N. Simões^1,2, A. Tadeu²

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 221-234, 2005, DOI:10.3970/cmes.2005.009.221

Abstract The use of the Boundary Element Method (BEM) to formulate the 3D transient heat transfer through cylindrical structures with irregular cross-sections, bounded by a homogeneous elastic medium, is described in this paper. In this formulation, both the conduction and the convection phenomena are modeled. This system can be subjected to heat emitted by either point or line sources located somewhere in the media. The solution is first obtained in the frequency domain for a wide range of frequencies and axial wavenumbers. Time domain responses are later calculated by means of (fast) inverse Fourier transforms into More >

Y.C. Shiah¹, T.L. Guao¹, C.L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 321-338, 2005, DOI:10.3970/cmes.2005.007.321

Abstract It is well known in elastic stress analysis using the boundary element method (BEM) that an additional volume integral appears in the basic form of the boundary integral equation if thermal effects are considered. In order to restore this general numerical tool as a truly boundary solution technique, it is perhaps most desirable to transform this volume integral exactly into boundary ones. For general 2D anisotropic thermo-elastostatics without heat sources, this was only achieved very recently. The presence of concentrated heat sources in the domain, however, leads to singularities at these points that pose additional More >

B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 185-194, 2005, DOI:10.3970/cmes.2005.007.185

Abstract This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady More >

Y.C. Hon¹, T. Wei²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >

S. Bargmann, P. Steinmann¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 133-150, 2005, DOI:10.3970/cmes.2005.009.133

Abstract The present contribution is concerned with the modeling and computation of non-classical heat conduction. In the 90s Green and Naghdi presented a new theory which is fully consistent. We suggest a solution method based on finite elements for the spatial as well as for the temporal discretization. A numerical example is compared to existing experimental results in order to illustrate the performance of the method. More >

P. A. C. Porto¹, A. B. Jorge¹, G. O. Ribeiro²

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 65-78, 2005, DOI:10.3970/cmes.2005.010.065

Abstract This work deals with a numerical solution technique for the self-regular gradient form of Green's identity, the flux boundary integral equation (flux-BIE). The required C^1,α inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C⁰ elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular More >

C.-W. Chang¹, C.-S. Liu², J.-R. Chang^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 13-38, 2005, DOI:10.3970/cmes.2005.010.013

Abstract In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index r = 1/2ν Δt is investigated. When the numerical results are compared with exact solutions, it 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 More >

Marcello Lappa¹

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 171-188, 2005, DOI:10.3970/fdmp.2005.001.171

Abstract The paper presents a comparative and critical analysis of some theoretical/experimental/numerical arguments concerning the possible stabilization of the surface-tension-driven (Marangoni) flow in the Floating Zone technique and in various related fluid-dynamic models. It is conceived as a natural extension of the focused overview published in Cryst. Res. Tech. 40(6), 531, (2005) where much room was devoted to discuss the intrinsic physical mechanisms responsible for three-dimensional and oscillatory flows in a variety of technological processes. Here, a significant effort is provided to illustrate the genesis of possible control strategies (many of which are still in a More >

C. W. Lan¹, B. C. Yeh

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.1, pp. 33-44, 2005, DOI:10.3970/fdmp.2005.001.033

Abstract The suppression of unstable Marangoni convection in floating-zone crystal growth by magnetic fields has enjoyed over recent years a widespread use as a reliable and useful strategy. A transversal direction of the field is particularly efficient, but asymmetric zone shapes and thus segregation are induced. Counter-rotation of the feed and of the crystal rods is a common way to improve dopant homogeneity. However, its effects under magnetic fields are complex and have not yet been studied in detail. In the present analysis, three-dimensional (3D) simulations based on a finite-volume/multigrid method are used to illustrate the More >