• 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.

• 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.