Laminar Free Convection in Three Dimensional Inclined Porous Annulus


A numerical method was utilized for the three dimensional natural convection heat transfer in an annulus enclosure concentric cylinders with (or without) annular fins attached to the inner cylinder. The annular was filled with porous media for annulus inclination angle of (δ = 0˚, 30˚, 60˚ and 90˚) and a range of modified Rayleigh number (0.2 ≤Ra*≤ 500). The governing equations used under assumptions used Darcy law and Boussinesq’s approximation and then solved numerically using finite difference approximation. It was found that the maximum value of the local Nusselt number for vertical cylinder was about two times larger than the horizontal case while the average Nusselt number was depend on (Ra*, Hf, δ and Rr ). The results showed that the increasing of the fin length increases the heat transfer rate for any fin pitch. All parameters, results showed that the average Nu number increases with an increase of modified Rayleigh number and hardly affected by δ for low values of Ra*.A comparison was made between the results of the present work and those of other researches for the case without fins and excellent agreement was obtained. A correlation for Nu with Ra, Rr and δ, has been developed for inner cylinder