The Onset of Convection in a Layered Porous Medium with Vertical Throughflow |
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Authors: | D. A. Nield A. V. Kuznetsov |
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Affiliation: | 1. Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand 2. Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC, 27695-7910, USA
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Abstract: | An analytical investigation of the effect of vertical throughflow on the onset of convection in a composite porous medium consisting of two horizontal layers has been made. The cases of iso-flux and iso-temperature boundaries are both investigated. The critical Rayleigh number depends on a Péclet number $Q$ , a permeability ratio $K_{r}$ , a thermal conductivity ratio $k_{r}$ , and a depth ratio $delta $ . For the case of small $Q$ an approximate solution is obtained, which shows that in general throughflow has a stabilizing effect whose magnitude may be increased or decreased by the heterogeneity. This solution is supplemented by an asymptotic solution valid for large $Q.$ |
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