Experimental and Numerical Studies of Natural Convection With Flow Separation in Upward-Facing Inclined Open Cavities

Steady two-dimensional laminar natural convection heat transfer from isothermal horizontal and inclined open cavities of rectangular cross section has been investigated experimentally using a Mach-Zehnder interferometer and numerically by a finite difference technique. Experimental results are presented for Prandtl number, Pr = 0.7, Rayleigh numbers from 10⁴ to 5 × 10⁵, cavity aspect ratios, A (or h/w) = 0.25, 0.5, and 1.0, and inclination angles (or angles of rotation about the longitudinal axis), θ = 0, 30, 45, and 60 deg to the horizontal. The numerical model uses a relaxation technique to solve the governing elliptic, partial differential equations. Numerical results are presented for the range of Rayleigh number, 10³ ≤ Ra_w ≤ 5 × 10⁵, θ = 0 and 45 deg, and A = 1. Flow and temperature patterns, velocity and temperature profiles, and local and average heat transfer rates are presented. Flow recirculation with two counterrotating convective rolls developed in the cavity at Ra ≥ 10⁵. The inclination of the cavity induced flow entrainment, causing flow separation at the lower corner and flow reattachment at the upper corner of the aperture opening except in shallow cavities, A < 0.5, where the flow reattachment occurred on the base of the inclined cavity. For all Ra numbers, the first inclination of the cavity from the horizontal caused a significant increase in the average heat transfer rate, but a further increase in the inclination angle caused very small increase in heat transfer rate. However, for every angle of inclination considered, the average heat transfer rate increased significantly as Ra was increased. The equation of the form Nu = mRaⁿ, where 0.018 ≤ m ≤ 0.088 and 0.325 ≤ n ≤ 0.484, correlates the experimental and numerical results satisfactorily for the range of Ra, 10⁴ ≤ Ra ≤ 5 × 10⁵ and of θ, 0 ≤ θ ≤ 60 deg. The present experimental and numerical results are in good agreement with the results reported in the literature.