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 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 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 Calibration and Rescaling Principles for Nonlinear Inverse Heat Conduction and Parameter Estimation Problems written by Yinyuan Chen and published by . This book was released on 2015 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation provides a systematic method for resolving nonlinear inverse heat conduction problems based on a calibration formulation and its accompanying principles. It is well-known that inverse heat conduction problems are ill-posed and hence subject to stability and uniqueness issues. Regularization methods are required to extract the best prediction based on a family of solutions. To date, most studies require sophisticated and combined numerical methods and regularization schemes for producing predictions. All thermophysical and geometrical properties must be provided in the simulations. The successful application of the numerical methods relies on the accuracy of the related system parameters as previously described. Due to the existence of uncertainties in the system parameters, these numerical methods possess bias of varying magnitudes. The calibration based approaches are proposed to minimize the systematic errors since system parameters are implicitly included in the mathematical formulation based on several calibration tests. To date, most calibration inverse studies have been based on the assumption of constant thermophysical properties. In contrast, this dissertation focuses on accounting for temperature-dependent thermophysical properties that produces a nonlinear heat equation. A novel rescaling principle is introduced for linearzing the system. This concept generates a mathematical framework similar to that of the linear formulation. Unlike the linear formulation, the present approach does require knowledge of thermophysical properties. However, all geometrical properties and sensor characterization are completely removed from the system. In this dissertation, a linear one-probe calibration method is first introduced as background. After that, the calibration method is generalized to the one-probe and two-probe, one-dimensional thermal system based on the assumption of temperature-dependent thermophysical properties. All previously proposed calibration equations are expressed in terms of a Volterra integral equation of the first kind for the unknown surface (net) heat flux and hence requires regularization owning to the ill-posed nature of first kind equations. A new strategy is proposed for determining the optimal regularization parameter that is independent of the applied regularization approach. As a final application, the described calibration principle is used for estimating unknown thermophysical properties above room temperature.
Download or read book Inverse Heat Conduction written by James V. Beck and published by James Beck. 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 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 Heat Conduction Fifth Edition written by Sadık Kakac and published by CRC Press. This book was released on 2018-07-11 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Conduction, Fifth Edition, upholds its reputation as the leading text in the field for graduate students, and as a resource for practicing engineers. The text begins with fundamental concepts, introducing the governing equation of heat conduction, and progresses through solutions for one-dimensional conduction, orthogonal functions, Fourier series and transforms, and multi-dimensional problems. Integral equations, Laplace transforms, finite difference numerical methods, and variational formulations are then covered. A systematic derivation of the analytical solution of heat conduction problems in heterogeneous media, introducing a more general approach based on the integral transform method, has been added in this new edition, along with new and revised problems, and complete problem solutions for instructors.
Download or read book Resolving Nonlinear Inverse Heat Conduction Problem by the Property Transformed Calibration Integral Equation Method Utilizing Novel Sequential and Phase Plane Strategies for Optimization written by Hongchu Chen and published by . This book was released on 2017 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic "parameter free" calibration integral equation method is proposed for estimating the surface temperature and surface heat flux in the context of one-dimensional, transient, nonlinear inverse heat conduction problems. The calibration integral equation method can be formulated in terms of various probes arrangements. Temperature-dependent thermophysical properties and probe locations are not specified a priori but are implicitly accounted through the calibration campaigns. The final mathematical formulations involve Volterra integral equations of the first kind for the unknown surface temperature or surface heat flux. A first kind Chebyshev expansion possessing undetermined coefficients is applied for approximating the introduced property transform function. The undetermined expansion coefficients associated with the Chebyshev expansion are then estimated through calibration tests with known surface thermal conditions and probe responses. A time sequential testing procedure is illustrated and demonstrated for the model building process leading to the optimal truncation for the Chebyshev expansion. A future-time method is applied for stabilizing the ill-posed first kind Volterra integral equations. Phase plane and cross-correlation analyses are employed for estimating the optimal regularization parameter (i.e., the future-time parameter) from a spectrum of chosen values. The feasibility and robustness of the proposed approach are verified by numerical simulations. The effectiveness of using phase plane and cross-correlation analyses as a statistical tool for estimating optimal regularization parameters is also verified in the "parameter required" space marching method. This additional study demonstrates the universal nature of phase plane and cross-correlation analyses for estimating the optimal regularization parameter necessary for alternative numerical implementations.
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-12 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 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 Inverse Heat Transfer Problems written by Oleg Mikhaĭlovich Alifanov and published by Springer. This book was released on 1994 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Optimal Methods for Ill Posed Problems written by Vitalii P. Tanana and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems
Download or read book Boundary Element Method for Heat Conduction written by E. Divo and published by WIT Press (UK). This book was released on 2003 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph represents a contribution to integral equation methods. It provides the formulation of a boundary-only integral equation for field problems governed by variable coefficient partial differential equations. Although the authors concentrate on the heat conduction equation, the method they propose is general and applicable to a variety of engineering field problems.
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-20 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering. Features Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analytical–numerical approaches
Download or read book Heat Conduction written by Renato M. Cotta and published by . This book was released on 1997-06-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this rigorous and thorough analysis three concepts of heat conduction are studied: improved lumped-differential formulations, the generalized integral transform technique, and symbolic computation. Addressing problem formulation, solution methodology and computational implementation, the authors develop an improved lumped-differential formulation for heat conduction problems, present a unified hybrid numerical?analytical solution methodology for linear and nonlinear problems, and provide an introduction to mixed symbolic?numerical computation. Special topics and applications illustrate the theory, including extended surfaces, drying, ablation, conjugated problems and anisotropic media. Sample computer programs, using mixed symbolic?numerical computation, are presented in notebook format, developed within the Mathematica system.
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:
