• Journal of the korean Society of Automotive Engineers
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• v.11 no.1
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• pp.20-30
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• 1989

The unsteady conjugate forced convection-conduction heat transfer from a plate fin is numerically studied. The external forced flow is steady but the temperature of the fin base is an exponential change with time. Therefore, the unsteady energy equations of the fluid and the fin are solved simultaneously under the conditions of equality in heat flux and temperature at the fluid-fin interface at every instant of time. Numerical results are given for various quantities of interest including the local heat transfer coefficient, the local heat flux, the total heat transfer rate and the temperature distribution of fin under the effects of the convection-conduction parameter and the ratio of thermal diffusivities. The results of the present numerical solution have been compared with those of the conventional fin theory.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.8 s.239
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• pp.903-910
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• 2005

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and finite-difference Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach that adopts the hybrid genetic algorithm as an initial value selector and uses the finite-difference Newton method as an optimization procedure.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.45-63
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• 2006

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.2
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• pp.741-751
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• 1996

The coupled conduction and convection heat transfer from the protruding heat source in a vertical channel is numerically investigated. Conjugate solution of the two-dimensional energy equation is obtained for the incompressible air flow over the rectangular block with local heat source. It was found that several recirculation zones and separation bubble near the block were related to Re and Gr. And the results show that fractions of the heat transfer through each of the block face, maximum temperature of the block and the relative effect of each parameter on the maximum temperature and heat transfer.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.143-153
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• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• Journal of Advanced Marine Engineering and Technology
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• v.31 no.7
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• pp.833-841
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• 2007

The aim of this paper is to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flow adjacent to a vertical flat plate under boundary layer approximation. Using the similarity transformations the governing boundary layer equations for momentum and energy are reduced to a system of partial differential equations and then solved numerically using Finite Difference Method(FDM) known as the Keller-box scheme. Computed solutions to the governing equations are obtained for a wide range of non-dimensional parameters that are present in this problem, namely the coupling parameter P. the Prandtl number Pr and the heat generation parameter Q. The variations of the local heat transfer rate as well as the interface temperature and the friction along the plate and typical velocity and temperature profiles in the boundary layer are shown graphically. Numerical solutions have been consider for the Prandtl number Pr=0.70

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.675-688
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• 2014

In this paper, we present an efficient way to determine a suitable value of the regularization parameter using the global generalized cross validation and analyze the experimental results from preconditioned global conjugate gradient linear least squares(Gl-CGLS) method in solving image deblurring problems. Preconditioned Gl-CGLS solves general linear systems with multiple right-hand sides. It has been shown in [10] that this method can be effectively applied to image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-CGLS method can give better reconstructions of the true image than other parameters considered in this study.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.5
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• pp.632-639
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• 2000

Conjugate heat transfer from a heat generating module ($31{\times}31{\times}7mm^3$) bonded through the module support on the floor of a parallel-plate channel(20mm high, 400mm wide, and 800mm long) to mixed convective air flow(0.2${\sim}$0.9m/s) is studied experimentally. The input power to the module is changed in a range 1.0${\sim}$4.5W, the floor thickness 0.2${\sim}$5mm, and the thermal resistance of module support, Rc:=0.06, 1.03 and 82.0K/W. Thermal conductance(Uc) of the board and convective thermal conductance($U_A$) from the module were derived, and the effect of V; Rc and t on Uc was investigated. It is found that the conjugate conductance (Uc) and the conductive heat transfer ratio ($Q_B$/Q) depend on the thermal resistance of the module support, the air velocity and the board thickness. The change of the module support resistance and the board thickness helps to elucidate the relative significance of heat transfer paths through the module support, the board, and from the board surface to the air. Additional information is investigated about the dependence of the heat transfer rate on the mixed convection parameter.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2100-2107
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• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.1-4
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• 1999

The Helmholtz equation is very important in physics and engineering. However, solution of the Helmholtz equation is in general known as a very difficult phenomenon. For if the ${\omega}$ is negative, the FDM discretized linear system becomes indefinite, whose solution by iterative method requires a very clever preconditioner. In this paper we assume that ${\omega}$ is nonnegative, and determine the optimal ${\rho}$ parameter for the three dimensional ADI iteration for the Helmholtz equation. The ADI(Alternating Direction Implicit) method is also getting new attentions due to the fact that it is very suitable to the vector/parallel computers, for example, as a preconditioner to the Krylov subspace methods. However, classical ADI was developed for two dimensions, and for three dimensions it is known that its convergence behaviour is quite different from that in two dimensions. So far, in three dimensions the so-called Douglas-Rachford form of ADI was developed. It is known to converge for a relatively wide range of ${\rho}$ values but its convergence is very slow. In this paper we determine the necessary conditions of the ${\rho}$ parameter for the convergence and optimal ${\rho}$ for the three dimensional ADI iteration of the Peaceman-Rachford form for the real Helmholtz equation with nonnegative ${\omega}$. Also, we conducted some experiments which is in close agreement with our theory. This straightforward extension of Peaceman-rachford ADI into three dimensions will be useful as an iterative solver itself or as a preconditioner to the the Krylov subspace methods, such as CG(Conjugate Gradient) method or GMRES(m).