• Journal of Advanced Marine Engineering and Technology
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• v.31 no.7
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• pp.833-841
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• 2007

The aim of this paper is to analyze the conjugate problems of heat conduction in solid walls coupled with laminar free convection flow adjacent to a vertical flat plate under boundary layer approximation. Using the similarity transformations the governing boundary layer equations for momentum and energy are reduced to a system of partial differential equations and then solved numerically using Finite Difference Method(FDM) known as the Keller-box scheme. Computed solutions to the governing equations are obtained for a wide range of non-dimensional parameters that are present in this problem, namely the coupling parameter P. the Prandtl number Pr and the heat generation parameter Q. The variations of the local heat transfer rate as well as the interface temperature and the friction along the plate and typical velocity and temperature profiles in the boundary layer are shown graphically. Numerical solutions have been consider for the Prandtl number Pr=0.70

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.160-161
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• 2003

Thermocapillary convection is a surface tension driven flow due to a temperature gradient along an interface. It occurs during a crystal-growth process and therefore understanding the convection is important to material processing in microgravity. Although modelling of the float-zone crystal-growth process has been of interest for a few decades, most studies of liquid bridges assumed non-deformable flat surfaces. In reality, the surface profile, g(t,z), is unknown and should be obtained as a solution to the coupled transport equations along with the surface force balance. Here we report on a numerical study of axisymmetric thermocapillary convection in liquid bridges with deformable surfaces. The interface is determined as part of the complete solution. The influence of the capillary number (Ca), Reynolds number (Re), Prandtl number (Pr) and aspect ratio(Ar) on the dynamics is explored.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.3
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• pp.259-266
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• 1994

Natural convection within a wedge-shaped enclosure has been studied numerically by finite difference method. Radial surfaces of the wedge are isothermally hot and cold while circumferential surfaces are insulated. Results show isotherms, streamlines and velocity profiles as well as Nusselt number distributions for a Rayleigh number range of $10^3$ to $10^5$. In addition, it is found that there is a wedge angle as shown the minimum mean Nusselt number for using an insulated enclosure.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1709-1719
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• 1995

The primary objective of the paper is to obtain the basic information of the natural convection of a stratified with various parametric conditions related to rotating speed, temperature and concentration gradient. For the purpose of it, experiments are performed in a stably stratified salt-water solution with lateral heating in a stationary or rotating annulus. The experiment covers the ranges of Ar=2, Le=100, R $a_{\ta}$=2 10$^{5}$ and Ta=0, 10$^{5}$ - 2.5*10$^{8}$ . Many interesting flow phenomena are observed and rotation effects are examined. Particularly as Taylor number increases (rotation increases) at a given R $a_{\ta}$, the generation of rolls at hot wall is inhibited and the formation and merging process of layers are delayed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.3
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• pp.433-441
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• 2001

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.3072-3083
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• 1995

The numerical simulation on the three-dimensional natural convection heat transfer in the enclosure with heat generating chip is performed, and the effects of convective heat loss and vents are also examined. The effects of the Rayleigh number and outer Nusselt number (Nu$_{0}$) on the maximum chip temperature and the fractions of heat loss from the hot surfaces are investigated. The results show that conduction through the substrate is dominant in heat dissipation. With the increase of Rayleigh number, heat dissipation through the chip surfaces increases and heat loss through the substrate decreases. Maximum dimensionless temperature with vents is found to decrease about 40% compared to the one without vents at Nu$_{0}$=0.l. It is also shown that effects of size and location of the vents are negligible.ble.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.8
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• pp.755-762
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• 2000

Natural convection of air in a horizontal annulus with the inner cylinder cooled by the application of a constant heat flux and the isothermally heated outer cylinder is considered. The bifurcation phenomenon of flow patterns and the heat transfer characteristics are numerically investigated. The zero initial condition induces a unicellular flow in a half annulus. A bicellular flow consisting of two counter-rotating eddies in a half annulus can be obtained above a certain critical Rayleigh number. A transition from the bicellular to the unicellular flow occurs with a decrease in Rayleigh number. Hysteresis phenomena have not been observed. In the regime of dual flows, the overall Nusselt number of the bicellular flow is greater than that of the unicellular flow.

• Korean Chemical Engineering Research
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• v.57 no.1
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.18 no.9
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• pp.698-706
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• 2006

Experiment and numerical calculation have been peformed to investigate mixed convection heat transfer between inclined parallel plates. Particle image velocimetry (PIV) with thermo-sensitive liquid crystal (TLC) tracers is used for visualizing and analysis. This method allows simultaneous measurement of velocity and temperature fields at a given instant of time. Quantitative data of the temperature and velocity are obtained by applying the color-image processing to a visualized image, and neural network is applied to the color-to-temperature calibration. The governing equations are discretized using the finite volume method. The results are presented for the Reynolds number ranges from 0.004 to 0.062, the angle of inclination, ${\Theta}$, from 0 to 45 degree and Prandtl number of the high viscosity fluid is 909. The results show velocity, temperature and mean Nusselt numbers distributions. It is found that the periodic flow of mixed convection between inclined parallel plates is shown at $0^{\circ}{\leq}{\Theta}<30^{\circ}$, Re<0.062, and the flow pattern can be classified into three patterns which depend on Reynolds number and the angle of inclination. The minimum Nusselt numbers occur at Re=0.05 regardless of the angle of inclination.

• Korean Chemical Engineering Research
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• v.52 no.2
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• pp.199-204
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• 2014

In binary solidification compositional convection in a porous mushy layer influences the quality of the final products. We consider the mushy layer solidifying from below with a constant solidification velocity. The disturbance equations for the mushy layer are derived using linear stability theory. The basic-state temperature fields and the distribution of the porosity in the mushy layer are investigated numerically. When the superheat is large, the thickness of the mushy layer is relatively small compared to the thickness of the thermal boundary layer. With decreasing the superheat the critical Rayleigh number based on the thickness of the mushy layer increases and the mushy layer becomes stable to the compositional convection. The critical Rayleigh number obtained from the continuity conditions of temperature and heat flux at the mush-liquid interface is smaller than that from the isothermal condition at the upper boundary of the mushy layer.