• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• 대한기계학회논문집B
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• 제25권7호
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• pp.989-996
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• 2001

High-speed and low-speed flows are simulated numerically by flowfield-dependent mixed explicit-implicit (FDMEI) method. This algorithm depends on implicitness parameters of convection, diffusion, diffusion gradients, and source terms which are calculated from the changes of local Mach, Reynolds, Peclet, and Damkohler numbers between adjacent nodes. Convection phenomena or shock waves are resolved from Mach number-dependent implicitness parameters whereas diffusion or viscous actions are simulated by Reynolds number or Peclet number-dependent implicitness parameters. Fluctuation components of all variables are properly accommodated spatially and temporally in the FDMEI procedure. To illustrate, some benchmark example problems are presented for comparisons of the FDMEI results with other available data. These results appear to be encouraging and point toward the need for further investigations of the FDMEI theory.

• 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)

• 한국결정성장학회지
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• 제31권3호
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• pp.127-136
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• 2021

This paper is dedicated to numerical simulation for diffusion-advective convection in a square cavity during physical vapor transport of Hg₂Br₂. Flow characteristics of the temperature difference between the source and crystal regions, 50℃ (300℃ → 250℃), partial pressures of component argon of 20 Torr and 100 Torr are investigated and presented as velocity vectors and streamlines, isotherms and iso-mass concentrations contours. Moreover, alterations of average Nusselt and average Sherwood numbers with (a) the source and crystal regions, (b) the pressures of component argon of 20 Torr and 100 Torr are analyzed and addressed in details. Both average Nusselt and average Sherwood numbers are seen to decrease with the increasing values of the partial pressures of component argon. Also, it is found that for the two different partial pressures of component argon, average Nusselt numbers at the source region are greater than at the crystal region, and inversely, average Sherwood numbers at the crystal region are greater than the source region by a factor of 3.

• 한국전산유체공학회지
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• 제19권1호
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• pp.15-20
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• 2014

Accurate simulation of free-surface wave flows around a ship is very important for better hull-form design. In this paper, a computational fluid dynamics (CFD) code, termed SNUFOAM, which is based on the open source libraries, OpenFOAM, was developed to predict the wave patterns around a ship. Additional anti-diffusion source term for minimizing a numerical diffusion, which was caused by convection differencing scheme, was considered in the volume-fraction transport equation. The influence of the anti-diffusion source term was tested by applying it to free-surface wave flow around the Wigley model ship. In results, the band width of the volume fraction contours between 0.1 to 0.9 at the hull surface was narrowed by considering the anti-diffusion term.

• 한국결정성장학회지
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• 제16권5호
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• pp.203-209
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• 2006

For $P_B=50,\;{\Delta}T=10K$, Ar=5, Pr=2.36, Le=0.015, Pe=1.26, Cv=1.11, the intensity of solutal convection (solutal Grashof number $Grs=3.44x10^4$) is greater than that of thermal convection (thermal Grashof number $Grt=1.81x10^3$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A($Hg_2Cl_2$) and B(He). With increasing the partial pressure of component B from 10 up to 200 Torr, the rate is decreased exponentially. The convective transport decreases with lower g level and is changed to the diffusive mode at 0.1 $g_0$. In other words, for regions in which the g level is 0.1 $g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than 0.1 $g_0$ can be adequate to ensure purely diffusive transport.

• 대한기계학회논문집B
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• 제25권7호
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• pp.958-966
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• 2001

This study has examined the microstructural development in the Bridgman type directional solidification of hyper-peritectic Sn-Cd alloys, and the temperature and flow field have been numerically simulated to see if there is any change induced by convection. The directional solidification experiments carried out in quartz tubes with inside diameters of 0.4∼6mm showed that the resulting microstructures are clearly dependent on the size of tube diameters. The bigger ampoules where the effect of convection is highly expected produced saw-like structures resulting from the primary $\alpha$ and peritectic $\beta$ phase growing together at a planar solid-liquid front, with the former being surrounded by the latter. In the smaller ampoules, where the effect of convection is expected low however, the saw structure disappears, and as is understood from the theoretical prediction based on diffusion-controlled solidification the initial growth of the primary $\alpha$ phase is replaced by the nucleation of the peritectic $\beta$ phase whose growth continues to the end of the solidification.

• 대한의용생체공학회:의공학회지
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• 제29권5호
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• pp.376-383
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• 2008

High-flux dialysis treatment removes various toxins via diffusion as well as convection, which is induced by ultrafiltration and backfiltration. In this study, in vitro (Using the distilled water and the bovine's blood) comparison test was performed to determine whether utilization of a high flux dialyzer paired with different pumps would increase the efficiency of convection. At the same blood flow rates, a pulsatile pump and a roller pump were employed to propel the distilled water and bovine whole blood to a high flux dialyzer. Pressures at the dialyzer inlet and outlet in the blood circuit and in the dialysate circuit were measured, respectively. From these data, we calculated the transmembrane pressure and predicted the ultrafiltration and backfiltration rates developed by both pumps. Using the bovine's blood experiment, ultrafiltration and backfiltration rates were 1.6 times higher with the pulsatile pump than with the roller pump. We conclude that utilization of a pulsatile pump in high flux hemodialysis treatments increases ultrafiltration volume, compared with a roller pump under conditions of the same blood flow rate.

• 공업화학
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• 제33권1호
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• pp.96-102
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• 2022

고분자전해질막 연료전지의 반응물인 수소와 산소는 기체 상태이므로, 반응물이 원활히 전달될수록 작동 전압의 손실을 줄일 수 있다. 높은 전류밀도 영역에서 산소 물질 전달이 전압 손실을 좌우하므로, 환원극 유로의 형상 변경에 대한 연구들이 진행되어 왔다. 환원극 유로 형상 중에서 유로를 막는 블록은 반응물을 다공성 매질인 기체확산층으로 강제 대류 하도록 사용되었다. 본 연구에서는 간단한 단 채널의 연료전지 모델에 블록을 배치하였다. 전산 유체역학을 사용하였고, 공기 공급 유량을 달리하였을 때 블록으로 인한 강제 대류 효과가 전압-전류 곡선과 국부 전류 밀도에 대한 영향을 연구하였다. 기체확산층으로의 강제 대류 현상을 통하여 적은 공기 공급 유량으로도 높은 전류 밀도를 얻을 수 있었다. 다수의 블록을 직렬로 배치한 경우에 1개의 블록만 배치한 것보다 강제 대류 효과를 증가시켜 높은 전류밀도를 얻을 수 있었다.

• 한국결정성장학회지
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• 제34권2호
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• pp.48-54
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• 2024

브로민화 수은(I)(Hg₂Br₂) 자체 확산 물리적 증착법 공정에서 자체 확산 전달현상 연구에서 얻어진 결론은 10^-3g₀ ≤ g ≤ 1g₀ 영역에서는 열 대류현상이 지배적이며, g = 10^-4g₀ 영역에서는 대류에서 확산영역으로 전이되는 영역이며, 10^-6g₀ ≤ g ≤ 10^-5g₀ 영역에서는 확산모드가 지배적이다. Hg₂Br₂의 총 몰플럭스는 중력가속도의 레벌(level)이 1/10 크기로 감소함에 따라 기하급수적으로 감소함을 나타내고 있다는 것이다. 10℃ ≤ ΔT ≤ 50℃의 온도차 범위에서는 온도차(ΔT)와 Hg₂Br₂의 총 몰플럭스에 대한 관계식은 선형적으로 직선적 비례관계성을 보여주고 있다.