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Antonio Barletta

Full Professor

Department of Industrial Engineering

Academic discipline: ING-IND/10 Thermal Engineering and Industrial Energy Systems


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.

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.

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.

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.

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