Ebook: Solving Direct and Inverse Heat Conduction Problems
- Tags: Engineering Thermodynamics Heat and Mass Transfer, Engineering Fluid Dynamics, Thermodynamics
- Year: 2006
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Fourier Law....Pages 3-6
Mass and Energy Balance Equations....Pages 7-27
The Reduction of Transient Heat Conduction Equations and Boundary Conditions....Pages 29-39
Substituting Heat Conduction Equation by Two-Equations System....Pages 41-46
Variable Change....Pages 47-50
Front Matter....Pages 51-51
Heat Transfer Fundamentals....Pages 53-139
Two-Dimensional Steady-State Heat Conduction. Analytical Solutions....Pages 141-160
Analytical Approximation Methods. Integral Heat Balance Method....Pages 161-169
Two-Dimensional Steady-State Heat Conduction. Graphical Method....Pages 171-182
Two-Dimensional Steady-State Problems. The Shape Coefficient....Pages 183-187
Solving Steady-State Heat Conduction Problems by Means of Numerical Methods....Pages 189-307
Finite Element Balance Method and Boundary Element Method....Pages 309-331
Transient Heat Exchange between a Body with Lumped Thermal Capacity and Its Surroundings....Pages 333-351
Transient Heat Conduction in Half-Space....Pages 353-383
Transient Heat Conduction in Simple-Shape Elements....Pages 385-467
Superposition Method in One-Dimensional Transient Heat Conduction Problems....Pages 469-513
Transient Heat Conduction in a Semi-Infinite Body. The Inverse Problem....Pages 515-539
Inverse Transient Heat Conduction Problems....Pages 541-572
Multidimensional Problems. The Superposition Method....Pages 573-586
Approximate Analytical Methods for Solving Transient Heat Conduction Problems....Pages 587-604
Front Matter....Pages 51-51
Finite Difference Method....Pages 605-657
Solving Transient Heat Conduction Problems by Means of Finite Element Method (FEM)....Pages 659-691
Numerical-Analytical Methods....Pages 693-731
Solving Inverse Heat Conduction Problems by Means of Numerical Methods....Pages 733-763
Heat Sources....Pages 765-797
Melting and Solidification (Freezing)....Pages 799-829
Back Matter....Pages 831-889
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.
Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Fourier Law....Pages 3-6
Mass and Energy Balance Equations....Pages 7-27
The Reduction of Transient Heat Conduction Equations and Boundary Conditions....Pages 29-39
Substituting Heat Conduction Equation by Two-Equations System....Pages 41-46
Variable Change....Pages 47-50
Front Matter....Pages 51-51
Heat Transfer Fundamentals....Pages 53-139
Two-Dimensional Steady-State Heat Conduction. Analytical Solutions....Pages 141-160
Analytical Approximation Methods. Integral Heat Balance Method....Pages 161-169
Two-Dimensional Steady-State Heat Conduction. Graphical Method....Pages 171-182
Two-Dimensional Steady-State Problems. The Shape Coefficient....Pages 183-187
Solving Steady-State Heat Conduction Problems by Means of Numerical Methods....Pages 189-307
Finite Element Balance Method and Boundary Element Method....Pages 309-331
Transient Heat Exchange between a Body with Lumped Thermal Capacity and Its Surroundings....Pages 333-351
Transient Heat Conduction in Half-Space....Pages 353-383
Transient Heat Conduction in Simple-Shape Elements....Pages 385-467
Superposition Method in One-Dimensional Transient Heat Conduction Problems....Pages 469-513
Transient Heat Conduction in a Semi-Infinite Body. The Inverse Problem....Pages 515-539
Inverse Transient Heat Conduction Problems....Pages 541-572
Multidimensional Problems. The Superposition Method....Pages 573-586
Approximate Analytical Methods for Solving Transient Heat Conduction Problems....Pages 587-604
Front Matter....Pages 51-51
Finite Difference Method....Pages 605-657
Solving Transient Heat Conduction Problems by Means of Finite Element Method (FEM)....Pages 659-691
Numerical-Analytical Methods....Pages 693-731
Solving Inverse Heat Conduction Problems by Means of Numerical Methods....Pages 733-763
Heat Sources....Pages 765-797
Melting and Solidification (Freezing)....Pages 799-829
Back Matter....Pages 831-889
....