• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.145-155
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• 2007

In this paper, we show the convergence of approximate solutions to the convective porous media equation using methodology developed in [8]. First, we obtain the approximate transport equation for the given convective porous media equation. Then using the averaging lemma, we obtain the convergence.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.357-378
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• 2012

In this paper, we consider the convective Cahn-Hilliard equation. Based on the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in $H^k$($k\geq0$) space, which attracts any bounded subset of $H^k({\Omega})$ in the $H^k$-norm.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1445-1465
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• 2015

In this paper, the long time behavior of the convective Cahn-Hilliard equation in two dimensions is considered, semidiscrete and completely discrete spectral approximations are constructed, error estimates of optimal order that hold uniformly on the unbounded time interval $0{\leq}t<{\infty}$ are obtained.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.621-632
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• 2014

In this paper, we study the dynamical behavior of the one-dimensional convective Cahn-Hilliard equation(CCHE) on a periodic cell [$-{\pi},{\pi}$]. We prove that as the control parameter passes through the critical number, the CCHE bifurcates from the trivial solution to an attractor. We describe the bifurcated attractor in detail which gives the final patterns of solutions near the trivial solution.

• Food Science and Preservation
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• v.2 no.1
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• pp.155-161
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• 1995

We examined the drying characteristics and the drying rate model equation of garlic(allium sativum L.) using computer aided convective drying. The drying chanacteristic curve of garlic divided into constant rate drying period and 2 stage of falling rate drying period. The drying rate was fairly affected by hot air temperatures during the total drying period, but air flow rates has nearly no effect on the drying rate except initial drying period. Of the several model equation, r2 values of page model equation was the highest, and the estimated drying profiles were comparatively coincided with the observed drying profiles. Page model equation was suitable to predict the drying rate and moisture content during drying of sliced garlic.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1111-1115
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• 2008

The relative magnitudes of the individual terms of the momentum equation are analyzed and compared by the analytical methods in open channel flow. The temporal variations of each term(local acceleration term, convective acceleration term, pressure force term, gravity force term, and friction force term) are analyzed for the influence factors to runoff expressed by the parameters of the momentum equation, stream slopes and roughness coefficients. The magnitudes of each term vary with the channel characteristics, especially when the roughness coefficients are dominant or for the mild stream slopes the pressure term can not be negligible. As a result of the characteristics of momentum equation in open channel flow, the acceleration terms are very small compared with the other terms. The magnitudes of local acceleration and convective acceleration offsets each other. The peak time of each term except the gravity term coincides with inflection point of the hydrograph rising limb each other.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.10
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• pp.1279-1287
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• 2004

The vaporization characteristics of a liquid heptane droplet in a supercritical nitrogen flow are numerically studied. The transient conservation equations of mass, momentum, energy, and species are expressed in an axisymmetric coordinate system. The governing equations are solved time marching method with preconditioning scheme. The modified Soave-Redlich-Kwong equation of state is employed for taking account of real gas effects such as thermodynamic non-ideality and transport anomaly. Changing the convective velocity and ambient pressure, several parametric studies are conducted. The numerical results show that the two parameters, Reynolds number and dimensionless combined parameter(${\mu}$s/${\mu}$d)(equation omitted), have influence on supercritical droplet vaporization.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05b
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• pp.227-232
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• 1996

The one-third calibrating relation by steady solution can cause large error when applied to an unsteady flow with large amplitude waves. Extended calibrating method, which can treat the normal convective contribution, is developed. The normal mass convective term is included into the 2-D mass transport equation by means of rms value and random function. The unknown shear rate is numerically determined by solving the 2-D mass transport equation inversely. This recovery method which predicts the unknown shear rate is constructed. It is found that it works very well without distortion. The inclusion of the normal convective term has a negligible effect on the mass transfer coefficient.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2995-3002
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• 1995

The cooling problem of the hot internal pipe flow has been investigated. Simultaneous conduction, convection, and radiation were considered with azimuthally varying convective heat loss at the pipe wall. A complex, nonlinear integro-differential radiative transfer equation was solved by the discrete ordinates method (or called S$_{N}$ method). The energy equation was solved by control volume based finite difference technique. A parametric study was performed by varying the conduction-to-radiation parameter, optical thickness, and scattering albedo. The results have shown that initially the radiatively active medium could be more efficiently cooled down compared with the cases otherwise. But even for the case with dominant radiation, as the medium temperature was lowered, the contribution of conduction became to exceed that of radiation.n.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.