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Maximizing the heat flux in steady unicellular porous media convection

The primary aim of the present study is to determine the maximum heat transport attainable in steady 2D unicellular porous media convection. By focusing on this restricted class of flows we are able to use an efficient iterative numerical scheme to systematically probe the way in which the heat transport depends on the inter-plume spacing. Guided by our numerical results, we also propose a large-Ra asymptotic reduction of the governing equations that yields the asymptotic structure of the solutions giving the maximum heat transport.