This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO-water nanofluid and differentially heated. Conservation of mass, momentum, and energy equations are solved numerically by a control volume finite-element method using the SIMPLER algorithm for pressure-velocity coupling. The Prandtl number is fixed at 7.02, corresponding to water. Aspect ratio and solid volume fraction are varied from 0.5 to 4 and from 0% to 4%, respectively. The inclination angle is varied from 0 degrees to 90 degrees and used as a control parameter to investigate flow mode-transition and the accompanying hysteresis phenomenon (multi-steady solutions). It is found that the efficiency of heat transfer is improved by the addition of nanoparticles into base fluid; however, there is an optimum solid volume fraction that maximizes the heat transfer rate. Numerical results show also that the diameter of solid particle is an important parameter that affects the heat transfer efficiency; its impact is more important than the concentration itself. Effects of inclination angle on streamlines and on thermal boundary layer are presented. Combined effects of aspect ratio and inclination angle on heat transfer and hysteresis region are analyzed.