The Effect of Enclosure Height on Natural Convection in a Rectangular Enclosure with Three Heated Sections on the Lower Surface and Cooled Side Walls

摘要

The development of unsteady natural 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 the enclosure is twice the longitudinal length of the enclosure while the height of the enclosure is between 0.5 and 1.5 times the longitudinal length of the enclosure. There are three square, symmetrically placed, isothermal heated sections on the lower surface, the rest of this surface being adia-batic. The vertical side-walls of the enclosure are kept at a uniform low temperature and the horizontal rectangular upper surface is adiabatic. The solution has been obtained by numerically solving the unsteady form of the governing equations, written in dimensionless form, using a iterative, semi-implicit finite-difference method. The solution has the following parameters: the Rayleigh number, Ra, the Prandtl number, Pr, the dimensionless size, ωh, of the square heated sections, the dimensionless distance between the heated sections on the lower surface, ωs and the dimensionless height of the enclosure, A. Results have been obtained for a Prandtl number of 0.7. In the situation considered, it is possible for the flow to be steady at low values of Ra, and for the flow to be unsteady at higher values of Ra. The conditions under which unsteady flow develops and the effect of A on these conditions and on the nature of the enclosure flow have been investigated.