Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above

A numerical study of natural convection in an isosceles triangular enclosure with a heated horizontal base and cooled upper walls is presented. Nearly every previous study conducted on this subject to date has assumed that the geometric plane of symmetry is also a plane of symmetry for the flow. This problem is re-examined over aspect ratios ranging from 0.2 to 1.0 and Grashof numbers from 10³ to 10⁵. It is found that a pitchfork bifurcation occurs at a critical Grashof number for each of the aspect ratios considered, above which the symmetric solutions are unstable to finite perturbations whereas two steady mirror image solutions are stable. Results are presented detailing the occurrence of the pitchfork bifurcation in each of the aspect ratios considered and the resulting flow patterns are described. Local and mean heat transfer coefficients are presented, and discrepancies with previously published results in which a symmetric flow pattern is assumed are discussed.