Mixed convection in a vertical tube partially filled with porous medium

The purpose of the present study is to analyze numerically the developing mired convection in a vertical tube partially filled with porous medium. The SIMPLEC algorithm combining the alternating directions implicit (ADI) and successive overrelation (SOR) techniques is used in this study. The diffusion and convection are handled by a hybrid scheme. The non-Darcy model, which includes inertia effect, boundary friction effect, and convection, is used in the momentum equations for the porous medium layer The velocity and temperature distributions, local Nusselt number (Nu(x)), local friction coefficient (C-f), pressure drop, and entrance length in a vertical tube partially piled with porous medium are obtained under various parameters, such as different thicknesses of porous medium (R(s)), Darcy number (Da), and Grashof number (Gr). The numerical results show that Nu(x) at about Z = 2, within the entrance region, increases slightly when R(s) = 0.5. Also, when the porous layer thickens, Nu, increases as Z < 0.6 and decreases as Z > 0.6. As Z > 2, there is a minimum local friction coefficient where R(s) approximate to 0.2. When Z and Da are small, there is a large velocity difference adjacent to the interface of the composite system. At Z = 5 and Gr = 10(4) the central line velocity is smaller than the inlet velocity. In all cases the local friction coefficient varies dramatically as Z < 1. The hydrodynamic entrance length is shorter as the value of R(s) is increased, and is longer as the values of Da and Gr are increased. The thermal entrance becomes longer as the values of R(s) and Da increase and shorter as the values of Gr increase.