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  • Open Access


    MLPG analysis of Nonlinear Heat Conduction in Irregular Domains

    Harishchandra Thakur1, K. M. Singh2, P. K. Sahoo3

    CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 117-150, 2010, DOI:10.3970/cmes.2010.068.117

    Abstract MLPG method is a meshfree method which removes the need of meshing of computational domain at any stage of numerical analysis. Current article extends MLPG method to nonlinear heat conduction in irregular domains including the problem of solid-liquid phase change. Moving least square (MLS) scheme is used to interpolate the trial function and a fourth order spline function is used as the test function. Method of direct interpolation is used to enforce essential boundary conditions. Nonlinearities in the problems are handled with an iterative predictor-corrector method. Time integration is performed using θ-method. MLPG method has More >

  • Open Access


    An Analysis of Backward Heat Conduction Problems Using the Time Evolution Method of Fundamental Solutions

    C.H. Tsai1, D.L. Young2, J. Kolibal3

    CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 53-72, 2010, DOI:10.3970/cmes.2010.066.053

    Abstract The time evolution method of fundamental solutions (MFS) is proposed to solve backward heat conduction problems (BHCPs). The time evolution MFS belongs to one of the mesh-free numerical methods and is essentially composed of a sequence of diffusion fundamental solutions which exactly satisfy the heat conduction equations. Through correct treatment of temporal evolution, the resulting system of the time evolution MFS is smaller, and effectively decreases the possibility of ill-conditioning induced by such strongly ill-posed problems. Both one-dimensional and two-dimensional BHCPs are examined in this study, and the numerical results demonstrate the accuracy and stability More >

  • Open Access


    A Dual-Reciprocity Boundary Element Simulation of Axisymmetric Dual-Phase-Lag Heat Conduction in Nonhomogeneous Media

    B.I. Yun1, W.T. Ang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.3, pp. 217-244, 2010, DOI:10.3970/cmes.2010.065.217

    Abstract A dual-reciprocity boundary element method is proposed for simulating numerically axisymmetric dual-phase-lag heat conduction in nonhomogeneous thermally isotropic media. The properties of the media, such as thermal conductivity and specific heat, are assumed to vary continuously in space. To check its validity and assess its accuracy, the proposed method is first applied to solve some specific test problems with known solutions. It is then used to simulate the axisymmetric dual-phase-lag heat conduction in a particular nonhomogeneous medium subject to a concentrated surface heating. The effects of the dual phase lags and the spatial variations of More >

  • Open Access


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

    J.H. Tian1,2, X. Han2, S.Y. Long2, G.Y. Sun2, Y. Cao1, G.Q. Xie3

    CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 101-116, 2010, DOI:10.3970/cmes.2010.063.101

    Abstract A transient 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 transient heat source acted on the FGM plates. The temperature distribution of the FGM plates is obtained in different time and different position. Some useful results for transient heat conduction are shown in figures. Applications of HNM to transient More >

  • Open Access


    Concurrent Atomistic/Continuum Simulation of Thermo-Mechanical Coupling Phenomena

    Xianqiao Wang1, James D. Lee1

    CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.2, pp. 150-170, 2010, DOI:10.3970/cmes.2010.062.150

    Abstract The concurrent methods for coupling molecular dynamics with continuum thermodynamics offer a myriad of challenging problems, mostly related with energy transmission, wave reflection, and damage propagation at the interfaces between the continuum description and the discrete description. In this work, by virtue of the atomistic field theory (AFT), we present an analysis to reconcile the compatibility between atomic region and continuum region and to calculate the matching temperature field of a heat conduction problem in a concurrent atomistic/continuum system. First, formulation of AFT with finite temperature and its corresponding finite element implementation are briefly introduced. More >

  • Open Access


    A Backward Group Preserving Scheme for Multi-Dimensional Backward Heat Conduction Problems

    Chih-Wen Chang1, Chein-Shan Liu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.3, pp. 239-274, 2010, DOI:10.3970/cmes.2010.059.239

    Abstract In this article, we propose a backward group preserving scheme (BGPS) to tackle the multi-dimensional backward heat conduction problem (BHCP). The BHCP is well-known as severely ill-posed because the solution does not continuously depend on the given data. When eight numerical examples (including nonlinear and nonhomogeneous BHCP, and Neumann and Robin conditions of homogeneous BHCP) are examined, we find that the BGPS is applicable to the multi-dimensional BHCP. Even with noisy final data, the BGPS is also robust against disturbance. The one-step BGPS effectively reconstructs the initial data from the given final data, which with More >

  • Open Access


    Analytic Closed Solution for the Heat Conduction with Time Dependent Heat Convection Coefficient at One Boundary

    Han Taw Chen1, Shao Lun Sun1, Hui Chen Huang1, Sen Yung Lee1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 107-126, 2010, DOI:10.3970/cmes.2010.059.107

    Abstract A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for More >

  • Open Access


    A Scalable Meshless Formulation Based on RBF Hermitian Interpolation for 3D Nonlinear Heat Conduction Problems

    David Stevens1, Henry Power1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111

    Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the More >

  • Open Access


    The Inverse Problem of Determining Heat Transfer Coefficients by the Meshless Local Petrov-Galerkin Method

    J. Sladek1, V. Sladek1, P.H. Wen2, Y.C. Hon3

    CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 191-218, 2009, DOI:10.3970/cmes.2009.048.191

    Abstract The meshless local Petrov-Galerkin (MLPG) method is used to solve the inverse heat conduction problem of predicting the distribution of the heat transfer coefficient on the boundary of 2-D and axisymmetric bodies. Using this method, nodes are randomly distributed over the numerical solution domain, and surrounding each of these nodes, a circular sub-domain is introduced. By choosing a unit step function as the test function, the local integral equations (LIE) on the boundaries of these sub-domains are derived. To eliminate the time variation in the governing equation, the Laplace transform technique is applied. The local… More >

  • Open Access


    Analytical Exact Solutions of Heat Conduction Problems for a Three-Phase Elliptical Composite

    Ching Kong Chao1,2, Chin Kun Chen1, Fu Mo Chen3

    CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.3, pp. 283-298, 2009, DOI:10.3970/cmes.2009.047.283

    Abstract Analytical exact solutions of a fundamental heat conduction problem for a three-phase elliptical composite under a remote uniform heat flow are provided in this paper. The steady-state temperature and heat flux fields in each phase of an elliptical composite are analyzed in detail. Investigations on the present heat conduction problem are tedious due to the presence of material inhomogeneities and geometric discontinuities. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and heat flux are derived explicitly in a More >

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