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.
Inhaltsverzeichnis
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).
