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밑면으로부터 등온 가열되는 수평 점탄성 유체층에서의 대류 안정성 해석

An Analysis of Convective Stability in a Horizontal Viscoelastic Fluid Layer Heated Isothermally from Below

이상조 최창균

Lee SJ Choi CK

HWAHAK KONGHAK, August 1993, 31(4), 439-447(9), NONE

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Abstract

아래로부터 등온 가열되는 수평 Oldroyd-B 유체층에서의 자연대류 발생 시점을 선형 안정성 이론을 적용하여 구하였다. Oldroyd-B 유체가 뉴튼 유체보다 더 불안정한 것으로 나타났으며, 자연대류 발생 시점에서 과도안정성에 기인한 진동성 거동이 발생함을 알 수 있었다. 계면에서 Biot 수의 증가는 계에 안정화 효과를 주었으며, 응력이완 시간이 커질수록 변형 지연 시간은 작아질수록 불안정성을 가중시켰다. Prandtl수는 작아질수록 계는 안정화되었고, Prandtl 수가 100보다 클 때에는 Prandtl수의 영향은 거의 없는 것으로 나타났다. 또한 자연대류의 발생시점에서 불안정성 유발 요인인 부력과 표면 장력은 서로의 효과를 강화하였다.

The onset of natural convection in a horizontal layer of Oldroyd-B Fluid heated isothermally from below is investigated by using linear stability theory. It is known that convective instabilities in the Oldroyd-B fluid layer set in more easily than those of Newtonian fluid and oscillatory motions caused by overstability will occur at the onset of natural convection. Also, it is shown that the Oldroyd-B fluid layer becomes more stable with a larger Biot number, a smaller stress relaxation time and a larger strian retardation time. The layer of Oldroyd-B fluid becomes more stable with decreasing the Prandtl number and the critical conditions are almost independent of the Prandtl number in the range of the Prandtl number values larger than 100. It is clear that the buoyancy effect and the surface tension effect reinforce each other at the onset of natural convection.

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