Laminar free convection in a vertical slot

This is largely an experimental study of the interaction of buoyancy and shear forces in the free convective flow of a liquid in a rectangular cavity across which there is a uniform temperature difference, ΔT, produced by maintaining the two vertical walls at two different temperatures. The height of the cavity, H , is made larger than the width of the cavity, L , and the cavity is sufficiently long in the third dimension for the mean flow to be nearly everywhere two-dimensional. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H | L , the aspect ratio; A = γ g Δ TL 3 |κν, the Rayleigh number. The experiments are generally restricted to h = 1–60, σ ÷ 10 3 and A < 10 8 . For A < 10 3 the temperature field closely satisfies Laplace's equation but a weak stable unicellular circulation is generated. The flow is vertical throughout the slot except for regions within a distance of order L from the ends. For 10 3 < A < 10 5 , large temperature gradients grow near the walls, and in an interior region a uniform vertical temperature gradient is established. The flow is similar to that near an isolated, heated, vertical plate except that the vertical growth of the wall layers is inhibited in the central part of the slot by the presence of the other layer which prevents entrainment of fluid. Near A = 10 5 the interior region of the flow generates a steady secondary flow. A regular cellular pattern becomes superimposed on the basic flow to produce a ‘cats-eye’ pattern of streamlines. Near A = 10 6 when the secondary cell amplitude is large, a further steady cellular motion is generated in the weak shear regions between each cell.