• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.5
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• pp.226-232
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• 2004

One predicts the crystal growth rate of ZnSe with a low vapor pressure system in a horizontal configuration based on one dimensional advection-diffusion and two-dimensional diffusion-convection model. The present results show that for the ratios of partial pressures, s = 0.2 and 2.9, the growth rate increases with the temperature differences between the source and crystal. As the ratio of partial pressure approaches the stoichiometric value, s = 2 from s = 1.5 (zinc-deficient case: s < 2) and 2.9 (zinc-rich case: s > 2), the rate increases sharply. For the ranges from 1.5 to 1.999 (zinc-deficient case: s < 2) and from s = 9 to 2.9 (zinc-rich case: s > 2), the rate are slightly varied. From the viewpoint of the order of magnitude, the one-dimensional model for low vapor pressure system falls within the 2D predictions, which indicates the flow fields would be advective-diffusive. For the effects of gravitational accelerations on the rate, the gravitational constants are varied from 1 g to $10^{-6}$ g for $\Delta$T = 50 K and s = 1.5, the rates remain nearly constant, i.e., 211 mg/hr, which indicates Stefan flow is dominant over convection.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.2
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• pp.130-140
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• 1993

Average particle deposition velocity toward a horizontal semiconductor wafer in vertical airflow is measured by a wafer surface scanner(PMS SAS-3600). Use of wafer surface scanner requires very short exposure time normally ranging from 10 to 30 minutes, and hence makes repetition of experiment much easier. Polystyrene latex (PSL) spheres of diameter between 0.2 and $1.0{\mu}m$ are used. The present range of particle sizes is very important in controlling particle deposition on a wafer surface in industrial applications. For the present experiment, convection, diffusion, and sedimentation comprise important agents for deposition mechanisms. To investigate confidence interval of experimental data, mean and standard deviation of average deposition velocities are obtained from more than ten data set for each PSL sphere size. It is found that the distribution of mean of average deposition velocities from the measurement agrees well with the predictions of Liu and Ahn(1987) and Emi et al.(1989).

• Water Engineering Research
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• v.2 no.3
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.128-140
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• 1994

Coastal areas, especially embayments are apt to be polluted easily and many embayments in Korea are already suffering from pollution problems. To manage such pollution, it is strongly needed to develop technique to trace movements of pollution. Such technique cove- ring the embayment affected by the tidal influence, should take account both of the convection and the diffusion motions which cause lots of problems in numerical calculation. In this study, a Eulerian-Lagrangian Analysis(ELA) model was applied to Young Il bay and tested for its applicablity, which was developed by using the Eulerian-Lagrangian Method that reduce the numerical disperison and oscillation by way of solving convection and diffusion terrns separately. Concentration of Chemical Oxygen Demand(COD) and Suspend Solid(SS) of the embay- ment area were estimated by the model and compared with the observed values and the sound results were obtained. At the same time the diffsion coefficient and decay coefficient for Chemical Oxygen Demand in the Young II Bay were found as Dx = Dy = 20m$^2$/sec, kd=2.5 ${\times}$ 10-5/sec respectively, and for Suspend Solid, Dx =Dy = 30m$^2$/sec, kd=5.0${\times}$ 10-5/sec

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.165-173
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• 1998

Analytical solutions to predict the movement rate of submerged mound are derived using the convection coefficient and the joint distribution function of wave heights and periods. Assuming that the sediment is moved onshore due to the velocity asymmetry of Stokes' second order nonlinear wave theory, the micro-scale bedload transport equation is applied to the sediment conservation. The nonlinear convection-diffusion equation can then be obtained which governs the migration of submerged mound. The movement rate decreases exponentially with increasing the water depth, but the movement rate tends to increase as the spectral width parameter, $ u$ increases. In comparison of the analytical solution with the measured data, it is found that the analytical solution overestimates the movement rate. However, the agreement between the analytical solution and the measured data is encouraging since this over-estimation may be due to the inaccuracy of input data and the limitation of sediment transport model. In particular, the movement rates with respect to the water depth predicted by the analytical solution are in very good agreement with the estimated result using the discritization technique with the hindcast wave data.

• Journal of Korea Water Resources Association
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• v.31 no.5
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• pp.599-612
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• 1998

Numerical analysis of convection-dominated transport problems are challenging because of dual characteristics of the governing equation. In the finite element method, a strategy is to modify the test function to weight more in the upwind direction. This is called as the Petrov-Galerkin method. In this paper, both N+1 and N+2 Petrov-Galerkin methods are applied to transport problems at high grid Peclet number. Frequency fitting algorithm is used to obtain optimal levels of N+2 upwinding, and the results are discussed. Also, a new Petrov-Galerkin method, named as "Optimal Test Function Petrov-Galerkin Method," is proposed in this paper. The test function of this numerical method changes its shape depending upon relative strength of the convection to the diffusion. A numerical experiment is carried out to demonstrate the performance of the proposed method.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.31-48
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• 2010

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• Journal of the Korean Chemical Society
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• v.5 no.1
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• pp.80-83
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• 1961

Solution of the diffusion problem applicable to steady state reduction at the ideal streaming mercury electrode are presented, with special attention being given to the influence of stream contraction caused by the gravity. To eliminate the convection occurring in the layer between the streaming mercury and the electrolytic solution, a new method have been invented, in this case the solution being tested was streamed with same velocity of the streaming mercury. Experiment have been made in order to compare the experimental value with the theoretical value and the experimental diffusion current was approached more to the theoretical value than the value obtained by earlier form of the streaming mercury electrode used by Heyrovsky.

• Applied Chemistry for Engineering
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• v.27 no.3
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• pp.335-341
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• 2016

In this study, impurity effects on diffusive-convection flow fields by physical vapor transport under terrestrial and microgravity conditions were numerically analyzed for the mixture of $Hg_2Cl_2-I_2$ system. The numerical analysis provides the essence of diffusive-convection flow as well as heat and mass transfer in the vapor phase during the physical vapor transport through velocity vector flow fields, streamlines, temperature, and concentration profiles. The total molar fluxes at the crystal regions were found to be much more sensitive to both the gravitational acceleration and the partial pressure of component $I_2$ as an impurity. Our results showed that the solutal effect tended to stabilize the diffusive-convection flow with increasing the partial pressure of component $I_2$. Under microgravity conditions below $10^{-3}g_0$, the flow fields showed a one-dimensional parabolic flow structure indicating a diffusion-dominant mode. In other words, at the gravitational levels less than $10^{-3}g_0$, the effects of convection would be negligible.