Natural convection in a cavity at high Rayleigh numbers

Numerical solution of a buoyancy-driving flow induced in a square enclosure by isothermally hot and cold vertical walls is presented. The calculations are performed for Prandtl number of 0.71 (air) and at Rayleigh number up to 10/sup 12/, using both laminar and turbulent theories. For the laminar flow, the equations derived using Boussinesq's approximation are solved by Newton's method and a sparse-matrix technique. At Rayleigh number of greater than 10/sup 9/, the computation utilizes the algebraic stress model. The calculation procedure for this turbulent flow employs Newton's method for the mean flow parameters as in the laminar case, an alternating direction implicit (ADI) method for the transport equations, and the Gauss-Seidel iterative technique for the algebraic stress relationships. The combination of these techniques seemed to converge reasonably well. The calculations are extended for the enclosure with diverse boundary conditions due to a local hot spot on the walls and/or floor of the enclosure. The computation is performed to obtain the velocity and temperature distributions and the heat transfer at the walls which are important in predicting thermal comfort and energy savings.