Convective instability of a horizontal fluid layer with a heat-conducting permeable partition

Abstract

The effect of the resistance of a permeable partition on the equilibrium stability of a fluid layer heated from below was previously considered in [1--3]. There it was assumed that the partition had no thermal inertia, which is valid for thin partitions with low thermal conductivity. For partitions with high thermal conductivity relative to the fluid the heat transfer along the partition must be taken into account. As shown below, this has a significant effect on the convection threshold. 1. We will consider a horizontal layer Izl -<h of viscous fluid located between rigid masses of the same thermal conductivity, in which at points distant from the layer a downward-directed (opposite to the z axis) temperature gradient is maintained. In the middle of the layer (z =0) there is a thin permeable partition with finite longitudinal thermal conductivity. With the fluid in mechanical equilibrium, a temperature difference 20 develops at the edges of the layer. For infinite boundary masses, the problem of the behavior of normal perturbations in the fluid-mass system can be formulated with respect to the amplitude of the vertical velocity component v(z) and the amplitude of l~ae temperature perturbation O(z) in the fluid layer. In the absence of a partition, in accordance with [4], the boundary-value problem for the neutral perturbations has the form: