N.S. Mera, L. Elliott, D.B. Ingham, D. Lesnic¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 101-106, 2000, DOI:10.3970/cmes.2000.001.403

Abstract In this paper the iterative algorithm proposed by [Kozlov and Maz'ya (1990)] for the backward heat conduction problem is extended in order to solve the Cauchy steady state heat conduction problem and the accuracy, convergence and stability of the numerical algorithm are investigated. The numerical results which are obtained confirm that this new iterative BEM procedure is accurate, convergent and stable with respect to increasing the number of boundary elements and decreasing the amount of noise which is added into the input data. More >

Antoine Fabre¹, Jordan Hristov^2*, 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±βT^m) 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 >

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 >

M. Mosaad², A. Ben-Nakhi², M. H. Al-Hajeri²

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.4, pp. 301-314, 2005, DOI:10.3970/fdmp.2005.001.301

Abstract This work deals with the problem of thermal interaction between two fluid media at two different bulk temperatures and separated by a vertical plate. The problem is analyzed by taking into account the heat conduction across the separating plate. The flow configuration considered is one in which the two vertical boundary layers of free and forced convection developed on plate sides are in parallel flow. The dimensionless parameters governing the thermal interaction mechanisms are analytically deduced. The obtained results are presented in graphs to demonstrate the heat transfer characteristics of investigated phenomenon. The work reports a means to estimate the… More >

Haolong Chen^1,2, Bo Yu¹, Huanlin Zhou^1*, Zeng Meng¹

CMC-Computers, Materials & Continua, Vol.53, No.4, pp. 271-290, 2017, DOI:10.3970/cmc.2017.053.271

Abstract The cuckoo search algorithm (CS) is improved by using the conjugate gradient method(CGM), and the CS-CGM is proposed. The unknown inner boundary shapes are generated randomly and evolved by Lévy flights and elimination mechanism in the CS and CS-CGM. The CS, CGM and CS-CGM are examined for the prediction of a pipe’s inner surface. The direct problem is two-dimensional transient heat conduction in functionally graded materials (FGMs). Firstly, the radial integration boundary element method (RIBEM) is applied to solve the direct problem. Then the three methods are compared to identify the pipe’s inner surfacewith the information of measured temperatures. Finally,… More >

H.-S. Wang^1,2, H. Jiang^3,4, B. Yang²

CMC-Computers, Materials & Continua, Vol.51, No.3, pp. 145-161, 2016, DOI:10.3970/cmc.2016.051.145

Abstract Potential field due to line sources residing on slender heterogeneities is involved in various areas, such as heat conduction, potential flow, and electrostatics. Often dipolar line sources are either prescribed or induced due to close interaction with other objects. Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect. In the present work, we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities. In a benchmark example of two parallel rods, we compare the line element solution with the boundary element solution to show… More >

Chien-Ching Ma^1,2, Yi-Tzu Chen²

CMC-Computers, Materials & Continua, Vol.36, No.2, pp. 177-201, 2013, DOI:10.3970/cmc.2013.036.177

Abstract Functionally graded material (FGM) is a particulate composite with continuously changing its thermal and mechanical properties in order to raise the bonding strength in the discrete composite made from different phases of material constituents. Furthermore, FGM is a potent tool to create an intermediate layer in metal–ceramic composites to avoid the properties discontinuities and reduce, thereby, the residual stresses. For the nonhomogeneous problem, the mathematical derivation is much complicated than the homogeneous case since the material properties vary with coordinate. To analyze the problem, the Fourier transform is applied and the general solution in transform domain is obtained. The inverse… More >

Chih-Wen Chang¹

CMC-Computers, Materials & Continua, Vol.24, No.3, pp. 209-238, 2011, DOI:10.3970/cmc.2011.024.209

Abstract In this study, we employ a semi-analytical scheme to resolve the three-dimensional backward heat conduction problem (BHCP) by utilizing a quasi-bound -ary concept. First, the Fourier series expansion method is used to estimate the temperature field u(x, y, z, t) at any time t < T. Second, we ponder a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for u(x, y, z, 0). The termwise separable property of the kernel function allows us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended.… More >

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 >

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 >