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Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

Published online by Cambridge University Press:  24 February 2014

P. Ripesi ,
L. Biferale ,
M. Sbragaglia  and
A. Wirth
P. Ripesi
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
L. Biferale*
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
M. Sbragaglia
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
A. Wirth
Affiliation:
Laboratoire LEGI (UMR 5519, CNRS), Université de Grenoble, 38041 Grenoble CEDEX 9, France
*
†Email address for correspondence: biferale@roma2.infn.it
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Abstract

We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh–Bénard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, at both low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of ‘bulk’ convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to $\mathit{Ra} \sim 10^{10}$.

JFM classification

Convection: Convection Instability: Instability Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 636 - 663
Copyright
© 2014 Cambridge University Press 

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