Heat transfer in a layered porous medium heated from below

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Abstract
Previous work by the present authors on the onset of convection in a layered porous medium heated from below is extended to an investigation of the heat transported by convection at slightly supercritical Rayleigh numbers.The two-dimensional convection patterns and associated values of the critical Rayleigh number, cell width and slope of the Nusselt-number graph are calculated for two- and three-layer configurations over a wide range of layer depth and permeability ratios. The results show that the commonly studied problem of a homogeneous layer bounded above and below by impermeable boundaries is a special case, in that the slope of the Nusselt-number graph at the critical point is nearly independent of cell width. For a homogeneous layer with a permeable upper boundary, and for multi-layered systems, the slope of this graph depends strongly on cell width.