Natural convection through vertical porous stratum

Abstract

The combined effect of Darcy and viscous resistances on the fully developed natural convection of a fluid between two heated vertical plates is investigated. When Darcy and viscous dissipations, in the energy equation, are negligible the energy and momentum equations become decoupled and we obtain the modified Poiseuille flow distribution through porous media. The deviation of the velocity and temperature distributions from those existing in modified Poiseuille flow are presented for various porous number σ =b/k b is the spacing between the plates and k is the permeability of the porous medium) when dissipations are not neglected. It is shown that the increase in porous number rapidly decreases the influence of both viscous and Darcy dissipations on velocity and temperature profiles. Therefore, by suitable adjustment of dissipation terms, it is possible to control the temperature distribution which will be of some use in plant physiology.