Natural convection in a cavity with fins attached to both vertical walls

Numerical calculations are presented for two-dimensional natural convection flow inside an air-filled cavity with fins/baffles—of length 0.1, 0.3, and 0.5 of the cavity width—attached along both the heated and the cooled side of the cavity. The governing equations in the stream function-vorticity formulation are solved using finite differences. The Arakawa differencing scheme is used to represent the convection terms. Flow characteristics are investigated for three baffle lengths and Grashof numbers in the range of 9.0 x 103 to 1.0 x 105. A multicellular flow structure is found to exist for a baffle length of 0.1. However, when the baffle length is equal to 0.3 or greater, the fluid flow breaks down into secondary circulations—in addition to the primary circulation— and that, in turn, results in higher heat transfer rates across the two sides of the cavity. Nomenclature Gr = Grashof number, g/3ATw3/v2 h = baffle length N = number of baffles Pr = Prandtl number, via T = temperature u' = nondimensional velocity in £ direction v' = nondimensional velocity in £ direction w = cavity width z = cavity length a = thermal diffusivity j8 = coefficient of thermal expansion d = baffle thickness £ = nondimensional spatial coordinate 0 = nondimensional temperature A = cavity aspect ratio, z/w v = kinematic viscosity £ = nondimensional spatial coordinate r = nondimensional time ^ = nondimensional stream function i// = stream function H = nondimensional vorticity co = vorticity