Well-resolved direct numerical simulations of 2D Rayleigh-B\'enard convection in a porous medium are presented for Rayleigh numbers Ra≤4×10⁴ which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu~Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra→∞ by a simple columnar ``heat-exchanger'' model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k~Ra0.4.
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Hewitt et al. (2012) studied this question.
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