AbstractMotivated by Malkus' marginally stable boundary layer theory, we design an optimization problem to predict the heat transport through a two-dimensional, horizontal porous layer heated from the below and cooled from above. We solve the optimization problem numerically using a implemented package in Matlab. Our results show that the linear stability constraint well captures the unit-scaling property of flux at large values of Rayleigh number. Moreover, the predicted mean temperature profile shares many …
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