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  • Open Access


    Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials

    Yiqiang Li1, Liang Ma2, Zhiqiang Yang3, Xiaofei Guan4, Yufeng Nie1, Zihao Yang1, 2

    CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 1-24, 2018, DOI:10.3970/cmes.2018.115.001

    Abstract This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition. A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is proposed. In the statistical multiscale formulations, a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations, which are our main contributions. Besides, a numerical algorithm based on the statistical multiscale method is given in details. Numerical results prove the accuracy and efficiency of our method for multiscale… More >

  • Open Access


    A Multi-Layered Model for Heat Conduction Analysis of Thermoelectric Material Strip

    Shenghu Ding1,*, Qingnan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.3, pp. 335-349, 2018, DOI:10.3970/cmes.2018.114.335

    Abstract A multi-layered model for heat conduction analysis of a thermoelectric material strip (TEMs) with a Griffith crack under the electric flux and energy flux load has been developed. The materials parameters of the TEMs vary continuously in an arbitrary manner. To derive the solution, the TEMs is divided into several sub-layers with different material properties. The mixed boundary problem is reduced to a system of singular integral equations, which are solved numerically. The effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied. More >

  • Open Access


    Solving the Cauchy problem of nonlinear steady-state heat conduction equations by using the polynomial expansion method and the exponentially convergent scalar homotopy method (ECSHA)

    Weichung Yeih, Chia-Min Fan, Zen-Chin Chang,Chen-Yu Ku

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.2, pp. 43-44, 2011, DOI:10.3970/icces.2011.020.043

    Abstract In this paper, the Cauchy problem of the nonlinear steady-state heat conduction is solved by using the polynomial expansion method and the exponentially convergent scalar homotopy method (ECSHA). The nonlinearity involves the thermal dependent conductivity and mixed boundary conditions having radiation term. Unlike the regular boundary conditions, Cauchy data are given on part of the boundary and a sub-boundary without any information exists in the formulation. We assume that the solution for a two-dimensional problem can be expanded by polynomials as: where T is the temperature distribution, np is the maximum order of polynomial expansion, x and y are Cartesian… More >

  • Open Access


    A Fictitious Time Integration Method for One-Dimensional Nonhomogeneous Backward Heat Conduction Problems

    Chih-Wen Chang

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.1, pp. 19-20, 2011, DOI:10.3970/icces.2011.016.019

    Abstract In this study, we propose a new numerical approach for solving the nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time I" is used to transform the dependent variable u(x, t) into a new one by (1+I")u(x, t)=: v(x, t, I"), such that the original nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, t, I"). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by utilizing a group preserving scheme. Several numerical instances illustrate that the present algorism… More >

  • Open Access


    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 initial conditions through a minimum… More >

  • Open Access


    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 three-dimensional examples. More >

  • Open Access


    Numerical Treatment of Domain Integrals without Internal Cells in Three-Dimensional BIEM Formulations

    Yoshihiro Ochiai1, Vladimir Sladek2

    CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 525-536, 2004, DOI:10.3970/cmes.2004.006.525

    Abstract The conventional boundary element method (BEM) uses internal cells for the domain integralsCwhen solving nonlinear problems or problems with domain effects. This paper is concerned with conversion of the domain integral into boundary ones and some non-integral terms in a three-dimensional BIEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. The method is based on a three-dimensional interpolation method in this paper by using a polyharmonic function with volume distribution. In view of this interpolation method, the three-dimensional numerical integration is replaced by boundary ones and preceding calculation of… More >

  • Open Access


    2.5D Green's Functions in the Frequency Domain for Heat Conduction Problems in Unbounded, Half-space, Slab and Layered Media

    António Tadeu1, Julieta António and Nuno Simões

    CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 43-58, 2004, DOI:10.3970/cmes.2004.006.043

    Abstract This Analytical Green's functions for the steady-state response of homogeneous three-dimensional unbounded, half-space, slab and layered solid media subjected to a spatially sinusoidal harmonic heat line source are presented. In the literature, this problem is frequently referred to as the two-and-a-half dimensional fundamental solution or 2.5D Green's functions.
    The proposed equations are theoretically interesting in themselves and they are also useful as benchmark results for validating numerical applications. They are also of great practical use in the formulation of three dimensional heat transfer problems in layered solid formations using integral transform methods and/or boundary elements.
    The final expressions… More >

  • Open Access


    A Differential Quadrature Method for Multi-Dimensional Inverse Heat Conduction Problem of Heat Source

    Jiun-Yu Wu1,2, Chih-Wen Chang3

    CMC-Computers, Materials & Continua, Vol.25, No.3, pp. 215-238, 2011, DOI:10.3970/cmc.2011.025.215

    Abstract In this paper, we employ the differential quadrature method (DQM) to tackle the inverse heat conduction problem (IHCP) of heat source. These advantages of this numerical approach are that no a priori presumption is made on the functional form of the estimates, and that evaluated heat source can be obtained directly in the calculation process. Seven examples show the effectiveness and accuracy of our algorism in providing excellent estimates of unknown heat source from the given data. We find that the proposed scheme is applicable to the IHCP of heat source. Even though the noise is added to the exact… More >

  • Open Access


    A Novel Spacetime Collocation Meshless Method for Solving Two-Dimensional Backward Heat Conduction Problems

    Chihyu Liu1, Chengyu Ku1,2,*, Jingen Xiao1, Weichung Yeih1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.1, pp. 229-252, 2019, DOI:10.31614/cmes.2019.04376

    Abstract In this article, a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem (BHCP) is proposed. The spacetime collocation meshless method (SCMM) is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of variables. Numerical solutions of the heat conduction problem are expressed as a series using the addition theorem. Because the basis functions are the general solutions of the governing equation, the boundary points may be collocated on the spacetime boundary of the domain. The proposed method is verified by conducting several heat conduction problems.… More >

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