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Heat Conduction Problem (heat + conduction_problem)
Selected AbstractsA quantitative identification technique for a two-dimensional subsurface defect based on surface temperature measurementHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2009Chunli Fan Abstract The inverse identification of a subsurface defect boundary is an important part of an inverse heat conduction problem, and is also the basis for the quantitative development of a nondestructive thermographic inspection technique. For the commonly encountered quantitative thermographic defect identification problem when the test piece is heated from one part of the outer boundary, our previous study showed that some parts of the defect boundary are sensitive to the initial defect boundary prediction of the conjugate gradient method. In this paper, the heat transfer mechanism inside a test piece with this problem is analyzed by building a two-dimensional model. A new method, the multiple measurements combination method (MMCM), is also presented which combines the identification algorithm study with the optimization of the thermographic detection technique to solve the problem. Numerical experiments certified the effectiveness of the present method. The temperature measurement error and the initial prediction of the defect boundary shape have little effect on the identification result. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20251 [source] Application of inverse solution in two-dimensional heat conduction problem using Laplace transformationHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2003Masanori Monde Abstract An inverse solution has been explicitly derived for two-dimensional heat conduction in cylindrical coordinates using the Laplace transformation. The applicability of the inverse solution is checked using the numerical temperatures with a normal random error calculated from the corresponding direct solution. For a gradual temperature change in a solid, the surface heat flux and temperature can be satisfactorily predicted, while for a rapid change in the temperature this method needs the help of a time partition method, in which the entire measurement time is split into several partitions. The solution with the time partitions is found to make an improvement in the prediction of the surface heat flux and temperature. It is found that the solution can be applied to experimental data, leading to good prediction. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 602,617, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10115 [source] DQ-based simulation of weakly nonlinear heat conduction processesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008S. Tomasiello Abstract In this paper, an explicit form for the numerical solution of problems in the space,time domain by using quadrature rules is proposed. The compact form of the shape functions recently proposed by the author is useful to the scope. Numerical solutions for the time-dependent one-dimensional nonlinear heat conduction problem are calculated by means of the iterative differential quadrature method, a method proposed by the author and based on quadrature rules. The accuracy of the solution and stability analysis show good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] Transient heat conduction in a medium with multiple circular cavities and inhomogeneitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009Elizaveta Gordeliy Abstract A two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two- and three-dimensional problems demonstrates the effect of the dimensionality. Copyright © 2009 John Wiley & Sons, Ltd. [source] The identification of a Robin coefficient by a conjugate gradient methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Fenglian Yang Abstract This paper investigates a non-linear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. The variational formulation of the problem is given. The conjugate gradient method combining with the discrepancy principle for choosing the suitable stop step are proposed for solving the optimization problem, in which the finite difference method is used to solve the direct problems. The performance of the method is verified by simulating four examples. The convergence with respect to the grid refinement and the amount of noise in the data is also investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Distributed parameter thermal controllability: a numerical method for solving the inverse heat conduction problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004Marios Alaeddine Abstract This paper addresses the inverse heat conduction problem encountered in thermal manufacturing processes. A numerical control algorithm is developed for distributed parameter conduction systems, based on Galerkin optimization of an energy index employing Green's functions. Various temperature profiles of variable complexity are studied, using the proposed technique, in order to determine the surface heat input distribution necessary to generate the desired temperature field inside a solid body. Furthermore, the effect of altering the iterative time step and duration of processing time, on the convergence of the solution generated by the aforementioned method is investigated. It is proved that despite the variations in numerical processing, the iterative technique is able to solve the problem of inverse heat conduction in the thermal processing of materials. Copyright © 2004 John Wiley & Sons, Ltd. [source] Compact difference schemes for heat equation with Neumann boundary conditionsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2009Zhi-Zhong Sun Abstract In this article, two recent proposed compact schemes for the heat conduction problem with Neumann boundary conditions are analyzed. The first difference scheme was proposed by Zhao, Dai, and Niu (Numer Methods Partial Differential Eq 23, (2007), 949,959). The unconditional stability and convergence are proved by the energy methods. The convergence order is O(,2 + h2.5) in a discrete maximum norm. Numerical examples demonstrate that the convergence order of the scheme can not exceeds O(,2 + h3). An improved compact scheme is presented, by which the approximate values at the boundary points can be obtained directly. The second scheme was given by Liao, Zhu, and Khaliq (Methods Partial Differential Eq 22, (2006), 600,616). The unconditional stability and convergence are also shown. By the way, it is reported how to avoid computing the values at the fictitious points. Some numerical examples are presented to show the theoretical results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001Yoshihiro Ochiai Abstract If the initial temperature is assumed to be constant, a domain integral is not needed to solve unsteady heat conduction problems without heat generation using the boundary element method (BEM).However, with heat generation or a non-uniform initial temperature distribution, the domain integral is necessary. This paper demonstrates that two-dimensional problems of unsteady heat conduction with heat generation and a non-uniform initial temperature distribution can be solved approximately without the domain integral by the triple-reciprocity boundary element method. In this method, heat generation and the initial temperature distribution are interpolated using the boundary integral equation. Copyright © 2001 John Wiley & Sons, Ltd. 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