• 한국해안해양공학회:학술대회논문집
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• 한국해안해양공학회 2003년도 한국해안해양공학발표논문집
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• pp.208-215
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• 2003

Convective-diffusion equations appear in various disciplines such as hydrology, chemical engineering and oceanography dealing with the transport problem of scalar quantities. Since it is nonlinear, numerical methods are generally used to obtain its solution. Very limited number of analytical solutions are available usually in cases when the convective velocity is constant or has a simple functional form (for some collection of the solutions, see Noye, 1987). There is however a continuing need to develop analytical solutions because of its practical importance. Analytical solutions of the convection-diffusion equation are valuable not only for the better understanding on the transport process but the verification of numerical schemes. (omitted)

• 대한기계학회논문집
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• 제14권2호
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• pp.453-462
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• 1990

The interaction of forced convection-conduction with thermal radiation in laminar boundary layer over a plate fin is studied numerically. The analysis is based on complete solution whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum and energy in the fluid boundary layer adjacent to the fin. The fluid is a gray medium and diffusion(Rosseland) approximation is used to describe the radiative heat flux in the energy equation. The resulting boundary value problem are convection-conduction parameter N$_{c}$ and radiation-conduction parameter m, Prandtl number Pr. Numerical results are presented for gases with the Prandtl numbers of 0.7 & 5 with values of N$_{c}$ and M ranging from 0 to 10 respectively. The object of this study is to provide the first results on forced convection-radiation interaction in boundary layer flow over a semi-infinite flay plate which can be used for comparisons with future studies that will consider a more accurate expression for the radiative heat flux. The agreement of the results from the complete solution presented by E. M. Sparrow and those from this paper for the special case of M=0 is good. The overall rate of heat transfer from the fin considering radiative effect is higher than that from the fin neglecting radiative effect. The local heat transfer coefficient with radiative effect is higher than that without radiative effect. In the direction from tip to base, those coefficients decrease at first, attain minimum, and then increase. The larger values of N$_{c}$ M, Pr give rise to larger fin temperature variations and the fin temperature without radiative effect is always higher than that with radiative effect.

• 한국해안해양공학회지
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• 제10권4호
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• pp.165-173
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• 1998

파고와 주기 그리고 수심의 함수로 정의된 이류계수를 파고와 주기에 대한 결합분포함수와 확률적으로 결합하여 수중둔덕의 이동율을 예측할 수 있는 해석해를 유도하였다. 파랑의 비선형성에 의하여 유발되는 하상에서의 흐름이 표사의 이동을 유발한다는 가정하에 개념적 모형의 표사이동량 방정식을 사용하였다. 표사보존식에 표사이동량을 대입하여 시간에 따른 해저면의 변동을 나타내는 비선형 이류-확산 방정식을 얻을 수 있었다. 해석해에 의하면 수심이 증가할 수록 수중둔덕의 이동율은 지수적으로 감소하는 경향을 보였다. 그러나 스펙트럼에서 주파수 영역의 폭을 정의하는 계수, v의 값이 커지면 수중둔덕의 이동율은 증가하였다. 해석해에 의하여 예측된 수중둔덕의 이동율은 관측자료보다 과대평가하는 경향을 나타내나, 해석해를 유도하는 과정에 내포된 이론식의 제약성 및 입력자료의 부정확성 등을 고려할 때 전반적으로 해석해의 결과는 관측자료와 잘\ulcorner 일치한다고 볼 수 있다. 특히, 수심의 변화에 따른 해석해의 거동은 대상영역 외해에서 추정된 자료를 이용하여 이산화 기법으로 추정된 결과와 매우 잘 일치하였다.

• 한국수자원학회논문집
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• 제31권5호
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• pp.599-612
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• 1998

수송방정식의 양면적은 특성으로 인하여 이송항이 지배적인 흐름에 있어서 수송방정식의 수채해석은 매우 난해하다. 특히 유한요소법을 사용하여 수치해석할 때, 상류방향으로 더 많은 가중치를 두기 위하여 변화된 시행함수를 사용한다. 이러한 방법을 Petrov-Galerkin 방법이라고 한다. 본 논문에서는 N+1 과 N+2 Petrov-Galerkin 방법을 격자 Peclet 수가 큰 수송문제에 적용하였다. 주파수맞춤 기법을 사용하여 N+2 Petrov- Galerkin 방법을 격자 Peclet 수가 큰 소송문제에 적용하였다. 주파수맞춤 기법을 사용하여 N+2 Petrov-Galerkin 방법의 적정 풍상정도를 찾아내었고, 그 결과를 토의하였다. 이 기법의 시행함수는 이송항과 확산항의 상대적 크기에 따라 그 모양이 변화된다. 수치실험을 통하여 제시된 새로운 수치해석기법의 우수성을 설명하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권2호
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• pp.123-140
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• 2009

The effect of a solute concentration difference on the osmotic transport of water through the semi-permeable membrane of a simple cell model is investigated. So far, most studies on osmotic phenomena are described by simple diffusion-type equations ignoring all fluid motion or described by Stokes flow. In our work, as the governing equations, we consider the coupled full Navier-Stokes equations which describe the fluid motion and the full transport equation that takes into account of convection and diffusion effects. A two dimensional finite difference model has been developed to simulate the velocity field, concentration field, and semi-permeable membrane movement. It is shown that the cell swells to regions of lower solute concentration due to the uneven water flux through the semi-permeable membrane. The simulation is applied on a red blood cell geometry and the relevant results are presented.

• 대한기계학회논문집
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• 제16권6호
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• pp.1171-1178
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• 1992

본 연구에서는 직접접촉식 열교환기를 이용한 실험을 통하여 열교환기 설계에 가장 중요한 열교환기 단위 체적당 총괄 열전달 계수를 시스템의 작동조건에 따라 구 하여 실제 설계자료로 이용하는 데 그 목적이 있다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1601-1606
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• 대한기계학회논문집B
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• 제28권7호
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• pp.809-817
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Water Engineering Research
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• 제2권3호
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• pp.179-185
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• 2001

The time consuming and expensive nature of experimental research on scouring processes caused by flowing water makes it attractive to develop numerical tools for the predication of the interaction of the fluid flow and the movable bed. In this paper the numerical simulation of scour by a wall jet is presented. The flow is assumed to be two-dimensional, and the alluvium is cohesionless. The solution process, repeated at each time step, involves simulation of a turbulent wall jet flow, solution of the convection-diffusion of sand concentration, and prediction of the bed deformation. For simulation of the jet flow, the governing equations for momentum, mass balance and turbulent parameters are solved by the finite volume method. The SIMPLE scheme with momentum interpolation is used for pressure correction. The convection-diffusion equation is solved for sediment concentration. A boundary condition for concentration at the bed, which takes into account the effect of bed-load, is implemented. The time rate of deposition and scour at the bed is obtained by solving the continuity equation for sediment. The shape and position of the scour hole and deposition of the bed material downstream of the hole appear realistic.