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 >

K. Han¹, Y. T. Feng¹, D. R. J. Owen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 143-162, 2009, DOI:10.3970/cmes.2009.049.143

Abstract Motivated by Hottel's crossed-string method, this paper presents an accurate algorithm for the evaluation of the geometric view factors in a randomly packed bed of circular particles of various sizes. The radiative heat exchange can thus be predicted accurately. The solution procedure is illustrated and the solution accuracy is assessed via a numerical example. 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 >

Alfredo Nicolás¹, Blanca Bermúdez², Elsa Báez³

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 83-106, 2009, DOI:10.3970/cmes.2009.048.083

Abstract Numerical results of natural convection flows in two-dimensional cavities, filled with air, are presented to study the effects on the characteristics of the flows as some parameters vary: the Rayleigh number Ra and the aspect ratio A of the cavity. This kind of thermal flows may be modeled by the unsteady Boussinesq approximation in stream function-vorticity variables. The results are obtained with a simple numerical scheme, previously reported for isothermal/mixed convection flows, based mainly on a fixed point iterative process applied to the non-linear elliptic system that results after time discretization. The evolution of the flows,… More >

Ching Kong Chao^1,2, Chin Kun Chen¹, Fu Mo Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.3, pp. 283-298, 2009, DOI:10.3970/cmes.2009.047.283

Abstract Analytical exact solutions of a fundamental heat conduction problem for a three-phase elliptical composite under a remote uniform heat flow are provided in this paper. The steady-state temperature and heat flux fields in each phase of an elliptical composite are analyzed in detail. Investigations on the present heat conduction problem are tedious due to the presence of material inhomogeneities and geometric discontinuities. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and heat flux are derived explicitly in a More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.047.001

Abstract In this paper an analytical method for approximating the solution of backward heat conduction problem is presented. The Fourier series expansion technique is used to formulate a first-kind Fredholm integral equation for the temperature field u(x,t) at any time t < T, when the data are specified at a final time T. Then we consider a direct regularization, instead of the Tikhonov regularization, by adding the term αu(x,t) to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us by transforming it to a two-point boundary value problem, and thus a closed-form solution More >

Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 107-128, 2009, DOI:10.3970/cmes.2009.046.107

Abstract We consider an inverse problem for estimating an unknown time dependent heat source H(t) in a heat conduction equation u_t(x,t) = u_xx(x,t) + H(t). First this inverse problem is formulated as a three-point boundary value problem (BVP) for ODEs discretized from the transformed homogeneous governing equation. To treat this three-point BVP we develop a two-stage Lie-group shooting method (TSLGSM). The novel approach is examined through numerical examples to convince that it is rather accurate and efficient; the estimation error is small even for identifying discontinuous and oscillatory heat sources under noise. More >

Chia-Yi Cheng, Cha’o-Kuang Chen¹, Yue-Tzu Yang

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 203-218, 2009, DOI:10.3970/cmes.2009.044.203

Abstract This paper seeks to utilize the residual correction method in coordination with the evolutionary monotonic iteration technique to obtain upper and lower approximate solutions of non-linear heat transfer problem of the annular hyperbolic profile fins whose thermal conductivity vary with temperature. First, the monotonicity of a non-linear differential equation is reinforced by using the monotone iterative technique. Then, the cubic spline method is applied to discretize and convert the differential equation into the mathematical programming problems. Finally, based on the residual correction concept, the complicated constraint inequality equations can be transferred into the simple iterative More >

Yueting Zhou¹, Xing Li², Dehao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 191-222, 2009, DOI:10.3970/cmes.2009.043.191

Abstract The transient response of an orthotropic functionally graded strip with a partially insulated crack under convective heat transfer supply is considered. It is modeled there exists thermal resistant in the heat conduction through the crack region. The mixed boundary value problems of the temperature field and displacement field are reduced to a system of singular integral equations in Laplace domain. The expressions with high order asymptotic terms for the singular integral kernel are considered to improve the accuracy and efficiency. The numerical results present the effect of the material nonhomogeneous parameters, the orthotropic parameters and More >