Laminar thermal convection of air confined to an isosceles triangular cavity heated from the base and symmetrically cooled from the upper inclined walls has been investigated numerically. The system of transient conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. The maximum height-to-base aspect ratio A is fixed at 0.5, while the Grashof number extends from a low Gr = 103 to a high Gr = 106. The influence of Gr on the flow and temperature patterns is analyzed and discussed for two opposing scenarios, one corresponds to increasing Gr and the other corresponds to decreasing Gr. It is found that two steady-state solutions are possible, excluding their solution images through a vertical mirror plane. The symmetrical solution prevails for relatively low Grashof numbers. However, as the Gr is gradually increased, a transition occurs at a critical value of Gr. Above this critical value of Gr, an asymmetrical solution exhibiting a pitchfork bifurcation arises and eventually becomes steady. The existing ranges of these unsteady and steady solutions are reported for the two opposing scenarios. Also, issues related to the observed hysteresis phenomenon are discussed in detail.
- Heat Transfer Division
Thermal Convection Bifurcation Within Isosceles Triangular Cavities
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Ridouane, EH, & Campo, A. "Thermal Convection Bifurcation Within Isosceles Triangular Cavities." Proceedings of the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference. ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 3. Vancouver, British Columbia, Canada. July 8–12, 2007. pp. 515-522. ASME. https://doi.org/10.1115/HT2007-32577
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