Application of the Finite-Element Method to Heat-Transfer Problems. Part I. Finite-Element Method Applied to Heat-Conduction Solids with Nonlinear Boundary Conditions

Application of the Finite-Element Method to Heat-Transfer Problems. Part I. Finite-Element Method Applied to Heat-Conduction Solids with Nonlinear Boundary Conditions

Author: Shih-Chi Chu

Publisher:

Published: 1971

Total Pages: 51

ISBN-13:

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The finite-element method was extended to solid heat conduction with a radiation-convection, nonlinear heat-flux, boundary condition. General finite-element models are developed that enable approximate solutions of transient heat in an arbitrary three-dimensional body subjected to the described initial conditions and nonlinear or linear heat flux across the surfaces of the body. Applications of the present approach involve: (a) heat in a semi-infinite solid with radiation taking place at the surface, (b) transient temperature in a slab subjected to radiation and convection boundary conditions at both surfaces, and (c) heat transfer of a small-caliber multilayer gun tube subjected to time-dependent heat convection and radiation boundary conditions under automatic firing situations. Numerical solutions to the first and the second problem are compared with the exact solution and with results obtained by use of the probability method. (Author).


Finite Element Method

Finite Element Method

Author: Michael R. Gosz

Publisher: CRC Press

Published: 2017-03-27

Total Pages: 430

ISBN-13: 1351992031

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The finite element method (FEM) is the dominant tool for numerical analysis in engineering, yet many engineers apply it without fully understanding all the principles. Learning the method can be challenging, but Mike Gosz has condensed the basic mathematics, concepts, and applications into a simple and easy-to-understand reference. Finite Element Method: Applications in Solids, Structures, and Heat Transfer navigates through linear, linear dynamic, and nonlinear finite elements with an emphasis on building confidence and familiarity with the method, not just the procedures. This book demystifies the assumptions made, the boundary conditions chosen, and whether or not proper failure criteria are used. It reviews the basic math underlying FEM, including matrix algebra, the Taylor series expansion and divergence theorem, vectors, tensors, and mechanics of continuous media. The author discusses applications to problems in solid mechanics, the steady-state heat equation, continuum and structural finite elements, linear transient analysis, small-strain plasticity, and geometrically nonlinear problems. He illustrates the material with 10 case studies, which define the problem, consider appropriate solution strategies, and warn against common pitfalls. Additionally, 35 interactive virtual reality modeling language files are available for download from the CRC Web site. For anyone first studying FEM or for those who simply wish to deepen their understanding, Finite Element Method: Applications in Solids, Structures, and Heat Transfer is the perfect resource.


The Finite Element Method in Heat Transfer Analysis

The Finite Element Method in Heat Transfer Analysis

Author: Roland W. Lewis

Publisher: John Wiley & Sons

Published: 1996-08-06

Total Pages: 296

ISBN-13: 9780471943624

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Heat transfer analysis is a problem of major significance in a vast range of industrial applications. These extend over the fields of mechanical engineering, aeronautical engineering, chemical engineering and numerous applications in civil and electrical engineering. If one considers the heat conduction equation alone the number of practical problems amenable to solution is extensive. Expansion of the work to include features such as phase change, coupled heat and mass transfer, and thermal stress analysis provides the engineer with the capability to address a further series of key engineering problems. The complexity of practical problems is such that closed form solutions are not generally possible. The use of numerical techniques to solve such problems is therefore considered essential, and this book presents the use of the powerful finite element method in heat transfer analysis. Starting with the fundamental general heat conduction equation, the book moves on to consider the solution of linear steady state heat conduction problems, transient analyses and non-linear examples. Problems of melting and solidification are then considered at length followed by a chapter on convection. The application of heat and mass transfer to drying problems and the calculation of both thermal and shrinkage stresses conclude the book. Numerical examples are used to illustrate the basic concepts introduced. This book is the outcome of the teaching and research experience of the authors over a period of more than 20 years.


Finite Element Analysis for Heat Transfer

Finite Element Analysis for Heat Transfer

Author: Hou-Cheng Huang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 205

ISBN-13: 1447120914

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This text presents an introduction to the application of the finite ele ment method to the analysis of heat transfer problems. The discussion has been limited to diffusion and convection type of heat transfer in solids and fluids. The main motivation of writing this book stems from two facts. Firstly, we have not come across any other text which provides an intro duction to the finite element method (FEM) solely from a heat transfer perspective. Most introductory texts attempt to teach FEM from a struc tural engineering background, which may distract non-structural engineers from pursuing this important subject with full enthusiasm. We feel that our approach provides a better alternative for non-structural engineers. Secondly, for people who are interested in using FEM for heat transfer, we have attempted to cover a wide range of topics, presenting the essential the ory and full implementational details including two FORTRAN programs. In addition to the basic FEM heat transfer concepts and implementation, we have also presented some modem techniques which are being used to enhance the accuracy and speed of the conventional method. In writing the text we have endeavoured to keep it accessible to persons with qualifications of no more than an engineering graduate. As mentioned earlier this book may be used to learn FEM by beginners, this may include undergraduate students and practicing engineers. However, there is enough advanced material to interest more experienced practitioners.


The Finite Element Method in Heat Transfer and Fluid Dynamics

The Finite Element Method in Heat Transfer and Fluid Dynamics

Author: J. N. Reddy

Publisher: CRC Press

Published: 2010-04-06

Total Pages: 515

ISBN-13: 1439882576

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As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. The Finite Element Method in Heat Transfer and Fluid Dynamics, Th


The Finite Element Method

The Finite Element Method

Author: Darrell W. Pepper

Publisher: Taylor & Francis

Published: 2005-10-31

Total Pages: 326

ISBN-13: 0203942353

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This much-anticipated second edition introduces the fundamentals of the finite element method featuring clear-cut examples and an applications-oriented approach. Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications, including structural analysis and fluid flow. Much attention is given to the development of the discrete set of algebraic equations, beginning with simple one-dimensional problems that can be solved by inspection, continuing to two- and three-dimensional elements, and ending with three chapters describing applications. The increased number of example problems per chapter helps build an understanding of the method to define and organize required initial and boundary condition data for specific problems. In addition to exercises that can be worked out manually, this new edition refers to user-friendly computer codes for solving one-, two-, and three-dimensional problems. Among the first FEM textbooks to include finite element software, the book contains a website with access to an even more comprehensive list of finite element software written in FEMLAB, MAPLE, MathCad, MATLAB, FORTRAN, C++, and JAVA - the most popular programming languages. This textbook is valuable for senior level undergraduates in mechanical, aeronautical, electrical, chemical, and civil engineering. Useful for short courses and home-study learning, the book can also serve as an introduction for first-year graduate students new to finite element coursework and as a refresher for industry professionals. The book is a perfect lead-in to Intermediate Finite Element Method: Fluid Flow and Heat and Transfer Applications (Taylor & Francis, 1999, Hb 1560323094).


Fundamentals of the Finite Element Method for Heat and Fluid Flow

Fundamentals of the Finite Element Method for Heat and Fluid Flow

Author: Roland W. Lewis

Publisher: John Wiley and Sons

Published: 2008-02-07

Total Pages: 357

ISBN-13: 0470346388

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Heat transfer is the area of engineering science which describes the energy transport between material bodies due to a difference in temperature. The three different modes of heat transport are conduction, convection and radiation. In most problems, these three modes exist simultaneously. However, the significance of these modes depends on the problems studied and often, insignificant modes are neglected. Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions. Problems with slow fluid motion and heat transfer can be difficult problems to handle. Therefore, the complexity of combined fluid flow and heat transfer problems should not be underestimated and should be dealt with carefully. This book: Is ideal for teaching senior undergraduates the fundamentals of how to use the Finite Element Method to solve heat transfer and fluid dynamics problems Explains how to solve various heat transfer problems with different types of boundary conditions Uses recent computational methods and codes to handle complex fluid motion and heat transfer problems Includes a large number of examples and exercises on heat transfer problems In an era of parallel computing, computational efficiency and easy to handle codes play a major part. Bearing all these points in mind, the topics covered on combined flow and heat transfer in this book will be an asset for practising engineers and postgraduate students. Other topics of interest for the heat transfer community, such as heat exchangers and radiation heat transfer, are also included.


Fundamentals of the Finite Element Method for Heat and Mass Transfer

Fundamentals of the Finite Element Method for Heat and Mass Transfer

Author: Perumal Nithiarasu

Publisher: John Wiley & Sons

Published: 2016-03-07

Total Pages: 467

ISBN-13: 047075625X

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Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer. • Addresses fundamentals, applications and computer implementation • Educational computer codes are freely available to download, modify and use • Includes a large number of worked examples and exercises • Fills the gap between learning and research