• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.1015-1027
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• 2019

A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.183-200
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• 2019

We have constructed a robust numerical method on Shishkin mesh for a class of convection diffusion type turning point problems with Robin type boundary conditions. Supremum norm is used to derive error estimates which is of order O($N^{-1}$ ln N). Theoretical results are verified by providing numerical examples.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.349-362
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• 2016

The numerical solutions of unsteady hydromagnetic natural convection Couette flow of a viscous, incompressible and electrically conducting fluid between the two vertical parallel plates in the presence of thermal radiation, thermal diffusion and diffusion thermo are obtained here. The fundamental dimensionless governing coupled linear partial differential equations for impulsive movement and uniformly accelerated movement of the plate were solved by an efficient Finite Element Method. Computations were performed for a wide range of the governing flow parameters, viz., Thermal diffusion (Soret) and Diffusion thermo (Dufour) parameters, Magnetic field parameter, Prandtl number, Thermal radiation and Schmidt number. The effects of these flow parameters on the velocity (u), temperature (${\theta}$) and Concentration (${\phi}$) are shown graphically. Also the effects of these pertinent parameters on the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically through tabular forms. These are in good agreement with earlier reported studies. Analysis indicates that the fluid velocity is an increasing function of Grashof numbers for heat and mass transfer, Soret and Dufour numbers whereas the Magnetic parameter, Thermal radiation parameter, Prandtl number and Schmidt number lead to reduction of the velocity profiles. Also, it is noticed that the rate of heat transfer coefficient and temperature profiles increase with decrease in the thermal radiation parameter and Prandtl number, whereas the reverse effect is observed with increase of Dufour number. Further, the concentration profiles increase with increase in the Soret number whereas reverse effect is seen by increasing the values of the Schmidt number.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.5
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• pp.1671-1678
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• 1996

In external chemical vapor deposition processes including VAD and OVD the distribution of flame-synthesized silica particles is determined by heat and mass transfer limitations to particle formation. Combustion gas flow velocities are such that the particle diffusion time scale is longer than that of gas flow convection in the zone of particle formation. The consequence of these effects is that the particles formed tend to remain along straight smooth flow stream lines. Silica particles are formed due to oxidation and hydrolysis. In the hydrolysis, the particles are formed in diffuse bands and particle formation thus requires the diffusion of SiCl$\_$4/ toward CH$\_$4//O$\_$2/ combustion zone to react with H$\_$2/O diffusing away from these same zones on the torch face. The conversion kinetics of hydrolysis is fast compared to diffusion and the rate of conversion is thus diffusion-limited. In the language of combustion, the hydrolysis occurs as a Burke-Schumann process. In selected conditions, reaction zone shape and temperature distributions predicted by the Burke-Schumann analysis are introduced and compared with experimental data available. The calculated centerline temperatures inside the reaction zone agree well with the data, but the calculated values outside the reaction zone are a little higher than the data since the analysis does not consider diffusion in the axial direction and mixing of the combustion products with ambient air. The temperatures along the radial direction agree with the data near the centerline, but gradually diverge from the data as the distance is away from the centerline. This is caused by the convection in the radial direction, which is not considered in the analysis. Spatial distribution of silica particles are affected by convection and diffusion, resulting in a Gaussian form in the radial direction.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.2
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• pp.97-102
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• 1991

Finite element method has been developed recently for the solution of the convection-diffusion problems. Finite element method has several advantages over finite difference method, but its requirement of the larger memory size of the computer has prevented from wide application. In the present study, line-by-line technique has been implemented to finite element method to overcome this disadvantage. Two dimensional laminar natural convection in square cavity was chosen as an example in this study. The numerical result shows good agreement with bench mark solution and the size of the coefficient marix has been reduced drastically.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.68-74
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• 1998

A finite element analysis for physical phenomenon which are governed by parabolic equation, has some inefficiencies caused by much computational time and large storage space. In this paper, a comparative study is performed to suggest the best efficient transient analysis algorithms for parabolic equations. First, the general finite element analysis techniques are summarized in views of formulation procedures, treatments of convection terms. and time stepping methods. Results of several combinations applied to one dimensional convection-diffusion equation and Burger equation are represented and compared using some criteria such as accuracy, stability, and computational time. Through the results, some guidelines to select a algorithm for solving parabolic equations are proposed for diffusion dominant and convection dominant cases. Finally applicability of two dimensional extension of the result is also discussed.

• Journal of Environmental Impact Assessment
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• v.21 no.1
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• pp.133-142
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• 2012

Convection Current Circulation System(CCCS) in stratified reservoir controls development of anaerobic condition and algal bloom during summer. In order to increase the CCCS effectiveness, we analyze diverse design parameters to make optimize the flow pattern in reservoir. In this study, we interpret the internal flow with installation and operation condition of CCCS based on CFD in reservoir. Design variables of CCCS is reservoir depth, stratification strength, distance of between CCCS and so on. Since reservoir depth and stratification strength in variables is depending on natural phenomenon, we evaluated current circulation effect by distance of CCCS and proposed the optimal design condition using CFD simulation. Flow and diffusion changes in water body was assessed by temperature and dye test. Changes in water floor temperature at 40m intervals was slowly descending over 37 hours. Dye diffusion simulation at 60m intervals, the radius of the spread between two devices were overlapped after 12 hours.

• Nuclear Engineering and Technology
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• v.36 no.5
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• pp.375-387
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• 2004

This paper presents a transient multicomponent mixture analysis tool developed to analyze the molecular diffusion, natural convection, and chemical reactions related to air ingress phenomena that occur during a primary-pipe rupture of a high temperature gas-cooled reactor (HIGR). The present analysis tool solves the one-dimensional basic equations for continuity, momentum, energy of the gas mixture, and the mass of each gas species. In order to obtain numerically stable and fast computations, the implicit continuous Eulerian scheme is adopted to solve the governing equations in a strongly coupled manner. Two types of benchmark calculations were performed with the data of prerious Japanese inverse U-tube experiments. The analysis program, based on the ICE technique, runs about 36 times faster than the FLUENT6 for the simulation of the two experiments. The calculation results are within a 10% deviation from the experimental data regarding the concentrations of the gas species and the onset times of natural convection.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.3
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• pp.528-536
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• 1987

In a turbulent free shear flow, the large scale motion is characterized by the intermittent flow which arises from the interaction between the turbulent fluid and the irrotational fluid of the environment through the mean velocity gradient. This large scale motion causes a bulk convection whose effect is similar to the spatial diffusion process. In this paper, the total diffusion process is proposed to be approximated by weighted sum of the bulk convection due to the large scale motion and the usual gradient diffusion due to small scale motion. The diffusion term in conventional .kappa.-.epsilon. model requires on more equation of the intermittency transport equation. A production term of this equation means mass entrainment from the irrotational fluid to the turbulent one. In order to test the validity of the proposed model, a plane jet is predicted by this method. Numerical results of this model is found to yield better agreement with experiment than the standard .kappa.-.epsilon. model and Byggstoyl & Kollmann's model(1986). Present hybrid diffusion model requires further tests for the check of universality of model and for the model constant fix.

• Journal of Korean Society of Water and Wastewater
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• v.18 no.2
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• pp.165-173
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• 2004

Behavior of hazardous organic compounds including bisphenol A, phtalic acid, and phosphoric acid in low pressure nanofiltration process were investigated. In the case of NTR729HF, rejection of all target organic compounds except 2-H-Benzothiazol and 2-isopropyl phenol was more than 90%. The lowest rejection for 2-H-Benzothiazol was observed in another membranes. The UTC60 and UTC20 showed similar rejection characteristics of hazardous organic compounds. Although the rejection of Bisphenol A, n-buthyl benzenesulfoneamide, N-ethyl-p-toluensulfonamide, 2-H-benzothiazol, p-t-butylphenol and 2-isopropyl phenol was less than 30%, the rejection of tributyl phosphate, triethyl phosphate, camphor, 2,2,4 trimethyl 1,3 pentandiol and diphenyl amine was more than 90% in the case of UTC60 and UTC20. The rejection characteristics of various hazardous organic compounds were converted into one parameter Ks, which was proposed in the diffusion-convection model. The Ks of hazardous organic compounds were discussed by comparing with their solute size represented by Stokes radius. The diffusion convection model considering Ks was successful to interpret rejection characteristics of hazardous organic compounds by low-pressure nanofiltration membranes.