Abstract
A two-dimensional time-dependent numerical computation method has been developed to determine laminar free convection in closed cavities and forced convection in ducts and open cavities. The transport equations for energy and vorticity are solved with the aid of the ADI-method, but the more recently established method of cyclic reduction is applied to the Poisson equation. The resulting implicit method remains stable up to a Rayleigh number of 10 12. Due to the acceptable large time step, the method is particularly qualified for transient problems with extremely slow changing properties. A transformation relation, q( x, ε), is proposed for sufficiently accurate determination of thermal and hydrodynamic boundary layers near the vertical side walls in cavities. The benefit of the present numerical computation technique has been demonstrated by solving two problems of free convection in a rectangular cavity, namely with differentially but uniformly heated side walls and with only one side wall non-uniformly heated.
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