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밑에서 일정하게 가열되는 유체층의 안정성(점근해)

The Stability of a Horizontal Fluid Layer Heated Uniformly from Below(Asymptotic Analysis)

김장주 최창균

Kim JJ Choi CK

HWAHAK KONGHAK, October 1980, 18(5), 359-366(8), NONE

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Abstract

대류가 일어나지 않는 상태에서 전도에 의한 비정상적인 온도분포를 유효 열깊이와 밑면의 온도를 이용하여 모사하고 이를 이용하여 간편하게 적용될 수 있는 점근해법을 제시하고 이를 이용하여 최초 정지상태에 있는 수평면상의 유체에 대한 안정성을 해석하였다.
Prandtl수가 큰 경우 열 disturbance는 유효 열깊이내에 한정된다는 것을 확인할 수 있었고 온도 분포의 비선형 정도가 큰 경우 점근해법은 안정성 해석 뿐만 아니라 자연대류의 시작시간을 구하는데 잘 적용되었다.

The extended Rayleigh-Benard problem, where an unperturbed temperature profile is nonlinear and time-dependent, was examined by linear stability theory. The unperturbed temperature profile induced by constant heat flux from below was approximated, using a bottom temperature and penetration distance. Applying this modified temperature profile to the present system, the asymptotic power-series method was developed and the onset of natural convection was analyzed. It was found that this analysis is well applied to the transient system with the Rayleigh number larger than 10⁴. It is evident that for large Prandtl numbers temperature disturbances are confined within the effective thermal depth.

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