Effects of cavity inclination on mixed convection heat transfer in lid-driven cavity flows

• We investigate effects of aspect ratio and inclination angle in lid-driven cavities.
• Increasing cavity inclination has no effect on average Nu for Ri = 0.01.
• Cavity inclination decreases average Nu for Ri = 1 in A = 0.2 and 1 cavities.
• Cavity inclination enhances average Nu for Ri = 100 in A = 1 and 5 cavities.
• The maximum heat transfer rate occurs at ϕ = 75° and Ri = 100.

Numerical simulations are performed to investigate systematically the effects of inclination angle (ϕ = 0–90°), Richardson number (Ri = 0.01, 1 and 100), and aspect ratio (A = 0.2, 1 and 5) on the flow structures and heat transfer in a air-filled (Pr = 0.71), two-dimensional (2-D) cavity where the flow is induced by a shear force resulting from the motion of the cooled upper lid combined with buoyancy force due to bottom heating. The governing equations for the 2-D velocity and temperature fields are discretized spatially into a fourth-order accurate compact form. Numerical results indicate that among the three aspect ratios investigated the increase of inclination angle does not affect the flow structures and heat transfer when the flow is in a forced convection dominated regime (Ri = 0.01). However, when the flow is in a pure natural convection dominated regime (Ri = 100, Ra = 7.1 × 105), the increase of inclination angle enhances the heat transfer rate for A = 1 and 5 cavities and the maximum heat transfer rate occurs at ϕ = 75°. In addition, the flow changes from a stable, laminar regime to an unstable, chaos regime under certain inclination angles. At these conditions, the total kinetic energy appears to be in periodic or non-periodic oscillation.