Laminar natural convection in cavities filled with circular and square rods

This work compares heat transfer characteristics across a square cavity partially filled with a fixed amount of conducting solid material. The solid phase is shaped into two different geometries, namely square and cylindrical rods, which are horizontally displaced inside the cavity. Comparisons are obtained by numerically solving a conjugate heat transfer problem that considers both the solid and the fluid space. Governing equations are solved using the finite volume method and the algebraic equation set is relaxed with the SIP procedure. The average Nusselt number at the hot wall, obtained from the cavity with square obstacles and for several Darcy numbers, are compared with those calculated with circular obstacles. When comparing the two geometries considering the same modified Rayleigh number Ra_m, this study shows that the average Nusselt number for cylindrical rods are slightly lower than those for square rods.