NonOberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol

¹  Physics of Fluids group, Department of Applied Physics, J. M. Burgers Centre for Fluid Dynamics, and Impact-, MESA-, and BMTI-Institutes, University of Twente - P. O. Box 217, 7500 AE Enschede, The Netherlands
²  Fachbereich Physik der Philipps-Universitaet - Renthof 6, D-35032 Marburg, Germany

Received: 1 July 2007
Accepted: 3 September 2007

Abstract

We numerically analyze NonOberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Bénard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number Ra up to 10⁸ (for fixed temperature difference between the top and bottom plates) and as functions of (“non-Oberbeck-Boussinesqness” or “NOBness”) up to (for fixed Ra). For this large NOBness the center temperature T_c is more than larger than the arithmetic mean temperature T_m between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decom- position of into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature T_c as compared to T_m. While for water the origin of the Nu deviation is totally dominated by the second effect (cf. Ahlers G. et al., J. Fluid Mech., 569 (2006) 409) for glycerol the first effect is dominating, in spite of the large increase of T_c as compared to T_m.