• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.3
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• pp.338-350
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• 1996

A numerical analysis is carried out to study the two-dimensional steady state natural convection from vertical wires immersed in cold pure water. The surface of the wire is $0^{\circ}C$ unifrom temperature. Results of the analysis are presented for free stream temperature from $0^{\circ}C$ to $25^{\circ}C$ and the aspect ratio N from $5.26{\times}10^{-3}$ to $1.0{\times}10^{-3}$. The effects of the density extremum and aspect ratio on the flow pattern and the heat transfer characteristics are discussed As the aspect ratio N becomes larger, in the range of $1.0^{\circ}C{\leq}T_{\infty}{\leq}4.4^{\circ}C$ and $6{^{\circ}C}{\leq}T_{\infty}{\leq}17^{\circ}C$, the effect of Pr number on the heat transfer is shown to be more significant than the aspect ratio. Investigating into the effect of the density extremum on the heat transfer from wires, the new heat transfer correlations are suggested with the relation of average Nu mumber vs. modified Ra number. Here, the coefficient values C of correlations are presented as the function of density extremum parameter $R^*$. The effects of the density extremum parameter are also discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.630-643
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• 1991

The hydrodynamic stability equations are formulated for buoyancy-induced flows adjacent to a vertical, planar, isothermal surface in cold pure water. The resulting stability equations, when reduced to ordinary differential equation by a similarity transformation, constitute a two-point boundary-value(eigenvalue) problem, which was numerically solved for various values of the density extremum parameter R=( $T_{m}$ - $T_.inf./) / ( $T_{o}$ - $T_.inf./). These stability equations have been solved using a computer code designed to accurately solve two-point boundary-value problems. The present numerical study includes neutral stability results for the region of the flows corresponding to 0.0.leq. R. leq.0.15, where the outside buoyancy force reversals arise. The results show that a small amount of outside buoyancy force reversal causes the critical Grashof number $G^*/ to increase significantly. A further increase of the outside buoyancy force reversal causes the critical Grashof number to decrease. But the dimensionless frequency parameter $B^*/ at $G^*/ is systematically decreased. When the stability results of the present work are compared to the experimental data, the numerical results agree in a qualitative way with the experimental data.erimental data.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.644-653
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• 1991

A wave instability problem is formulated for natural convection flows adjacent to a inclined isothermal surface in pure water near the density extremum. It accounts for the nonparallelism of the basic flow and temperature fields. Numerical solutions of the hydrodynamic stability equations constitute a two-point boundary value problem which are accurately solved using a computer code COLSYS. Neutral stability results for Prandtl number of 11.6 are obtained for various angles of inclination of a surface in the range from-10 to 30 deg. The neutral stability curves are systematically shifted toward modified Grashof number G=0 as one proceeds from downward-facing inclined plate(.gamma.<0.deg.) to upward-facing inclined plate (.gamma.>0.deg.). Namely, an increase in the positive angle of inclination always cause the flows to be significantly more unstable. The present results are compared with the results for the parallel flow model. The nonparallel flow model has, in general, a higher critical Grashof number than does the parallel flow model. But the neutral stability curves retain their characteristic shapes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.677-684
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• 1991

A numerical analysis is performed about the effects of aspect ratio on natural convective heat transfer from a vertical isothermal cylinder of 0.deg. C immersed in cold pure water. The results of analysis include velocity profiles, temperature profiles and mean Nusselt number of the steady flow region. As aspect ratio of vertical cylinder increases, the flow and heat transfer characteristics of vertical isothermal cylinder approach to those of vertical isothermal flat plate. Numerical solutions obtained for Rayleigh number and aspect ratio indicate the cylinders can be classified as short cylinder and long cylinder. In the cases of short cylinder and long cylinder, new heat transfer correlations are presented. Here, the coefficient values C of new heat transfer correlations are presented as the function of density extremum parameter $R^*/. Numerical results show that theoretical results are in close agreement with experimental results.ts.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1737-1746
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• 1991

본 연구에서는 저온의 순수물 속의 등온 수직원기둥에 의해 야기되는 열전달 특성을 구명함에 있어서 짧은 원기둥 범주에 속하는 종횡비 0.5인 얼음 원기둥을 이용 하여 실험적으로 열전달 특성을 구명하였다. 그리고 전 유동장을 가시화 하였으며, 얼음의 융해율로써 누셀트(Nusselt)수를 측정하여 기존의 결과들과 비교검토하였다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.197-206
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• 1990

Numerical results of heat transfer from a horizontal isothermal surface are presented for wall temperature T$_{w}$ = 0 .deg. C and ambient water temperature, T$_{\infty}$, from 1 .deg. C to 15 .deg. C. They include streamlines, temperature profiles, local heat transfer coefficients and average Nusselt numbers for the entire flow fields. For a upward-facing horizontal isothermal surface, the results show steady two dimensional flow regimes for T$_{\infty}$ .leg. 4.4 .deg. C, but no solution was obtained above T$_{\infty}$ = 4.4 .deg. C. For a downward-facing horizontal isothermal surface, the flow regimes are steady two dimensional flow for T$_{\infty}$ .geq. 4.9 .deg. C, and the numerical calculation was failed below this ambient water temperature. The mean Nusselt number has its maximum value at about T$_{\infty}$ = 3.4 .deg. C for upward-facing horizontal isothermal surface. For the case of downward-facing horizontal isothermal surface, the mean Nusselt number increases as the ambient water temperature increases.es.s.s.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1195-1204
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• 1992

The natural convection from upward and downward facing horizontal isothermal plate immersed in water is studied numerically. The temperature of the plate is from 0.0 .deg. C to 8.0 .deg. C and the ambient water temperature is from 1.0 .deg. C to 10.0 .deg. C. Numerical results are presented for the velocity profiles, temperature profiles, local heat transfer coefficients, and average Nusselt numbers over the entire flow fields. Flow patterns are shown in the upward and downward facing surfaces at different ambient water temperatures. For the upward facing surface, there are upflow and unsteady flow. And the regions of the ambient water temperatures which give rise to the upflow are more extensive as the temperatures of the isothermal surface become more distant from the density extremum temperature. For the downward facing surface, only the downflow region is shown. For the upward facing horizontal isothermal surface, the average Nusselt number(= N $u_{1}$$^{*}$) is 28.86(Ra)$^{0.01}$. And for the downward facing surface, the average Nusselt number(= N $u_{2}$$^{*}$) is $C_{2}$(Ra)$^{0.2}$ and the values of $C_{2}$ are enlarged in the range of 0.785 .leq. $C_{2}$ .leq. 1.250 as increasing of the temperatures of the isothermal surface.ace.ace.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.3
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• pp.437-450
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• 1996

A set of stability equations is formulated for natural convection flows adjacent to a vertical isothermal surface melting in cold pure water. It takes account of the nonparallelism of the base flows. The melting rate is regarded as a blowing velocity at the ice surface. The numerical solutions of the linear stability equations which constitute a two-point boundary value problem are accurately obtained for various values of the density extremum parameter $R=(T_m-T_{\infty})/(T_0-T_{\infty})$ in the range $0.3{\leq}R{\leq}0.6$, by using a computer code COLNEW. The blowing effects on the base flow becomes more significant as ambient temperature ($T_{\infty}$) increases to $T_{\infty}=10^{\circ}C$. The maximum decrease of heat transfer rate is about 6.4 percent. The stability results show that the melting at surface causes the critical Grashof number $G^*$ and the maximum frequency of disturbances to decrease. In comparision with the results for the conventional parallel flow model, the nonparallel flow model has a higher critical Grashof number but has lower amplification rates of disturbances than does the parallel flow model. The spatial amplification contours exhibit that the selective frequency $B_0$ of the nonparallel flow model is higher than that of the parallel flow model and that the effects of melting are rather small. The present study also indicates that the selective frequency $B_0$ can be easily predicted by the value of the frequency parameter $B^*$ at $G^*$, which comes from the neutral stability results of the nonparallel flow model.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.2 no.4
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• pp.268-278
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• 1990

Hydrodynamic stability equations are formulated for natural convection flows adjacent to a heated or cooled, inclined, isothermal surface in pure water at $4^{\circ}C$, where the density variation with temperature becomes nonlinear. The resulting stability equations, when reduced to ordinary differential equations by a similarity transformation, constitute a two-point boundary-value problem, which was solved numerically. It is found from the obtained stability results that the neutral stability curves are systematically shifted to have lower critical Grashof numbers, as the inclination angle of upward-facing plate increases. Also, the nose of the neutral stability curve becomes blunter as the angle increases. It implies that the greater the inclination of the upward-facing plate, the more susceptible of the flow to instability for the wide range of disturbance wave number and frequency.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1799-1807
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• 1994

Natural convection from a slightly inclined circular cylinders immersed in quiescent cold pure water was studied experimentally. The experiment was carried out for circular cylinders with uniform heat flux ranging from $100W/m^{2} to 800 W/m^{2}$ and inclined angle ranging from horizontal $({\phi}=0^{\circ}) to 15^{\circ}$. The flow fields around cylinder were visualized and heat transfer characteristics investigated by measuring the surface temperatures for each case. As the results, it is shown that flow patterns are changed consecutively through the sequence of steady state downflow, unsteady state flow and steady state upflow with increasing heat flux. At the same inclined angle, as heat flux increases, the average Nusselt number decreases and then increases. At the same heat flux, as inclined angle increases, the average Nusselt number decreases.