Download or read book Solution of General Two dimensional Inverse Heat Conduction Problems and One dimensional Inverse Melting Problems written by John Siuming Tu and published by . This book was released on 1988 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Heat Transfer Problems written by Oleg M. Alifanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion a.nd absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize to the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.
Download or read book Inverse Heat Conduction written by Hamidreza Najafi and published by John Wiley & Sons. This book was released on 2023-03-02 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Heat Conduction A comprehensive reference on the field of inverse heat conduction problems (IHCPs), now including advanced topics, numerous practical examples, and downloadable MATLAB codes. The First Edition of the classic book Inverse Heat Conduction: III-Posed Problems, published in 1985, has been used as one of the primary references for researchers and professionals working on IHCPs due to its comprehensive scope and dedication to the topic. The Second Edition of the book is a largely revised version of the First Edition with several all-new chapters and significant enhancement of the previous material. Over the past 30 years, the authors of this Second Edition have collaborated on research projects that form the basis for this book, which can serve as an effective textbook for graduate students and as a reliable reference book for professionals. Examples and problems throughout the text reinforce concepts presented. The Second Edition continues emphasis from the First Edition on linear heat conduction problems with revised presentation of Stolz, Function Specification, and Tikhonov Regularization methods, and expands coverage to include Conjugate Gradient Methods and the Singular Value Decomposition method. The Filter Matrix concept is explained and embraced throughout the presentation and allows any of these solution techniques to be represented in a simple explicit linear form. Two direct approaches suitable for non-linear problems, the Adjoint Method and Kalman Filtering, are presented, as well as an adaptation of the Filter Matrix approach applicable to non-linear heat conduction problems. In the Second Edition of Inverse Heat Conduction: III-Posed Problems, readers will find: A comprehensive literature review of IHCP applications in various fields of engineering Exact solutions to several fundamental problems for direct heat conduction problems, the concept of the computational analytical solution, and approximate solution methods for discrete time steps using superposition of exact solutions which form the basis for the IHCP solutions in the text IHCP solution methods and comparison of many of these approaches through a common suite of test problems Filter matrix form of IHCP solution methods and discussion of using filter-form Tikhonov regularization for solving complex IHCPs in multi-layer domain with temperature-dependent material properties Methods and criteria for selection of the optimal degree of regularization in solution of IHCPs Application of the filter concept for solving two-dimensional transient IHCP problems with multiple unknown heat fluxes Estimating the heat transfer coefficient, h, for lumped capacitance body and bodies with temperature gradients Bias in temperature measurements in the IHCP and correcting for temperature measurement bias Inverse Heat Conduction is a must-have resource on the topic for mechanical, aerospace, chemical, biomedical, or metallurgical engineers who are active in the design and analysis of thermal systems within the fields of manufacturing, aerospace, medical, defense, and instrumentation, as well as researchers in the areas of thermal science and computational heat transfer.
Download or read book Solving Direct and Inverse Heat Conduction Problems written by Jan Taler and published by Springer Science & Business Media. This book was released on 2010-04-16 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a solution for direct and inverse heat conduction problems, discussing the theoretical basis for the heat transfer process and presenting selected theoretical and numerical problems in the form of exercises with solutions. The book covers one-, two- and three dimensional problems which are solved by using exact and approximate analytical methods and numerical methods. An accompanying CD-Rom includes computational solutions of the examples and extensive FORTRAN code.
Download or read book Inverse Heat Transfer written by M. Necat Ozisik and published by Routledge. This book was released on 2018-05-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the fundamental concepts of inverse heat transfer problems. It presents in detail the basic steps of four techniques of inverse heat transfer protocol, as a parameter estimation approach and as a function estimation approach. These techniques are then applied to the solution of the problems of practical engineering interest involving conduction, convection, and radiation. The text also introduces a formulation based on generalized coordinates for the solution of inverse heat conduction problems in two-dimensional regions.
Download or read book On the Approximate Solution of a Two dimensional Inverse Heat Conduction Problem written by J. Baumeister and published by . This book was released on 1986 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Heat Conduction written by James V. Beck and published by Wiley-Interscience. This book was released on 1985-10-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the only commercially published work to deal with the engineering problem of determining surface heat flux and temperature history based on interior temperature measurements. Provides the analytical techniques needed to arrive at otherwise difficult solutions, summarizing the findings of the last ten years. Topics include the steady state solution, Duhamel's Theorem, ill-posed problems, single future time step, and more.
Download or read book A New Implicit in Time with Space Marching Two dimensional Inverse Heat Conduction Method written by and published by . This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new combination of methods used to solve the transient, two-dimensional inverse heat conduction problem (IHCP) is presented in this thesis. A simple implicit in time with space marching approach is used in combination with digital filtering for regularization. Results are presented for both one-dimensional and two-dimensional problems. As much as 10% measurement error is added to the data to simulate experimental results. One-dimensional results with "perfect" data suggested that refining the spatial and temporal meshes improved the accuracy of the inverse solution. However, the nodal Fourier number was found to have no effect on accuracy. Further investigation into the effect of the Fourier number on the inverse solution led to the discovery of a precisely defined stability criterion, which is presented for the one-dimensional problem. The digital filter was proven to be a highly effective regularization method for both the one-dimensional and two-dimensional cases. The Gauss low pass filter employed a cutoff frequency as the regularization parameter, which has an exact definition with physical significance. No trial and error method of choosing a regularization parameter was necessary. Temperature and heat flux data were given at the sensor sites, noise was added to the data, filtered, and used as input data to the inverse code. The prediction error resulting from the use of "perfect" data suggested a bias (over-prediction). With this bias removed from the noisy, filtered results, the inverse solution was accurate to 2% for the 1D case and 3% for the 2D case. The dramatic reduction of error through an inverse process was striking, since the inverse problem is well-known to magnify measurement errors. An additional case using only one line of temperature data and no heat flux data was used as alternate approach to the inverse problem. The new strategy relies on a recently developed integral relationship between the heating rate and the heat flux, which is valid on the half-space. The relationship allows for the heat flux to be found at the sensor site using only temperature and heating rate data. This data could be experimentally obtained using one line of thermocouples combined with numerical differentiation to obtain the heating rate; no heat flux gauges or second series of thermocouples are necessary. This thesis is the first to take advantage of heat flux -- heating rate relationship. Results from this method with a measurement error of 5% predicted a surface heat flux error of only 5%.
Download or read book Solution to Two dimensional Non linear Boundary Inverse Heat Conduction Problems Using Finite Element Method written by Premanand Balagangadhar and published by . This book was released on 1996 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Starting Solution for Two dimensional Heat Conduction Problems with Change of Phase written by Bruno A. Boley and published by . This book was released on 1967 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short-time solution for two-dimensional change-of-phase problems for a half space is developed. The problems are such that melting starts at a point of the surface and spreads both along the surface and towards the interior of the body. Heating is applied by an analytic but otherwise general heat input. It is found that the shape of the melt interface is, when normalized, a universal function, i.e. independent of both the applied heat input and the material properties. Initial melt propagation normal to and along the surface are proportional to y to the 3/2 power and y to the 1/2 power respectively, where y is the non-dimensional time measured from the start of melting. (Author).
Download or read book Estimates of Error Introduced when One dimensional Inverse Heat Transfer Techniques are Applied to Multi dimensional Problems written by and published by . This book was released on 2000 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the errors introduced when one-dimensional inverse heat conduction techniques are applied to problems involving two-dimensional heat transfer effects was performed. The geometry used for the study was a cylinder with similar dimensions as a typical container used for the transportation of radioactive materials. The finite element analysis code MSC P/Thermal was used to generate synthetic test data that was then used as input for an inverse heat conduction code. Four different problems were considered including one with uniform flux around the outer surface of the cylinder and three with non-uniform flux applied over 360°, 180°, and 90° sections of the outer surface of the cylinder. The Sandia One-Dimensional Direct and Inverse Thermal (SODDIT) code was used to estimate the surface heat flux of all four cases. The error analysis was performed by comparing the results from SODDIT and the heat flux calculated based on the temperature results obtained from P/Thermal. Results showed an increase in error of the surface heat flux estimates as the applied heat became more localized. For the uniform case, SODDIT provided heat flux estimates with a maximum error of 0.5% whereas for the non-uniform cases, the maximum errors were found to be about 3%, 7%, and 18% for the 360°, 180°, and 90° cases, respectively.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Steady State Two dimensional Inverse Heat Transfer Problems written by Craig T. Wilberding and published by . This book was released on 1995 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for the Solution of a Three dimensional Anisotropic Inverse Heat Conduction Problem written by Marcus Soemers and published by . This book was released on 2008 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Two dimensional Formulation and Quasi one dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method CIEM written by Hongchu Chen and published by . This book was released on 2013 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recently devised calibration integral equation method developed at the University of Tennessee for resolving transient inverse heat conduction in one-dimensional applications is extended and studied in the context of two-dimensional linear inverse heat conduction. This study investigates a simplified plate geometry possessing three known boundary conditions and one unknown boundary condition. This plate contains a series of temperature sensors located on a fixed plane below the surface of interest. To begin the investigation, a quasi-one-dimensional formulation is proposed for predicting the surface heat flux (W/m2) based on a zonal formulation where each zone contains a single thermocouple. In this way, a locally one-dimensional view is proposed for predicting the local or zonal surface heat flux. The thermocouple data set is composed of physically two-dimensional information; however, each surface projection only considers one-dimensional heat flow based on its zone. In this concept, each zone produces a spatial constant heat flux that can temporally vary from zone-to-zone. Each zonal surface heat flux is mathematically described in terms of a Volterra integral equation of the first kind. Being ill posed, regularization based on a local future time method is introduced for stabilization. A new metric is proposed and demonstrated for extracting the optimal regularization parameter. This zonal approximation for materials composed of a low thermal conductivity is shown to yield favorable results. The second study presented in this thesis considers the development of a total heat transfer (W) calibration integral equation based on a fully two-dimensional analysis. In this form, the total surface heat transfer (i.e., the spatially integrated value along the entire surface of interest), is directly derived and implement bypassing the need to determine the local surface heat flux (W/m2). This formulation yields a Volterra integral equation of the first kind similar to the mathematical structure previously described. In many applications, the total surface heat transfer is more important than the local surface heat flux. As such, this new formulation appears highly pertinent. This formulation is shown to produce favorable results over a large range of thermal conductivities and thermal diffusivities.
Download or read book Finite Difference Methods in Heat Transfer written by Necati Ozisik and published by CRC Press. This book was released on 1994-04-25 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions.
Download or read book The Mollification Method and the Numerical Solution of Ill Posed Problems written by Diego A. Murio and published by John Wiley & Sons. This book was released on 2011-03-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations.
