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 >

Shaligram Tiwari¹, Koichi Nishino²

FDMP-Fluid Dynamics & Materials Processing, Vol.6, No.1, pp. 109-136, 2010, DOI:10.3970/fdmp.2010.006.109

Abstract The present work reports about an experimental study investigating the influence of air convection and of ambient temperature around a half-floating zone on the transition behavior from steady to oscillatory flow, i.e. the influence on the critical Marangoni number (Macr). Increase of heat loss from the free surface of the half-floating zone or liquid bridge by increased convection and ambient cooling decreases Macr. Heat input to the free surface increases Macr. An add-on numerical simulation of the air convection around the zone clarifies the influence of air convection and the ambient temperature on the temperature, 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 >

Zhang¹ WD, DS Liu², JC Tian^1*, FL He¹

Phyton-International Journal of Experimental Botany, Vol.78, pp. 147-154, 2009, DOI:10.32604/phyton.2009.78.147

Abstract Soil arsenic contamination becomes a potential agricultural and environmental hazard worldwide, and has been a serious problem for safe food production. A field experiment on soil contamination was conducted on four wheat varieties (Jimai, Gaoyou, Weimai and Wennong) in Eastern China, using 50 or 100 mg arsenic/kg soil. Biomass production and yield components were determined and arsenic concentrations were measured in plant tissues. Differential arsenic effects on wheat varieties were determined at maturity. Results showed that addition of arsenic significantly (p<0.05) reduced root, stem and spike dry weight and yield components, which resulted in the… More >

Janja Kramer, Renata Jecl, Leopold Skerget

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 147-148, 2009, DOI:10.3970/icces.2009.012.147

Abstract A numerical study of double diffusive natural convection in porous media due to opposing buoyancy forces is reported, using the Boundary Domain Integral Method (BDIM). There have been several reported studies dealing with natural convection in porous media, mainly because of its importance in several industrial and technological applications. Less attention, however, has been dedicated to the so-called double diffusive problems, where density gradients occur due to the effects of combined temperature and concentration buoyancy. The current investigation is focused on the special problem, where the thermal and solutal buoyancy forces are opposing each other.
The… More >

Kai-Long Hsiao¹, Cheng-Hsing Hsu²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.9, No.1, pp. 3-22, 2009, DOI:10.3970/icces.2009.009.003

Abstract A conjugate forced convection with viscous dissipation heat transfer problem of a second-grade visco-elastic fluid past a flat plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, were analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat plate shape (wedge flow β = 0.0) on the fin surface were obtained by a generalized Falkner-Skan flow derivation.… More >