The Effect of Conducting Boundaries on the Onset of Convection in a Porous LayerWhich is Heated from Below by Internal Heating

Afiqah Nadzirah Mohammad (1) , D. Andrew Rees (1) , Abdelkader Mojtabi (2)

1 University of Bath [Bath]
2 IMFT - Institut de mécanique des fluides de Toulouse

The onset of convection in a porous layer heated from below is considered, and we determine how the presence of two solid but heat-conducting bounding plates of finite thickness alters the manner in which convection ensues. Heat is generated by the lower plate (with an insulating lower boundary), but the upper one is passive with a fixed upper boundary temperature. It is shown that this composite layer may mimic in turn one of the three different types of classical single-layer onset problems which are well-known in the literature. The type which is selected (or indeed whether it corresponds to a transitional case) depends quite critically on the precise values of the relative thickness of the solid layers and their conductivity ratio. It is also shown that care needs to be taken over declaring that the solid plates are thin: extreme values of the conductivity ratio can yield a stability criterion which appears to be different from that suggested by the imposed boundary conditions.

Mots clés: Natural convection; Porous medium; Linear stability; Dispersion relation; Conducting bounding layers

Domaines: Mécanique des fluides [physics.class-ph]

Afiqah Nadzirah Mohammad, D. Andrew Rees, Abdelkader Mojtabi. The Effect of Conducting Boundaries on the Onset of Convection in a Porous LayerWhich is Heated from Below by Internal Heating. Transport in Porous Media, 2017, vol. 117 (n° 2), pp. 189-206. ⟨10.1007/s11242-017-0828-x⟩. ⟨hal-01542773⟩