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Linear Stability of Variable-Viscosity Fluid Layer under Convection Boundary Condition

대류 조건하의 가변 점성 유체층의 선형 안전성

  • 송태호 (한국과학기술원 기계공학과)
  • Published : 1992.01.01

Abstract

The critical condition for onset of Benard convection with variable viscosity .nu.=.nu.$_{0}$exp(-CT) has been obtained using a linear stability theory. The bottom wall is rigid while the upper surface may be either free or rigid. The two boundaries are subject to convective heat transfer. The critical Rayleigh numbers are presented up to maximum viscosity ratio of 3000. It is greater for smaller upper and/or lower surface Biot numbers. Its dependence on the viscosity ratio is complicated. However, a simple sublayer theory is found to be applicable for extremely large viscosity ratio. In such cases, the critical Rayleigh number and the critical wave number are functions of viscosity ratio and lower surface Biot number.r.