Natural convection in a rectangular enclosure with two heated sections on the lower surface

The development of unsteady free convective flow in a rectangular enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower and upper surfaces and vertical side surfaces. The horizontal width of enclosure is twice the vertical height and longitudinal length of the enclosure. There are two square isothermal heated sections on the lower surface, the rest of this surface being adiabatic. The vertical side-walls of the enclosure are kept at a uniform low temperature. The horizontal rectangular upper surface of the enclosure is either (a) adiabatic or (b) isothermal and at the same low temperature as the vertical side-walls. The governing unsteady, three-dimensional flow equations, written in dimensionless form, have been solved using an iterative, semi-implicit finite-difference method. The solution has the following parameters: the Rayleigh number, Ra, the Prandtl number, Pr, the dimensionless size, wH, of the square heated sections and the dimensionless distance between the heated sections on the lower surface, wS. Results have been obtained for a Prandtl number of 0.7. Most of the results presented here are for wH = wS = 1/3. The results indicate that for the flow situation considered the flow is steady at low Rayleigh numbers, becomes unsteady at intermediate Rayleigh numbers and then again becomes steady at higher Rayleigh numbers The conditions under which unsteady flow develops and the nature of the unsteady flow have been investigated and the variation of mean Nusselt number with Rayleigh number has been explored.