# Solving Direct and Inverse Heat Conduction Problems

• Jan Taler
• Piotr Duda
Book

1. Front Matter
Pages i-xxvi
2. ### Heat Conduction Fundamentals

1. Front Matter
Pages 1-1
2. Pages 3-6
3. Pages 7-27
4. Pages 47-50
3. ### Exercises. Solving Heat Conduction Problems

1. Front Matter
Pages 51-51
2. Pages 53-139
3. Pages 353-383
4. Pages 385-467
5. Pages 541-572
6. Pages 573-586
7. Pages 605-657
8. Pages 693-731
9. Pages 765-797
10. Pages 799-829
4. Back Matter
Pages 831-889

### Introduction

The book presents a solution for direct and inverse heat conduction problems. In the first part, the authors discuss the theoretical basis for the heat transfer process. In the second part, they present selected theoretical and numerical problems in the form of exercises with their subsequent solutions. Such layout of the book will allow the reader to become more familiar with step-by-step calculation methods and with the practical application of the equations to the solution of design and utilization problems of thermal machinery. It will also help to master complex mathematics behind the heat transfer theory.

The book covers one-, two- and three dimensional problems which are solved by using 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 method. Unlike other books on the subject, the superposition method is thoroughly presented. Particular attention is paid to the solution of inverse heat conduction problems.

The authors took special care that the solved inverse problems can be implemented in indirect measurements of boundary heat flux and heat transfer coefficient. Included in this text is the determination of optimal fluid temperature changes during heating and cooling of solids. In great detail the problems of temperature transients caused by both moveable and immovable heat sources is discussed. They analyze the melting and freezing processes, including the freezing of food products. Moreover, they use computing programs written in Fortran language for solving mathematical equations. The book content is strengthened by additional materials presented at the back of the book, which include, among others, the description of basic mathematical functions characteristic of heat transfer problems, calculation of the inverse Laplace transformation, the property tables for stable thermophysical bodies and shape coefficients for isothermal surfaces of various shapes and programs that are typically used for solving differential equations. This book is strongly recommended for undergraduate and PhD students, researchers and academics of Power, Process, Mechanical and Environmental Engineering Faculties. The book should also appeal to those who conduct research in the area of thermal engineering, house-heating, air-conditioning systems and cooling processes, combustion engines and welding technology.

### Keywords

Heat Conduction Thermal Conduction energy finite element method heat transfer

#### Authors and affiliations

• Jan Taler
• 1
• Piotr Duda
• 1
1. 1.Institute of Process and Power EngineeringCracow University TechnologyKrakówPoland

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-540-33471-2
• Copyright Information Springer-Verlag Berlin Heidelberg 2006
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-540-33470-5
• Online ISBN 978-3-540-33471-2
• Buy this book on publisher's site