H. Htike^1,2, W. Chen^1,2,3, Y. Gu^1,2

CMC-Computers, Materials & Continua, Vol.24, No.1, pp. 1-14, 2011, DOI:10.3970/cmc.2011.024.001

Abstract In this paper, we investigate the application of the singular boundary method (SBM) to two-dimensional problems of steady-state heat conduction in isotropic bimaterials. A domain decomposition technique is employed where the bimaterial is decomposed into two subdomains, and in each subdomain, the solution is approximated separately by an SBM-type expansion. The proposed method is tested and compared on several benchmark test problems, and its relative merits over the other boundary discretization methods, such as the method of fundamental solution (MFS) and the boundary element method (BEM), are also discussed. More >

H. T. Chen¹,K. H. Hsu¹, S. K. Lee¹, L. Y. Haung¹

CMC-Computers, Materials & Continua, Vol.22, No.3, pp. 239-260, 2011, DOI:10.3970/cmc.2011.022.239

Abstract The inverse scheme of the finite difference method in conjunction with the least-squares scheme and experimental measured temperatures is proposed to solve a two-dimensional steady-state inverse heat conduction problem in order to estimate the natural-convection heat transfer coefficient under the isothermal situation [`h] iso from three vertical fins mounted on a vertical plate and fin efficiency hf for various values of the fin spacing and fin height. The measured fin temperatures and ambient air temperature are measured from the present experimental apparatus conducted in a small wind tunnel. The heat transfer coefficient on the middle fin of three vertical fins… More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 17-40, 2011, DOI:10.3970/cmc.2011.021.017

Abstract Only the left-boundary data of temperature and heat flux are used to estimate an unknown parameter function α(x) in T_t(x,t) = ∂(α(x)T_x)/∂x + h(x,t), as well as to recover the right-boundary data. When α(x) is given the above problem is a well-known inverse heat conduction problem (IHCP). This paper solves a mixed-type inverse problem as a combination of the IHCP and the problem of parameter identification, without needing to assume a function form of α(x) a priori, and without measuring extra data as those used by other methods. We use the one-step Lie-Group Adaptive Method (LGAM) for the semi-discretizations of… 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 integration of the discretized equations… 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 to the generalized cross-validation (GCV)… 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 tested,… More >

W.F.Yuan¹, K.H.Tan ¹

CMC-Computers, Materials & Continua, Vol.13, No.1, pp. 49-62, 2009, DOI:10.3970/cmc.2009.013.049

Abstract A simple cellular automaton (CA) scheme is proposed to simulate heat conduction in anisotropic domains. The CA is built on random nodes rather than an irregular grid. The local rule used in the CA is defined by physical concepts instead of differential equations. The accuracy of the proposed approach is verified by classical examples. As an application of the proposed method, the CA approach is incorporated into fibre model which is widely used in finite element analysis to calculate the temperature distribution on the cross-section of composite beams. Numerical examples demonstrate that the proposed scheme can be conveniently applied to… More >

Chih-Ping Wu^1,2, Shao-En Huang²

CMC-Computers, Materials & Continua, Vol.12, No.3, pp. 251-282, 2009, DOI:10.3970/cmc.2009.012.251

Abstract A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, doubly curved functionally graded (FG) piezo-thermo-elastic shells under thermal loads. Four different loading conditions, applied on the lateral surfaces of the shells, are considered. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of multilayered composite elastic plates/shells, is modified to be feasible for the present analysis of FG piezo-thermo-elastic plates/shells. The modifications include that a displacement-based formulation is replaced by a mixed… More >

Silieti, M.¹, Divo, E.², Kassab, A.J.¹

CMC-Computers, Materials & Continua, Vol.12, No.2, pp. 121-144, 2009, DOI:10.3970/cmc.2009.012.121

Abstract A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given… More >

LiviuMarin ¹

CMC-Computers, Materials & Continua, Vol.12, No.1, pp. 71-100, 2009, DOI:10.3970/cmc.2009.012.071

Abstract In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which 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 to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise… More >