Laminar natural convection heat transfer in a differentially heated cavity with a thin porous fin attached to the hot wall

Laminar natural convection heat transfer in a differentially heated square cavity with a thin porous fin attached to the hot wall is studied numerically under steady state condition. Various pertinent parameters were employed, such as the Rayleigh number, Darcy number, fin inclination angle, length and position of the fin. Three different fin lengths (L = 0.2, 0.35, and 0.5) and positions (S = 0.25, 0.5, and 0.75) are considered. The inclination fin angle is varied between 30° and 150°. The left wall of the cavity, to which the fin is attached, is assumed uniformly heated while the right wall is kept at a lower temperature. In addition, the horizontal walls of the cavity were considered insulated. Furthermore, the governing transport equations within the porous media are treated according to the volume-average theory while the Navier-Stokes equations were employed to represent the transport phenomena in the rest of the cavity. Moreover, the governing equations are solved using a finite element formulation based on the Galerkin method of weighted residuals. The results of this investigation showed that the presence of a porous fin increases the average Nusselt number when compared with the differentially heated cavity for various lengths, positions, and inclination angle of the fin. To achieve optimum heat transfer, the present results suggests that the porous fin should be placed either close to the bottom surface or in the middle of the vertical hot surface and an angle of 90°. Finally, a numerical correlation for the average Nusselt number was developed as a function of the employed range of the Rayleigh number, Darcy number, fin's length and position.