Three-Dimensional Natural Convective Flow in a Rectangular Enclosure With a Rectangular Heated Section on One Vertical Wall and With the Other Vertical Walls Cooled

Abstract

Three-dimensional natural convective flow in a rectangular enclosure with vertical sidewalls and horizontal top and bottom surfaces has been considered. A heated rectangular element is mounted in the middle of one vertical wall of the enclosure, the remainder of this wall being adiabatic. The remaining vertical walls are cooled to a uniform low temperature. The horizontal top and bottom walls are adiabatic. The flow has been assumed to be steady and laminar. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. Radiation effects have been neglected. The numerical solution was obtained using the governing equations written in terms of dimensionless variables. The enclosure height, H′, was used as the characteristic length scale and the difference between the temperatures of the hot wall section and the cooled walls were used as the characteristic temperature scale. The dimensionless governing equations have been solved using FIDAP, a commercial software package that employs the finite element method. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless height of the heated wall section compared to the overall enclosure height; the dimensionless width of the heated wall section compared to its height; the dimensionless width of the enclosure between the vertical sidewall on which the heated wall section is mounted and the opposite vertical sidewall, and the dimensionless width of the enclosure between the other two vertical sidewalls. Because of the application being considered, results have only been obtained for Pr = 0.7. Attention has been restricted to the case where the dimensionless width of the enclosure between the vertical sidewall on which the heated wall section is mounted and the opposite vertical sidewall is 0.5 and where the dimensionless width of the enclosure between the other two vertical sidewalls is 1.0. A wide range of the other parameters has been considered particular attention having been given to the effect of the dimensionless width of the heated wall section compared to its height on the mean Nusselt number for the heated wall section.