• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.382-390
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• 1992

The problem of natural convection from a vertical fin is solved by coupling the thermal diffusion equation in the fin to the constitutive equations of the ambient medium involving the radiation of the medium. The analysis is accomplished by employing an integral method. The governing equations for the problem are solved by shooting method based on the Runge-Kutta Scheme at Pr= 0.7. For the range of values of the fin parameter and the radiation-conduction parameter in the analysis, the numerical results show that the radiation effects play an important role in the heat transfer and enhance the heat transfer.

• Journal of the Korean Society of Safety
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• v.5 no.2
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• pp.6-16
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• 1990

In this paper, the natural convection in a square enclosure, partly heated from below, with two adiabatic vertical wall and one upper horigental wall is studied nomerically. In numerical study, SIMPLE(Semi-Implicit for Pressure Linked Equation) algorithems are applied for the integration of momentum and energy equation. The grid size used in this study is the coordinates of size (22$\times$22). As a result of numerical analysis, the initial fluid flow depends on the thermal diffusion, but, as time passes, the fluid flow depends on convection and buoyancy of the enclosure. In Case 1, the heating region was been in the central position of the bottom wall. In case 2, the heating region was in the left position of the bottom. In case of Case 1, the lapse time of sensing the temperature of 72$^{\circ}C$ is approximately 15 sec almost at the same time in the coordinates (6, 22), (11, 22). In case of Case 2, the lapse time in the coordinates (6, 22), (11, 22) was 27 sec, 25 sec repectively. Also in case of Case 1 or Case 2, the gradients of y-position of the two sensors are transposed each other.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.2
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• pp.48-60
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• 2016

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 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 and KCS model ships. In results, the wave patterns and hull wave profiles of the Wigley and KCS model ships for various anti-diffusion coefficients showed quite close patterns. While, the band width of the water volume-fraction values between 0.1 to 0.9 at the Wigley and KCS model hull surfaces was narrowed by considering the anti-diffusion term. From the results, anti-diffusion source term decreased free-surface smearing.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.483-492
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• 1995

In this paper we discuss the existence and uniqueness of singular solutions for equations of the form $$ (F) u_t = u{xx} - $\mid$u$\mid$^{q-1} u_x - $\mid$u$\mid$^{p-1}u, p,q > 1, $$ in the domain $Q = {(x,t) : x \in R, t > 0}$. This equation represents a model of diffusion-convection with absorption.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• Journal of the Korean Society of Safety
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• v.6 no.3
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• pp.40-49
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• 1991

To better understand the phenomena inside an absorber, where heat and mass transfer coexist, this study selected the most baslc absorption model from in whifh water vapor is absorbed on the surface of a stationary lithium bromide absurbent solution. The purpose of this study is to obtain basic knowledge of heat and mass transfer processes as affected by Marangoni convection induced by addition of surfactant. We apply a non-flowing bulk absorption model and assume that dropwise surfactant is fixed on the absorbent surface. Four governing equation-continuity, laminar monentum, energy and diffusion are solved numerically to obtain temperature and concentraion distributions during steam absorption with Marangonl convection.. In conclusion, Sh and Nu genrally increase at the initial absorption stage.

• Journal of computational fluids engineering
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• v.18 no.4
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• pp.53-60
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• 2013

The boron transport model has been implemented into the CUPID code to simulate the boron transport phenomena of the PWR. The boron concentration conservation was confirmed through a simulation of a conceptual boron transport problem in which water with a constant inlet boron concentration injected into an inlet of the 2-dimensional vertical flow tube. The step wise boron transport problem showed that the numerical diffusion of the boron concentration can be reduced by the second order convection scheme. In order to assess the adaptability of the developed boron transport model to the realistic situation, the ROCOM test was simulated by using the CUPID implemented with the boron transportation.

• Journal of Wetlands Research
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• v.5 no.1
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• pp.67-78
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• 2003

The unsteady 2D convection and diffusion equation is solved numerically for the real-time simulation of suspended load propagation. The streamlined upwind scheme efficiently reduces numerical oscillations due to the high Peclet number in the convection dominant flow. By using the mixed boundary condition to express the external source terms or externally induced suspended load as a function of time in the algorithm, the model is capable of handling not only continuous load cases but also non-continuous suspended load influx. The suspended load transport modelwas verified using a case study for which an analytical exact solution is available and was applied to the real-time simulation of a suspended load influx case on the Mississippi River. The model algorithm can provide a framework upon which water quality as well as contaminant transport models can be built.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• Journal of computational fluids engineering
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• v.18 no.4
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• pp.25-34
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• 2013

A numerical study of a laminar natural convection of the CuO-water nanofluid in a square cavity using the Buongiorno's nonhomogeneous model is presented. All the governing equations including the volume fraction equation are discretized on a cell-centered, non-uniform grid employing the finite-volume method with a primitive variable formulation. Calculations are performed over a range of Rayleigh numbers and volume fractions of the nanopartile. From the computed results, it is shown that both the homogeneous and nonhomogeneous models predict the deterioration of the natural convection heat transfer well with an increase of the volume fraction of nanoparticle at the same Rayleigh number, which was observed in the previous experimental studies. It is also shown that the differences in the computed results of the average Nusselt number at the wall between the homogeneous and nonhomogeneous models are very small, and this indicates that the slip mechanism of the Brown diffusion and thermophoresis effects are negligible in the laminar natural convection of the nanofluid. The degradation of the heat transfer with an increase of the volume fraction of the nanoparticle in the natural convection of nanofluid is due to the increase of the viscosity and the decrease of the thermal expansion coefficient and the specific heat. It is clarified in the present study that the previous controversies between the numerical and experimental studies are owing to the different definitions of the Nusselt number.