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It is a well-known fact that there are several possible convecting patterns for a given Rayleigh number, when a saturated porous square section is heated from below and cooled at the top, with adiabatic side boundaries. The question is which pattern among them is selected preferably or naturally by the system for a fixed value of the Rayleigh number. A pseudospectral numerical method was employed in order to investigate the problem. There are two important findings. One is that the convecting pattern carrying the greatest heat from the bottom to the top boundaries is more stable against disturbances than other possible patterns. This finding is consistent with the Constructal law, as well as the Maximum entropy production hypothesis proposed by Malkus. The other one is that once the system has selected a certain pattern, it persists despite the more heat carrying pattern exists, unless sufficient disturbances are introduced into the system. The system exhibits a strong initial value dependency.

On realizable convection patterns in a saturated porous square section