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  • Open Access

    ARTICLE

    An Analysis of the Heat Conduction Problem for Plates with the Functionally Graded Material Using the Hybrid Numerical Method

    J.H. Tian1,2, X. Han2, S.Y. Long3, G.Q. Xie4

    CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 229-242, 2009, DOI:10.3970/cmc.2009.010.229

    Abstract A heat conduction analysis of the functionally graded material (FGM) plates has been investigated based on the hybrid numerical method (HNM). HNM combines the layer element method with the method of Fourier transforms and proves to be efficient and reliable. The FGM plates are infinite large and the material properties vary continuously through thickness. The heat source continually acted one the FGM plates. The temperature distribution of the FGM plates is obtained in different time and different position. Some useful results for heat conduction problems are shown in figures. This article applies HNM to heat More >

  • Open Access

    ARTICLE

    Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

    J. Sladek1, V. Sladek1, C.L. Tan2, S.N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 161-174, 2008, DOI:10.3970/cmes.2008.032.161

    Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by More >

  • Open Access

    ARTICLE

    The Method of Fundamental Solutions for Inverse Problems Associated with the Steady-State Heat Conduction in the Presence of Sources

    Liviu Marin1

    CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 99-122, 2008, DOI:10.3970/cmes.2008.030.099

    Abstract The application of the method of fundamental solutions (MFS) to inverse boundary value problems associated with the steady-state heat conduction in isotropic media in the presence of sources, i.e. the Poisson equation, is investigated in this paper. Based on the approach of Alves and Chen (2005), these problems are solved in two steps, namely by finding first an approximate particular solution of the Poisson equation and then the numerical solution of the resulting inverse boundary value problem for the Laplace equation. The resulting MFS discretised system of equations is ill-conditioned and hence it is solved More >

  • Open Access

    ABSTRACT

    The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems

    Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 69-80, 2007, DOI:10.3970/icces.2007.003.069

    Abstract By using a quasi-boundary regularization we can formulate a two-point boundary value problem of the backward heat conduction equation. The ill-posed problem is analyzed by using the semi-discretization numerical schemes. Then, the resulting ordinary differential equations in the discretized space are numerically integrated towards the time direction by the Lie-group shooting method to find the unknown initial conditions. The key point is based on the erection of a one-step Lie group element G(T) and the formation of a generalized mid-point Lie group element G(r). Then, by imposing G(T) = G(r) we can seek the missing More >

  • Open Access

    ARTICLE

    Meshless Local Petrov-Galerkin Collocation Method for Two-dimensional Heat Conduction Problems

    WU XueHong1, SHEN ShengPing2, TAO WenQuan1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.1, pp. 65-76, 2007, DOI:10.3970/cmes.2007.022.065

    Abstract Meshless local Petrov-Galerkin collocation method is applied to compute two-dimensional heat conduction problems in irregular domain. By taking the Dirac's Delta function as the test function, the local domain integration is avoided. The essential boundary conditions can be implemented easily in this method. A case that has analytical solution shows the present method can obtain desired accuracy and efficient. Two cases in engineering are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present More >

  • Open Access

    ARTICLE

    Development of Heat Input Estimation Technique for Simulation of Shell Forming by Line-Heating

    N. Osawa1, K. Hashimoto1, J. Sawamura1, J. Kikuchi2, Y. Deguchi2, T. Yamaura2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 43-54, 2007, DOI:10.3970/cmes.2007.020.043

    Abstract A new hypothesis regarding heat transmission during line heating is proposed. It states that the distribution of the temperature of the gas adjacent to the plate, TG, and the overall local heat transfer coefficient, α, depend only on the distance from the torch. An identification technique for TG and α is developed. The validity of the employed hypothesis and the proposed technique is demonstrated by comparing the measured and identified TG during a spot heating test. The plate temperature calculated by direct heat conduction analysis closely approximates the one measured for the spot and line heating tests, More >

  • Open Access

    ARTICLE

    An Efficient Simultaneous Estimation of Temperature-Dependent Thermophysical Properties

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 77-90, 2006, DOI:10.3970/cmes.2006.014.077

    Abstract In this paper we derive the first-order and second-order one-step GPS applied to the estimation of thermophysical properties. Solving the resultant algebraic equations, which usually converges within ten iterations, it is not difficult to estimate the unknown temperature-dependent thermal conductivity and heat capacity simultaneously, if some supplemented data of measured temperature at a time T is provided. When the measured temperature in the conducting slab is contaminated by noise, our estimated results are also good. The new method does not require any prior information on the functional forms of thermal conductivity and heat capacity. Numerical examples More >

  • Open Access

    ARTICLE

    Stability analysis for inverse heat conduction problems

    Xianwu Ling1, S.N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 219-228, 2006, DOI:10.3970/cmes.2006.013.219

    Abstract In this paper, two matrix algebraic tools are provided for studying the solution-stabilities of inverse heat conduction problems. The propagations of the computed temperature errors, as caused by a noise in temperature measurement, are presented. The spectral norm analysis reflects the effect of the computational time steps, the sensor locations and the number of future temperatures on the computed error levels. The Frobenius norm analysis manifests the dynamic propagations of the computed errors. As an application of the norm analysis, we propose a method for the best positioning of the thermocouples. More >

  • Open Access

    ARTICLE

    Past Cone Dynamics and Backward Group Preserving Schemes for Backward Heat Conduction Problems

    C.-S. Liu1, C.-W. Chang2, J.-R. Chang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067

    Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X˙ = B(X,t)X with t ∈ R, X ∈ Mn+1 lying on the past cone and Bso(n,1), was derived for the backward differential equations system x· =f(x,t), t ∈ R, x ∈ Rn. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step algorithm… More >

  • Open Access

    ARTICLE

    The method of fundamental solution for solving multidimensional inverse heat conduction problems

    Y.C. Hon1, T. Wei2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

    Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >

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