Numerical analysis of the effect of porous structure on free convection heat transfer inside an eccentric annular space

In the literature, there are some conclusions seem to be conflicting about the effect of porous structure of a packed bed of spheres, in particular the effects of the sphere diameter and the porosity on the heat transfer by convection. For this reason, the present numerical analysis investigates the effects of these two parameters on natural convection heat transfer inside an eccentric annulus packed with stationary spheres. More reliable models for energy and momentum transport in porous media, namely the two-phase energy model that fails to postulate local thermal equilibrium “LTE” status between the solid spheres and the flowing fluid, and the full Darcy–Brinkman–Forchheimer momentum model, are employed. This non-dimensional analysis is conducted for different spheres’ sizes (annulus interior cylinder/sphere diameter ratio, D_i/d=20−100), porosities (ɛ=0.3−0.7), and sphere materials (solid/fluid thermal conductivity ratio, Kr=1−10⁵), and at various heating represented by Rayleigh number (Ra=8×10⁷−2×10⁸). The results show that the effects of these parameters depends strongly on the thermal conductivity of the spheres material. Thus, it was found that at lower thermal conductivity ratio, the bigger sphere size or the larger porosity produces the higher convection heat transfer. However, at moderate thermal conductivity ratio, the convection heat transfer can be increased or decreased as the sphere size or the porosity increases. But, at higher thermal conductivity ratio, the increase in the sphere size or the porosity causes a decrease in the convection heat transfer.