Antonio Barletta | antonio.barletta@unibo.it
Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Abstract: The effect of viscous dissipation may be the sole cause of a thermoconvective instability either in a fluid clear of solid material or in a fluid saturated porous medium. Several recent investigations have recently contributed to illustrate this result under different flow and thermal conditions. The elementary physical nature of the dissipation induced instability is just the same as that of the Rayleigh-Bénard instability, namely the onset of a secondary buoyant flow taking place when the basic temperature gradient becomes sufficiently intense. The fundamental difference is that the dissipation instability is not induced by an external thermal forcing, due to the temperature boundary conditions, as it happens for the Rayleigh-Bénard instability. On the other hand, the cause of the dissipation instability is the basic flow rate itself, acting thermally as a heat generation mechanism. Thence, the fundamental parameter determining the transition from stability to instability is not the Rayleigh number, as in the classical Rayleigh-Bénard problem, but the product between the Gebhart number and the square Péclet number.
Keywords: Viscous dissipation, Linear instability, Rayleigh-Bénard problem, Porous medium