Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides

Steady natural convection in an enclosure heated from below and symmetrically cooled from the sides is studied numerically, using a streamfunction-vorticity formulation. The Allen discretization scheme is adopted and the discretized equations were solved in a line by line basis. The Rayleigh number based on the cavity height is varied from 10 3 to 10 7. Values of 0.7 and 7.0 for the Prandtl number are considered. The aspect ratio L H (length to height of the enclosure) is varied from 1 to 9. Boundary conditions are uniform wall temperature and uniform heat flux. For the range of the parameters studied, a single cell is observed to represent the flow pattern. Numerical values of the Nusselt number as a function of the Rayleigh number are reported, and the Prandtl number is found to have little influence on the Nusselt number. A scale analysis is presented in order to better understand the phenomenon.