Steady two-dimensional natural convection in air-filled, regular and irregular inclined enclosures has been investigated numerically. 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 comer points of the cavity and its effect on the calculated Nusselt number has been discussed. Rayleigh numbers range between 103 and 104, aspect ratio (width/height) =1,2,4, and angle of inclination in the range between 0 and 90°. While the cavity bottom and top walls were kept at constant temperatures at Th (heated) and at Tc (cooled), respectively, thermal conditions of end walls were varied. In addition to the base case of insulated end walls, seven different configurations of thermal conditions of the two side walls have been studied. Results show that numerically predicted heat transfer rates strongly depend on the numerical treatment of temperature discontinuities at cavity comer points. Results also 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 occurred as the cavity angle of inclination varied from zero (horizontal position) to 90 ° (vertical position) and back to zero. The effect of curved bottom is carried out by replacing flat bottom of the cavity with a curved one. Only insulated end walls were discussed in curved case. Results indicated that heat transfer rate and mode transition are strongly dependent on the height of curvature of the bottom wall, which offers more flexibility in controlling flow mode-transition, and hence, effectiveness of heat transfer inside the cavity. / Thesis / Master of Applied Science (MASc)