Bénard–Marangoni convection in a small circular container: influence of the Biot and Prandtl numbers on pattern dynamics and free surface deformation

Rahal, Samir; Cerisier, P.; Azuma, Hisao

doi:10.1007/s00348-007-0323-1

Cited by 23 publications

(15 citation statements)

References 27 publications

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“…The 20 cSt silicon oil was used as experimental liquid. Properties of the silicon oil were taken from [11] and are listed in Table. The governing parameters are derived as Pr = 206, Gr = 2391∆T , Re = 101ω [rad/s], Ma = 658∆T , where ∆T is the temperature dierence between the crucible wall and the crystal dummy, and ω is the angular velocity of the crystal dummy rotation. Since results here are reported for the single experimental liquid, the ratio Ma/Gr = 0.275 is always constant, so that below we report mainly Grashof number values and dependences.…”

Section: Methodsmentioning

confidence: 99%

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

Haslavsky¹,

Gelfgat

Kit³

2013

Acta Phys. Pol. A

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This study examines the eect of slow crystal dummy rotation on three-dimensional oscillatory instability and time-dependent supercritical ow states in a Czochralski melt ow experimental model. To enable further comparison with numerical modelling, the experiments are carried out using a 20 cSt silicone oil as an experimental liquid and in a large diameter crucible, which allows one to work in a narrow temperature interval, so that temperature dependence of all the thermophysical properties of the experimental liquid can be neglected. The measurements conrm, partially qualitatively and partially quantitatively, earlier numerical predictions on destabilization ofthe Czochralski convective ow by a slow rotation. A simple power dependence of ow oscillations frequency on the Grashof and rotational Reynolds numbers that ts all the experimental runs was found.

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Section: Methodsmentioning

confidence: 99%

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

Haslavsky¹,

Gelfgat

Kit³

2013

Acta Phys. Pol. A

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“…The first term on the right-hand side of Equation (19) follows from Equation (18). Owing to the linearity of T 0 and the fact that T 0 is defined to equilibrate the thermal fluxes in the quiescent state, we can write the second term on the right-hand side of Equation (19) as…”

Section: Free Surface Heat Transfer Boundary Conditionmentioning

confidence: 98%

“…In such cases, the aspect ratio, which is already large, does not play as important a role in determining which convection patterns can form. In small ( 10) aspect ratio layers, on the other hand, experimental [17,18,[85][86][87][88][89][90][91][92] and numerical [19,[93][94][95][96][97] studies of RBM convection suggest that the domain aspect ratio is a much more important parameter in the pattern selection process.…”

Section: Numerical Studiesmentioning

confidence: 99%

Parallel adaptive solution of coupled Rayleigh–Bénard–Marangoni problems with the Navier‐slip

Peterson

Carey

2011

Numerical Methods in Fluids

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SUMMARYThis study deals with modeling certain nonlinear interactions that give rise to cellular flow in heated thin fluid layers with thermocapillary surface-tension at the free surface. Of particular interest in these Rayleigh-Bénard-Marangoni (RBM) studies is the effect of varying roughness (stick and slip) on the base or sides of the fluid container. This stick-slip behavior at container boundaries and thermocapillary shear stress at the free surface may lead to strongly varying local gradients in the solution that are addressed here using local adaptive mesh refinement. In turn, these local effects influence the global structure of cell patterns resulting from competing buoyancy, surface-tension and stick-slip effects. This behavior is illustrated by the results of numerical simulations of cellular flow structure in containers of varying aspect ratio and with spatially varying base boundary treatments. Details of the Navier-slip approximation and the adaptive mesh refinement strategy are given, together with a brief description of the relevant features of the parallel adaptive software framework, LibMesh, and associated algorithms employed in the present simulations.

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“…Lyons et al [4] have investigated solid body friction of brake discs with an active cooling by impinging jets which are enhancing the local heat transfer significantly. A more fundamental research in heat transfer was done by Rahal et al [5]. Using an infrared camera, they studied flow patterns in Bénard-Marangoni convection where a fluid layer is heated from below by a rigid boundary and cooled from above by a gaseous layer to realize a stress-free boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Local wall heat flux in confined thermal convection

Kaiser

Puits

2014

International Journal of Heat and Mass Transfer

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Bénard–Marangoni convection in a small circular container: influence of the Biot and Prandtl numbers on pattern dynamics and free surface deformation

Cited by 23 publications

References 27 publications

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

Parallel adaptive solution of coupled Rayleigh–Bénard–Marangoni problems with the Navier‐slip

Local wall heat flux in confined thermal convection

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