순수한 찬물속에 잠겨있는 경사진 등온벽면 부근의 자연대류에 관한 수동력학적 안정성

The Hydrodynamic Stability of Natural Convection Flows Adjacent to an Inclined Isothermal Surface Submerged in Cold, Pure Water

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.