• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.453-462
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• 1990

The interaction of forced convection-conduction with thermal radiation in laminar boundary layer over a plate fin is studied numerically. The analysis is based on complete solution whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum and energy in the fluid boundary layer adjacent to the fin. The fluid is a gray medium and diffusion(Rosseland) approximation is used to describe the radiative heat flux in the energy equation. The resulting boundary value problem are convection-conduction parameter N$_{c}$ and radiation-conduction parameter m, Prandtl number Pr. Numerical results are presented for gases with the Prandtl numbers of 0.7 & 5 with values of N$_{c}$ and M ranging from 0 to 10 respectively. The object of this study is to provide the first results on forced convection-radiation interaction in boundary layer flow over a semi-infinite flay plate which can be used for comparisons with future studies that will consider a more accurate expression for the radiative heat flux. The agreement of the results from the complete solution presented by E. M. Sparrow and those from this paper for the special case of M=0 is good. The overall rate of heat transfer from the fin considering radiative effect is higher than that from the fin neglecting radiative effect. The local heat transfer coefficient with radiative effect is higher than that without radiative effect. In the direction from tip to base, those coefficients decrease at first, attain minimum, and then increase. The larger values of N$_{c}$ M, Pr give rise to larger fin temperature variations and the fin temperature without radiative effect is always higher than that with radiative effect.

• Applied Chemistry for Engineering
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• v.26 no.6
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• pp.746-752
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• 2015

This study investigates the effects of aspect ratio (transport length-to-width) on diffusive-convection for physical vapor transport processes of $Hg_2Cl_2-NO$ system. For a system with the temperature difference of 20 K between an interface at the source material region and growing crystal interface, the linear temperature profiles at walls, the total molar fluxes at Ar = 2 are much greater than Ar = 5 as well as the corresponding nonuniformities in interfacial distributions due to the effect of convection. The maximum total molar flux at the gravitational acceleration of 1 $g_0$ is greater twice than at the level of 0.1 $g_0$, where g0 denotes the gravitational acceleration on earth. With increasing aspect ratio from 2 to 5, a diffusive-convection mode is transited into the diffusion mode, and then the strength of diffusion is predominant over the strength of diffusive-convection.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1720-1730
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• 1995

Finite-difference analysis was conducted to study the natural convection of a stably stratified salt-water solution in an annulus due to lateral heating. The main purpose of this study is to examine in detail the multi-layered flow structure. Calculation was thus made for R $a_{\eta}$=2*10$^{5}$ and 6.5*10$^{5}$ . Formation of layered flow structure, merging process of layers, the corresponding temperature and concentration distributions, Nusselt number variations with time are examined. Numerical results show that in each layer, the temperature profile looks 'S`-shaped and the concentration profile is uniform due to the convective mixing. The formation of the roll and the layer is governed by natural convection due to the temperature gradient and the merging process of the layer by diffusion of the concentration.ation.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.171-176
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• 2007

A comparative study on the treatment of the turbulent heat flux with the elliptic mlending second moment closure for a natural convection is performed. Four cases of different treating the turbulent heat flux are considered. Those are the generalized gradient diffusion hypothesis (GGDH) the algebraic flux model (AFM) and the differential heat flux model (DFM). These models are implemented in the computer code specially designed for evaluation of turbulent models. Calculations are performed for a turbulent natural convection in the 1:5 rectangular cavity and the calculated results are compared with the experimental data. The results show that three models produce nearly the same accuracy of solutions.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.37-44
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• 2000

Numerical investigation is made to study the effects of natural convection on the formation of macrosegregation of a Pb-Sn alloy solidification process in a 2-D confined rectangle mold. The governing equations are calculated using previous continuum models with SIMPLE algorithm doring the solidification process. In addition. to track the solid-liquid interface with time variations. the moving boundary condition Is adopted and irregular interface shapes are treated with Boundary-Fitted Coordinate system. As the temperature reduce from the liquidus to the solidus, the liquid concentration of Sn. the lighter constituent, increases. Then the buoyancy-driven flow due to temperature and liquid composition gradients, called thermosolutal convection or double diffusion, occurs in the mushy region and forms the complicated macrosegregation maps. Related to this phnomena, effects on the macrosegregation formation depending on the cooling condition and gravity values are described.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.121-129
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• 1999

Double-diffusive convection with verical temperature and concentration gradients in thermally stratified fluids has been investigated experimentally using an electrochemical technique. Cupric sulfuric-sulffuric acid solution confined between two horizontal copper electrodes was used. The change of thermal and solutal buoyance has no influence on the range of voltage for the limiting current. Due to Soret effect, the onset time of natural convection is delayed as the stabilizing thermal buoyancy decreases. Also it is found that the shrinkage of the unstabilizing solutal buoyancy makes the onset of natural convection retard. Multi-layered convective phenomena do not appear because cupric sulfate-sulfuric acid solution is thermally stratified, and heat diffuses faster than cupric sulfate solfate solution.

• Journal of computational fluids engineering
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• v.7 no.1
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• pp.10-19
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• 2002

The non-staggered(collocated) grid approach in which all the solution variables are located at the centers of control volumes is very popular for incompressible flow analyses because of its numerical efficiency on the curvilinear or unstructured grids. Rhie and Chow's paper is the first in using non-staggered grid method for SIMPLE algorithm, where pressure weighted interpolation was used to prevent decoupling of pressure and velocity. But it has been known that this non-staggered grid method has stability problems when pressure fields are nonlinear like in natural convection flows. Also Rhie-Chow scheme generates large numerical diffusion near curved walls. The cause of these unwanted problems is too large pressure damping term compared to the magnitude of face velocity. In this study the magnitude of pressure damping term of Rhie-Chow's method is limited to 1∼10% of face velocity to prevent physically unreasonable solutions. The wall pressure extrapolation which is necessary for cell-centered FVM is another source of numerical errors. Some methods are applied in a unstructured FV solver and analyzed in view of numerical accuracy. Here, two natural convection problems are solved to check the effect of the Rhie-Chow's method on numerical stability. And numerical diffusion from Rhie-Chow's method is studied by solving the inviscid flow around a circular cylinder.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.283-296
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• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.10a
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• pp.117-121
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• 1997

It is shown theoretically that uniform axial dopant concentration distribution can be made throughout the crystal by continuous Czochralski process. Numerical simulation are performed for the transient two-dimensional convection-diffusion model. A typical value of the growth and system parameters for Czochralski growth of p-type, 4 inches silicon crystal was used in the numerical calculations. Using this model with proper model parameter, the axial segregation in batchwise Czochralski growth can be described. It is studied by comparing with the experimental data. With this model parameter, the uniform axial concentration distribution of dopant is predicted in continuous Czochralski process.