Effect of thin fin on non-darcy buoyancy flow in a square cavity filled with porous medium

A penalty finite element analysis is performed for a natural convection flow in a differentially heated square cavity filled with porous matrix with a solid thin fin attached at the hot left wall, whereas the horizontal walls are thermally insulated. A Darcy-Forchheimer model is used to predict the temperature field and the flow circulations in the porous medium, and it is assumed that the porosity of the medium is φ = 0.4 and that the Forchheimer number is F = 0.011 throughout this study. The effect of the highly conductive fin of three different lengths L _p = 0.3, 0.5, 0.7, located at three different positions S _p = 0.25, 0.5, and 0.75, is examined for Da = 10 ^-4, 10 ^-3, and 10 ^-5 with Ra = 10 ⁶ and Pr = 0.7 and 10. It is identified that due to attaching the fin on the hot wall, the primary vortex is modified, and the modification depends on the fin's location and length. For Da = 10 ^-3 and Pr = 0.7, it is observed that there is a counterclockwise secondary flow formation around the tip of the fin for S _p = 0.5 for all length L _p. Moreover, when Da = 10 ^-2, the secondary circulation behavior has been observed for S _p = 0.25, and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation. However, these secondary circulation features are not observed for Pr = 10. The fin's conductivity effects on the heat transfer rates are investigated through local Nusselt number and average Nusselt number as a function of fin length L _p. It is found that the average Nusselt number at the left wall decreases as the length of the fin increases for all locations. However, the rate of decrease of average Nusselt number becomes slower as the location of the fin moves from the bottom wall to the top wall.