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  • Open Access


    A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

    Chengxin Zhang1, Chao Wang1, Shouhai Chen2,*, Fajie Wang1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2407-2424, 2023, DOI:10.32604/cmes.2023.024884

    Abstract This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively.… More >

  • Open Access


    A Novel Meshfree Analysis of Transient Heat Conduction Problems Using RRKPM

    Hongfen Gao1, Gaofeng Wei2,3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1793-1814, 2022, DOI:10.32604/cmes.2022.019687

    Abstract By introducing the radial basis functions (RBFs) into the reproducing kernel particle method (RKPM), the calculating accuracy and stability of the RKPM can be improved, and a novel meshfree method of the radial basis RKPM (meshfree RRKPM) is proposed. Meanwhile, the meshfree RRKPM is applied to transient heat conduction problems (THCP), and the corresponding equations of the meshfree RRKPM for the THCP are derived. The two-point time difference scheme is selected to discretize the time of the THCP. Finally, the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP. More >

  • Open Access


    Isogeometric Boundary Element Analysis for 2D Transient Heat Conduction Problem with Radial Integration Method

    Leilei Chen1, Kunpeng Li1, Xuan Peng2, Haojie Lian3,4,*, Xiao Lin5, Zhuojia Fu6

    CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 125-146, 2021, DOI:10.32604/cmes.2021.012821

    Abstract This paper presents an isogeometric boundary element method (IGABEM) for transient heat conduction analysis. The Non-Uniform Rational B-spline (NURBS) basis functions, which are used to construct the geometry of the structures, are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations. B´ezier extraction technique is employed to accelerate the evaluation of NURBS basis functions. We adopt a radial integration method to address the additional domain integrals. The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis. More >

  • 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


    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


    MLPG Method for Transient Heat Conduction Problem with MLS as Trial Approximation in Both Time and Space Domains

    D. Mirzaei1, M. Dehghan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.3, pp. 185-210, 2011, DOI:10.3970/cmes.2011.072.185

    Abstract The meshless local Petrov-Galerkin (MLPG) method with an efficient technique to deal with the time variable are used to solve the heat conduction problem in this paper. The MLPG is a meshless method which is (mostly) based on the moving least squares (MLS) scheme to approximate the trial space. In this paper the MLS is used for approximation in both time and space domains, and we avoid using the time difference discretization or Laplace transform method to overcome the time variable. The technique is applied for continuously nonhomogeneous functionally graded materials (FGM) in a finite strip and a hallow cylinder.… 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 heat conduction are firstly presented… More >

  • Open Access


    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 a spherical subdomain to which… More >

  • Open Access


    Transient Heat Conduction in Materials with Linear Power-Law Temperature-Dependent Thermal Conductivity: Integral-Balance Approach

    Antoine Fabre1, Jordan Hristov2*, Rachid Bennacer1

    FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.2, pp. 69-85, 2016, DOI:10.3970/fdmp.2016.012.069

    Abstract Closed form approximate solutions to nonlinear transient heat conduction with linear power-law k = k0(1±βTm) temperature-dependent thermal diffusivity have been developed by the integral-balance integral method under transient conditions. The solutions use improved direct approaches of the integral method and avoid the commonly used linearization by the Kirchhoff transformation. The main steps in the new solutions are improvements in the integration technique of the double-integration technique and the optimization of the exponent of the approximate parabolic profile with unspecified exponent. Solutions to Dirichlet boundary condition problem have been developed as examples by the classical Heat-balance Integral method (HBIM) and the… More >

  • Open Access


    A Bond Graph Model Validation of an Experimental Single Zone Building

    A. Merabtine1, S. Mokraoui1, R. Benelmir1, N. Laraqi2

    FDMP-Fluid Dynamics & Materials Processing, Vol.8, No.2, pp. 215-240, 2012, DOI:10.3970/fdmp.2012.008.215

    Abstract Modeling of the thermal behavior of buildings needs effective strategies of analysis and tools. This is particularly true when conduction of heat through walls and/or slabs has to be properly taken into account. This article is concerned with a new modeling strategy for solving the transient heat conduction equation in a finite medium (with extensive background application to the different elements of a building structure). The developed approach is based on the Bond Graph technique, a graphical modeling language which is particularly suitable to the treatment of problems involving energy transfer. With this model, two typical transient heat conduction situations… More >

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