Solving direct and inverse heat conduction problems

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.

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 Met…