B.I. Yun¹, W.T. Ang^1,2

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 >

J.H. Tian^1,2, 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 >

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 >

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 >

Han Taw Chen¹, Shao Lun Sun¹, Hui Chen Huang¹, Sen Yung Lee^1,2

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 >

David Stevens¹, Henry Power^1,2

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 >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.19, No.3, pp. 285-314, 2010, DOI:10.3970/cmc.2010.019.285

Abstract In this article, we propose a new numerical approach for solving these multi-dimensional nonlinear and nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time t is employed to transform the dependent variable u(x, y, z, t) into a new one by (1+t)u(x, y, z, t)=: v(x, y, z, t, t), such that the original nonlinear and nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, y, z, t, t). In addition, a fictitious viscous damping coefficient can be used to strengthen the stability of numerical More >

Liviu Marin¹

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 233-274, 2010, DOI:10.3970/cmc.2010.017.233

Abstract We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according More >

Chih-Wen Chang¹, Chein-Shan Liu², Jiang-Ren Chang³

CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 45-66, 2010, DOI:10.3970/cmc.2010.015.045

Abstract In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were More >

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 >