Influence of a linear concentration heat source and a quadratic density on the onset of penetrative convection (Q2467917)

The authors investigated the penetrative convection in horizontal fluid layer \(\{{(x,y,z)} \in {\mathbb{R}^{3}} \mid 0\leq z \leq d\}\) with quadratic equation of state for the density under the action of a vertical gravity field and an internal heating due to a linear concentration source, according to the Navier-Stokes model. As in the previous article they perform the nonlinear stability analysis and find sufficient conditions ensuring that the penetrative convection can not occur.