   Pages i-xxvi

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2. Heat Conduction Fundamentals

   1. Front Matter

      Pages 1-1

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   2. Fourier Law

      Pages 3-6

   3. Mass and Energy Balance Equations

      Pages 7-27

   4. The Reduction of Transient Heat Conduction Equations and Boundary Conditions

      Pages 29-39

   5. Substituting Heat Conduction Equation by Two-Equations System

      Pages 41-46

   6. Variable Change

      Pages 47-50

3. Exercises. Solving Heat Conduction Problems

   1. Front Matter

      Pages 51-51

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   2. Heat Transfer Fundamentals

      Pages 53-139

   3. Two-Dimensional Steady-State Heat Conduction. Analytical Solutions

      Pages 141-160

   4. Analytical Approximation Methods. Integral Heat Balance Method

      Pages 161-169

   5. Two-Dimensional Steady-State Heat Conduction. Graphical Method

      Pages 171-182

   6. Two-Dimensional Steady-State Problems. The Shape Coefficient

      Pages 183-187

   7. Solving Steady-State Heat Conduction Problems by Means of Numerical Methods

      Pages 189-307

   8. Finite Element Balance Method and Boundary Element Method

      Pages 309-331

   9. Transient Heat Exchange between a Body with Lumped Thermal Capacity and Its Surroundings

      Pages 333-351

   10. Transient Heat Conduction in Half-Space

       Pages 353-383

   11. Transient Heat Conduction in Simple-Shape Elements

       Pages 385-467

   12. Superposition Method in One-Dimensional Transient Heat Conduction Problems

       Pages 469-513

   13. Transient Heat Conduction in a Semi-Infinite Body. The Inverse Problem

       Pages 515-539

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.

• Heat Conduction
• Thermal Conduction
• energy
• finite element method
• heat transfer

From the reviews:

"The present book is devoted to direct and inverse heat conduction problems. … The methods for solving problems involved with welding and laser technology are also discussed in great detail. The present book is addressed to undergraduate and PhD students of mechanical, power, process and environment engineering. … it can also serve as a reference book to be used by nuclear, industrial and civil engineers." (Lubomira Softova, Zentralblatt MATH, Vol. 1122 (24), 2007)

• Institute of Process and Power Engineering, Cracow University Technology, Kraków, Poland

  Jan Taler, Piotr Duda

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.

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