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A numerical analysis has been performed to investigate two-dimensional natural convection inside a differentially heated inclined rectangular enclosure with several porous fins attached to the hot wall. Various parameters were studied including Rayleigh number (103 ≤ Ra ≤ 106), Darcy number. (10−8 ≤ Da ≤ 10−2), relative thermal conductivity ratio of solid phase to fluid (1 ≤ Ke ≤ 100), cavity inclination angle (0 ≤ φ ≤ π/3), cavity aspect ratio (AR = 2:1 and 3:1), fin number (0 ≤ N ≤ 4), dimensionless fin position (0.25 ≤ S ≤ 0.75) and dimensionless fin length (0.25 ≤ L ≤ 0.75). Left vertical wall is maintained at a higher temperature Th, while the right vertical wall is kept at lower temperature Tc and horizontal walls are insulated. Cavity is filled with an incompressible Newtonian fluid with Prandtl number of 0.71. Fins with length of lf are attached to the hot vertical wall. Due to a small temperature difference between the hot and cold vertical walls, all of the thermo-physical properties, except the density variation in the body force term, which is modeled using the Boussinesq approximation, are assumed constant. Governing steady state equations for mass, momentum and energy within the porous fin is based on volume-averaging method and the finite volume code based on SIMPLE method was utilized in the present investigation to solve the governing equations. The investigated results illustrated that using several conductive porous fins, increase the average Nusselt number within the cavity up to 41% compared to enclosures with solid fins and up to 20% compared to cavities without any fins. Furthermore, it was found that increasing heat transfer using more porous fins highly depends on the relative thermal conductivity ratio of solid phase to fluid and rising the thermal conductivity ratio from 10 to 100, results in 17% of heat transfer enhancement. It was found that Da = 10−5 is a limit for positive performance of the porous fins, below which no heat transfer enhancement occurs compared to cavities with solid fins. Optimum porous fin length was found to be a decreasing function of Rayleigh number.

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This page is a summary of: Comprehensive investigation of solid and porous fins influence on natural convection in an inclined rectangular enclosure, International Journal of Heat and Mass Transfer, April 2019, Elsevier, DOI: 10.1016/j.ijheatmasstransfer.2018.12.156.
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