Solving Direct And Inverse Heat Conduction Problems

Solving Direct and Inverse Heat Conduction Problems Jan Taler Piotr Duda Solving Direct and Inverse Heat Conduction Problems ~ Springer Preface This book is devoted to the concept of simple and inverse heat conduction problems. The process of solving direct problems is based on the temperature determination when initial and boundary conditions are known, while the solving of inverse problems is based on the search for boundary conditions 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. The accuracy of the results obtained by means of various numerical methods was evaluated by way of comparison with accurate analytical solutions. The presented solutions not only allow to illustrate mathematical methods used in thermal conduction but also show the methods one can use to solve concrete practical problems, for example during the designing and life-time calculations of industrial machinery, combustion engines and in refrigerating and air conditioning engineering. Many examples refer to the topic of heating and thermo-renovation of apartment buildings. The methods for solving problems involved with welding and laser technology are also discussed in great detail. This book is addressed to undergraduate and PhD students of mechanical, power, process and environmental engineering. Due to the complexity of the heat conduction problems elaborated in this book, this edition can vi Preface also serve as a reference book that can be used by nuclear, industrial and civil engineers. Jan Taler is the author of the theoretical part of this book, mathematical exercises (excluding 12.1 & 12.3), and C, D & H attachments (found at the back of this book). Piotr Duda wrote in the FORTRAN language all presented programs and solved with their help exercises 7.3, 11.2-11.7, 15.1, 15.2, 15.4, 15.5, 15.7, 15.8, 15.11, 15.13, 15.15, 16.5, 16.9, 16.10, 17.7, 18.5-18.8,21.5, 21.7-21.10, 22.7, 23.3-23.7, 24.4 and 24.5. He also carried out calculations using the following programs: ANSYS (in Exercises 11.18-11.22, 12.4, 21.9 and 25.10), BETIS (in Exercise 12.4) and MathCAD (in Exercises 14.10, 16.2,16.4,17.6