Three-dimensional numerical analysis of natural convection in a saturated porous matrix (Stability of convection patterns)

Three-dimensional natural convection heat transfer in a saturated porous cube heated from below is analyzed by a finite-element method. The Rayleigh numbers between 50 and 140 are considered. When the Darcy-modified Rayleigh number is high, the convection pattern can take various modes in the cube for a given value of the Rayleigh number. It is found that the convection modes of (1, 0, 1) and (1, 1, 1) are the only stable ones below Ra = 100. Moreover, the (1, 0, 2) mode also becomes stable when Ra is greater than 100. The other modes, however, are unstable at 50≤Ra≤100 in spite of the fact that the corresponding Rayleigh numbers exceed critical values according to the linear stability theory. The Nusselt numbers for respective stable modes are also calculated.