Comparison study of natural convection between rectangular and triangular enclosures

Abstract

The steady laminar natural convective heat transfer for air has been compared numerically between cavities with rectangular and triangular structures. The equations of momentum, heat, and mass transfer were solved using the finite difference method, and central difference approximations that have second-order accuracy were used; furthermore, a good convergence was guaranteed by using the successive under-relaxation method. The Prandtl number is fixed at 0.71, while the Rayleigh number and the aspect ratio of the enclosures were changed in the range of 103–106 and varied over 1, 0.5, 0.2, and 0.1, respectively. The cavity was heated from one vertical wall and cooled from one side, while the horizontal walls were insulated. The influence of the Rayleigh number and the aspect ratio of the both kinds of cavities on the rate of heat transfer was investigated. Results were presented using flow patterns and isotherms plots; additionally, local and mean Nusselt numbers are also obtained for all cases. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh numbers significantly augments the heat transfer, the intensity of natural convection, and average Nusselt number. Another important finding is that conduction is the dominated mechanism when the aspect ratio is small originally, and then, as the aspect ratio increases, the role of the convection boosts, and finally, the convection is overwhelmed by the convection. It can be concluded that for a given aspect ratio, only when the Rayleigh number is large enough can it induce a significant convection.