| Abstract: | A numerical analysis was performed to compare natural convection velocities in two-dimensional enclosures of various shape. The following shapes were investigated: circle, square, horizontal and upright 2 × 1 aspect ratio rectangles, horizontal and upright half-circles, diamond (square oriented with diagonal vertical) and triangle (equilateral and horizontal base). In all cases, the length scale in the various dimensionless parameters, such as Rayleigh number, is defined as the diameter of the equal area circle. Natural convection velocities were calculated for Rayleigh numbers of 100 and 500 with the temperature difference taken to be across (a) the maximum horizontal dimension, (b) the median horizontal line (line through centroid) and (c) the horizontal distance such that the temperature gradient is the same for shapes of equal area. A Rayleigh number of 1000 is within the “low Rayleigh number” range for agreement with first order theory for circular enclosures. A Rayleigh number of 5000 is slightly out of this range. For the class of shapes including the square, upright half-circle and upright rectangle, the computed velocities were found to agree very closely with that of the equal area circle when the temperature difference is taken to be across the maximum horizontal dimension condition (a)]. The velocities for the horizontal rectangle and half circle were found to be approximately one-half that of the equal area circle for the same condition. Better overall agreement among all shapes was obtained by setting the temperature difference across a distance such that the temperature gradients were equal for shapes of equal area. |
