• Journal of applied mathematics & informatics
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• v.26 no.5_6
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.7
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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.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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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)

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.31 no.3
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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.

• Journal of computational fluids engineering
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• v.19 no.1
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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.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.5
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.7
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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.

• Journal of Biomedical Engineering Research
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• v.29 no.5
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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.

• Applied Chemistry for Engineering
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• v.33 no.1
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• pp.96-102
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• 2022

Reactants of PEMFC are hydrogen and oxygen in gas phases and fuel cell overpotential could be reduced when reactants are smoothly transported. Numerous studies to modify cathode flow field design have been conducted because oxygen mass transfer in high current density region is dominant voltage loss factor. Among those cathode flow field designs, a block in flow field is used to forced supply reactant gas to porous gas diffusion layer. In this study, the block was installed on a simple fuel cell model. Using computational fluid dynamics (CFD), effects of forced convection due to blocks on a polarization curve and local current density contour were studied when different air flow rates were supplied. The high current density could be achieved even with low air supply rate due to forced convection to a gas diffusion layer and also with multiple blocks in series compared to a single block due to an increase of forced convection effect.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.34 no.2
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• pp.48-54
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• 2024

During the Hg₂Br₂ physical vapor transport process with self-diffusion, it is concluded that for 10^-3g₀≤ g ≤ 1g₀ the thermal buoyancy driven convection is dominant in the vapor phase; at the gravitational level of g = 10^-4g₀, the transition region from the convection to diffusion occurs; for 10^-6g₀ ≤ g ≤ 10^-5g₀, the diffusion mode is predominant. The total molar flux of Hg₂Br₂ decays exponentially with the decreasing of one tenth of gravitational magnitude. For 10℃ ≤ ΔT ≤ 50℃, the total molar flux increases linearly and directly with the temperature difference between the source and crystal regions.