Laminar free convection in a nonrectangular inclined cavity

Numerical calculations are presented for two-dimensional natural convection flow in a nonrectangular inclined cavity. The governing equations in the stream function-vorticity formulation are solved using finite differences. Arakawa's differencing scheme is used to represent the convection terms. Flow characteristics are investigated for Grashof numbers and inclination angles in the range of 9.0 x 10 3 to 1.25 x 10 5, and —30 to 30 deg (from the vertical), respectively. A multicellular flow structure is found to exist for all angles of inclination considered. Although steady-state solutions were achieved for all Grashof numbers and angles of inclination considered, the flow structure that was predicted (steady vs unsteady) was found to depend strongly on the initial condition and, in some cases, unsteady flows were predicted if the wrong initial condition was specified. Nomenclature a = cavity width d = cavity length Gr = Grashof number, g/3ATa3/v2 Pr = Prandtl number, via T = temperature u' = nondimensional velocity u, v = velocity component in x and y direction v' = nondimensional velocity a — thermal diffusivity j8 = volumetric expansion coefficient £ = nondimensional spatial coordinate 0 = nondimensional temperature # = inclination angle A — cavity aspect ratio, dla v — kinematic viscosity f = nondimensional spatial coordinate p = density T = nondimensional time ty = nondimensional stream function i/r = stream function 11 = nondimensional vorticity a) = vorticity