Flow mode-transition of natural convection in inclined rectangular enclosures subjected to bidirectional temperature gradients

Steady two-dimensional natural convection in air-filled, rectangular, inclined enclosures has been investigated numerically. Conservation of mass, momentum, and energy equations have been solved using finite volume approach employing a staggered grid arrangement. The physical covariant velocity components and temperature have been selected as the independent variables in the momentum and energy equations and the coupling between the continuity and momentum equations has been accounted for using the SIMPLE algorithm.The effect of various configurations of bidirectional temperature gradients on mode transition of thermal convection inside the cavity has been investigated. Numerical treatment of temperature discontinuity at the corner points of the cavity and its effect on the calculated Nusselt number has been discussed.Simulations have been carried out for Rayleigh numbers in the range between 103 and 104, aspect ratio (width/height) =4, and angle of inclination between 0 and 90°. Results indicate that thermal conditions of cavity end walls have a significant effect on mode-transition of thermal convection flows; and hence, on heat transfer effectiveness inside the cavity, and on the Hysteresis phenomenon (multi-steady solutions) occurred as the cavity angle of inclination (γ) varied. The existence of such multi-steady solutions strongly depends on the value of Rayleigh number.