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NUMERICAL STUDY OF THE ONSET OF NATURAL CONVECTION BASED ON LYAPUNOV-SCHMIDT METHOD

DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.450
page 8

Konstantin A. Nadolin
Mechanical and Mathematical Department Rostov State University, Rostov-on-Don, Russia

Abstract

The Rayleigh-Benard problem is examined numerically by the non-Boussinesq approximation. We correctly derive this approximation from general equations for fluid whose specific volume depends linearly only on temperature and does not depend on pressure. Unlike the Oberbeck—Boussinesq approximation the negligibility of thermal expansion is not assumed in this model and all terms with coefficient of thermal expansion are taken into account. We assume the dynamic viscosity, the thermal conductivity and the specific heat of the fluid to be constant. We further assume that the work of pressure forces and viscous energy dissipation are negligible. We assume the boundaries of the layer are isothermal.
The onset of convection motion is studied on the basis of proposed model both numerically and analytically. The results of linear and weakly non-linear stability analysis are compared with known for Oberbeck-Boussinesq approximation.

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