Free Convection in a Rectagular Enclosure With Three Heated Sections on the Lower Surface and Isothermal Side and Top Surfaces

Abstract

The development of unsteady, three-dimensional free convective flow in a rectangular enclosure with multiple heated elements on the bottom horizontal surface has been numerically studied. The enclosure considered has rectangular horizontal lower and upper surfaces and rectangular vertical side surfaces. The horizontal width of enclosure is twice the vertical height of the enclosure while the longitudinal length of the enclosure is equal to the vertical height of the enclosure. There are three square symmetrically placed isothermal heated sections on the lower surface, the rest of this surface being adiabatic. The vertical side-walls and the horizontal rectangular upper surface of the enclosure are kept at a uniform low temperature. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the unsteady, three-dimensional governing equations written in dimensionless form, the solution being obtained in terms of the vorticity vector and vector potential functions. 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 only been obtained for a Prandtl number of 0.7. In a given geometrical situation it was found in all cases that a steady flow exists at low Rayleigh numbers, that an unsteady flow develops at higher Rayleigh numbers and that the flow then again becomes steady at still higher Rayleigh numbers. The conditions under which unsteady flow develops and ceases and the variation of mean Nusselt number with Rayleigh number have been explored.