Keywords:
stability analysis
mixed convection
viscous dissipation
forced convection
free convection
analytical solutions
rheological effects
Research activities on forced, free and mixed convection are
carried out with the main purpose of enhancing, from a
physical/mathematical viewpoint, methods and models commonly used
in the industrial design. It is a known fact that fluid dynamic
processes of forced, free and mixed convection are of great
importance in the analysis of heat exchangers and thermal control
devices, including the recent applications for the MEMS (Micro
Electro Mechanical Systems), in the study of flows in pipelines for
oil and in the design of devices for the extrusion of polymers.
Methodological issues of great scientific interest arise especially
in the flow regimes involving complex interactions between
different physical effects such as those related to fluid saturated
porous media, or the presence of fluids with a non-Newtonian
behaviour, or those related to the viscous dissipation in the
fluid, to the unsteady regime and to the presence of complex
boundary conditions. Among the main lines of research addressed, I
quote the following topics.
1) ANALYSIS OF STABILITY OF CONVECTION FLOWS IN POROUS MEDIA
A topic of interest in the framework of mixed convection in porous
media 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
design. Possible applications include the analysis of water streams
in porous rocks, the underground dispersion of pollutants, the
improved performance in the insulation of buildings, in solar
collectors and in solar ponds. Many authors have examined the basic
problem of stability in a horizontal channel (Darcy-Bénard problem)
both using porous flow models more complicated than Darcy's law and
changing external conditions. The objective of this research topic
is the analysis of stability of mixed convection, with reference to
horizontal channels. 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. In circular and annular
ducts containing a porous medium saturated by a fluid,
non-axisymmetric boundary conditions can give rise to instability
of Rayleigh-Bénard type as well. In such cases the analysis of the
linear instability leads to the formulation of eigenvalue problems
on two-dimensional circular or annular domains. The numerical
solution of these problems can be tackled using the Galerkin finite
element method.
2) INSTABILITY OF DISSIPATIVE AND NON-NEWTONIAN FLUID FLOWS
The hydrodynamic and thermoconvective instability in 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 modeling of the flows relative to
the processes of convection, and challenging issues related to the
instability of these flows. Recently, I have contributed to a
research program analyzing the instability of Rayleigh-Bénard type
in porous media saturated with a power-law fluid. A goal of the
future research in this area is the extension to the case of fluids
with a yield-stress and of viscoelastic fluids.
3) NEW ISSUES FOR THE INSTABILITY OF FLOWS OF COUETTE OR POISEUILLE
TYPE IN PLANE CHANNELS
It is well known that the Poisuille laminar flow in a plane
parallel channel may be subject to linear hydrodynamic instability,
and that this instability does not arise in the case of the Couette
flow. A new perspective on this issue is based on the study of
fluids with a high viscosity (high Prandtl number), for which the
effect of viscous dissipation appears to be an important phenomenon
with respect to the energy balance. For these fluids, the
activation of the linear instability is observed both in the
Poiseuille flow and in the Couette flow. Such instability, although
of thermoconvective type, is linked to the viscous dissipation in
the fluid and may be more critical than the hydrodynamic
instability in the case of the Poiseuille flow.