In this paper we apply the ideas introduced with the so-called extended-quasi-thermal-incompressible (EQTI) model, recently proposed by Gouin and Ruggeri (Int. J. Non-Linear Mech. 47 (2012) 688–693) [12]. In particular, in the Oberbeck–Boussinesq approximation we consider the more realistic constitutive equation compatible with the thermodynamical stability by putting in the buoyancy term a density which depends not only by the temperature but also on the pressure. The equation for the pressure is then modified by an extra dimensionless parameter β^ which is proportional to the positive compres- sibility factor β. The 2-D linear instability of the thermal conduction solution in horizontal layers heated from below (Bénard problem) is investigated. It is shown that for any β^ : (i) the rest state pressure profile is different from the parabolic one; (ii) if convection arises, then it first arises via a stationary state and the strong principle of exchange of stability holds; for small β^ : (iii) convection certainly arises provided Ra is sufficiently large; (iv) the related critical Rayleigh number coincides -in the limit of vanishing β^ – with the classical one, and decreases as β^ increases.
Passerini, A., Ruggeri, T. (2014). The Bénard problem for quasi-thermal-incompressible materials: A linear analysis. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 67, 178-185 [10.1016/j.ijnonlinmec.2014.09.003].
The Bénard problem for quasi-thermal-incompressible materials: A linear analysis
RUGGERI, TOMMASO ANTONIO
2014
Abstract
In this paper we apply the ideas introduced with the so-called extended-quasi-thermal-incompressible (EQTI) model, recently proposed by Gouin and Ruggeri (Int. J. Non-Linear Mech. 47 (2012) 688–693) [12]. In particular, in the Oberbeck–Boussinesq approximation we consider the more realistic constitutive equation compatible with the thermodynamical stability by putting in the buoyancy term a density which depends not only by the temperature but also on the pressure. The equation for the pressure is then modified by an extra dimensionless parameter β^ which is proportional to the positive compres- sibility factor β. The 2-D linear instability of the thermal conduction solution in horizontal layers heated from below (Bénard problem) is investigated. It is shown that for any β^ : (i) the rest state pressure profile is different from the parabolic one; (ii) if convection arises, then it first arises via a stationary state and the strong principle of exchange of stability holds; for small β^ : (iii) convection certainly arises provided Ra is sufficiently large; (iv) the related critical Rayleigh number coincides -in the limit of vanishing β^ – with the classical one, and decreases as β^ increases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
