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) More >

Dye-Zone A. Chen, Gang Chen^*

Frontiers in Heat and Mass Transfer, Vol.1, No.2, pp. 1-6, 2010, DOI:10.5098/hmt.v1.2.3005

Abstract We present a calculation of the thermally generated electromagnetic flux propagating along the in-plane direction of a polar, thin film. The approach is based on fluctuational electrodynamics and the fluctuation-dissipation theorem. We find that for silicon carbide films between 5 nm and 100 nm thick, the thinner films transport more in-plane flux due to the long propagation length of the anti-symmetric surface phonon-polariton mode. Comparison of results obtained from the fluctuation-dissipation approach and the kinetic theory approach shows favorable agreement. More >

Moran Wang^a, Bin-Yang Cao^b, Zeng-Yuan Guo^b,*

Frontiers in Heat and Mass Transfer, Vol.1, No.1, pp. 1-8, 2010, DOI:10.5098/hmt.v1.1.3004

Abstract The thermomass theory regards heat owning mass-energy duality, exhibiting energy-like features in conversion and mass-like features in transfer processes. The equivalent mass of thermal energy is determined by the mass-energy equivalence of Einstein, which therefore leads to the inertia of heat in transfer. In this work, we build up a thermomass gas model based on this theory to describe the fluid-flow-like heat conduction process in a medium. The equation of state and the governing equations for transport for the thermomass gas have been derived based on methodologies of the classical mechanics since the drift speed… More >

Harishchandra Thakur¹, K. M. Singh², P. K. Sahoo³

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 117-150, 2010, DOI:10.3970/cmes.2010.068.117

Abstract MLPG method is a meshfree method which removes the need of meshing of computational domain at any stage of numerical analysis. Current article extends MLPG method to nonlinear heat conduction in irregular domains including the problem of solid-liquid phase change. Moving least square (MLS) scheme is used to interpolate the trial function and a fourth order spline function is used as the test function. Method of direct interpolation is used to enforce essential boundary conditions. Nonlinearities in the problems are handled with an iterative predictor-corrector method. Time integration is performed using θ-method. MLPG method has More >

C.H. Tsai¹, D.L. Young², J. Kolibal³

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 53-72, 2010, DOI:10.3970/cmes.2010.066.053

Abstract The time evolution method of fundamental solutions (MFS) is proposed to solve backward heat conduction problems (BHCPs). The time evolution MFS belongs to one of the mesh-free numerical methods and is essentially composed of a sequence of diffusion fundamental solutions which exactly satisfy the heat conduction equations. Through correct treatment of temporal evolution, the resulting system of the time evolution MFS is smaller, and effectively decreases the possibility of ill-conditioning induced by such strongly ill-posed problems. Both one-dimensional and two-dimensional BHCPs are examined in this study, and the numerical results demonstrate the accuracy and stability More >

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 >