1) STABILITY ANALYSIS OF CONVECTIVE FLOWS
A topic of interest in the framework of natural and mixed convection in a channel is the stability analysis of basic flow solutions. In the literature, a great attention has been devoted to this topic, of interest both for research in geophysics and for the engineering/biomedical design. Within this research area, the stability analysis of fluid saturated porous media has a number of possible applications including the analysis of water streams in porous rocks, the underground dispersion of pollutants, the improved performance in the insulation of buildings, in advanced heat exchangers, in solar collectors and in solar ponds. Many authors have examined the basic problem of stability in a horizontal channel (Darcy-Bénard problem) both by using porous flow models more complicated than Darcy's law and by changing external conditions. The objective of this research topic is the analysis of stability of natural and mixed convection, with reference to horizontal and inclined channels of different section shape. Special attention is devoted to the linear stability analysis of basic solutions describing flows in the presence of important effects of viscous dissipation. The instability induced by the viscous dissipation in fact represents an exciting new frontier in the context of the current knowledge on the thermoconvective instability of Rayleigh-Bénard type. Usually, the thermoconvective instability is activated through the thermal boundary conditions. The thermoconvective instability of dissipative type is generated by the fluid flow itself, due to the heat generated by the viscous friction.
2) INSTABILITY OF DISSIPATIVE AND NON-NEWTONIAN FLUID FLOWS
The thermoconvective instability for non-Newtonian fluids is an important topic of applied research, for the technological problems related to the chemical engineering as, for instance, the processing of polymers and liquid foods. The complexity of the rheological behaviour of the fluid, the important effect of viscous dissipation, as well as the strong variation of the fluid properties with temperature, lead to interesting problems for the physical and mathematical modelling of the flows relative to the processes of convection, and challenging issues related to the instability of these flows.
