Rayleigh-Bénard convection with imposed heat flux

2007 ◽  
Vol 17 (4) ◽  
pp. 041103 ◽  
Author(s):  
Hans Johnston ◽  
Charles R. Doering
Keyword(s):  
Heat Flux ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The effect of boundary properties on controlled Rayleigh–Bénard convection

2000 ◽  
Vol 411 ◽  
pp. 39-58 ◽  
Author(s):  
LAURENS E. HOWLE
Keyword(s):  
Heat Flux ◽  
Control Method ◽  
Lower Boundary ◽  
Bénard Convection ◽  
Benard Convection ◽  
Boundary Properties ◽  
Parameter Ranges ◽  
Differential Control ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We investigate the effect of the finite horizontal boundary properties on the critical Rayleigh and wave numbers for controlled Rayleigh–Bénard convection in an infinite horizontal domain. Specifically, we examine boundary thickness, thermal diffusivity and thermal conductivity. Our control method is through perturbation of the lower-boundary heat flux. A linear proportional-differential control method uses the local amplitude of a shadowgraph to actively redistribute the lower-boundary heat flux. Realistic boundary conditions for laboratory experiments are selected. Through linear stability analysis we examine, in turn, the important boundary properties and make predictions of the properties necessary for successful control experiments. A surprising finding of this work is that for certain realistic parameter ranges, one may find an isola to time-dependent convection as the primary bifurcation.

scholarly journals Rayleigh–Bénard convection with a melting boundary

2018 ◽  
Vol 858 ◽  
pp. 437-473 ◽  
Author(s):  
B. Favier ◽  
J. Purseed ◽  
L. Duchemin
Keyword(s):  
Heat Flux ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Convection Cell ◽  
Solid Boundary ◽  
Melting Front ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

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