• 설비공학논문집
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• 제8권3호
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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.

• 태양에너지
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• 제8권1호
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• pp.33-40
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• 1988

The characteristics of thermal instabilities of natural convection in a horizontal fluid layer bounded below by a rigid plate and above by an interface with a passive gas is presented. The critical Grashof number decreases as the surface tension gradient effect (Marangoni effect) at the interface increases and the flow remains unstable for a critical Marangoni number depending on Prandtl numbers. These results are in substantial agreement with those of Smith and Davis.

• 대한기계학회논문집
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• 제15권2호
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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.

• 대한기계학회논문집
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• 제15권2호
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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.

• 대한설비공학회지:설비저널
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• 제13권4호
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• pp.215-222
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• 1984

An analytical study on the thermal instability of fluid in a vertical solt between two permeable walls has been carried out using fast converging power series solution method. For given values of prandtl number Pr and permeability paramter ${\sigma}$, the critical Grashof number $Gr_c$ and the critical wave number ac are found as eigenvalues of the problem formulated by the stability equations and the appropriate boundary conditions which are derived on the basis of linear stability theory. In the case of ${\sigma}\;>\;10^4$, the results approach those of solid boundary case, but in the case of ${\sigma}\;<\;10^3$, the decrease of $Gr_c$ and $a_c$become more prominent. In other words, the permeable walls cause the flow to be more unstable than the solid walls. This is considered to be due to the slip of the fluid on the wail, which decrease the friction force.

• 설비공학논문집
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• 제2권4호
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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.