Summary
The effects of a nonuniform temperature gradient and inertia arising due to throughflow on the onset of convection in a porous layer for different types of boundaries are investigated. Closed form solutions are obtained for the boundaries which are insulating to temperature perturbations, and for the conducting boundaries solutions are obtained using Galerkin technique. It is found that when the two boundaries are of the same type, the effect of throughflow is to stabilize the system irrespective of its direction. However, when the lower and upper boundaries are of different types, a small amount of throughflow in one particular direction destabilizes the system depending upon the values of the Prandtl number and the porous parameter. The standard results available are obtained as limiting cases.
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Shivakumara, I.S. Boundary and inertia effects on convection in porous media with throughflow. Acta Mechanica 137, 151–165 (1999). https://doi.org/10.1007/BF01179206
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DOI: https://doi.org/10.1007/BF01179206