Issue
EPL
Volume 80, Number 3, November 2007
Article Number 34002
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/80/34002
Published online 28 September 2007
EPL, 80 (2007) 34002
DOI: 10.1209/0295-5075/80/34002

Non$\hbox{--} $Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol

K. Sugiyama1, E. Calzavarini1, S. Grossmann2 and D. Lohse1

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 in final form 3 September 2007; published November 2007
published online 28 September 2007

Abstract
We numerically analyze Non$\hbox{--} $Oberbeck-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 $\Delta $ between the top and bottom plates) and as functions of $\Delta $ ("non-Oberbeck-Boussinesqness" or "NOBness") up to $50\,{\rm K}$ (for fixed Ra). For this large NOBness the center temperature Tc is more than $5\,{\rm K}$ larger than the arithmetic mean temperature Tm 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 NuNOB/NuOB 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 Tc as compared to Tm. 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 Tc as compared to Tm.

PACS
47.27.te - Turbulent convective heat transfer.
47.20.Bp - Buoyancy-driven instabilities (e.g., Rayleigh-Bénard).
47.27.ek - Direct numerical simulations.

© Europhysics Letters Association 2007