The Rayleigh-Benard instability in an enclosure having finite thickness walls

Natural convection in an enclosure having finite thickness heat-conducting walls at local heating at the bottom of the cavity has been numerically studied. Heat exchange with an environment due to convection and radiation has been considered on one of external sides of the decision region. The governing unsteady three-dimensional flow equations in the Boussinesq approximation for the gas cavity and heat conduction equation for the solid walls, written in dimensionless variables such as vector potential functions, the vorticity vector and the temperature, have been solved using finite difference method. Results have been obtained for a Prandl number of 0.7 and for a Grashof number ranging from 10⁴ to 10⁶.