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Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Published online by Cambridge University Press:  06 July 2010

PH. TRAORÉ ,
A. T. PÉREZ ,
D. KOULOVA  and
H. ROMAT
PH. TRAORÉ*
Affiliation:
Laboratoire d'Etudes Aérodynamiques, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
A. T. PÉREZ
Affiliation:
Departamento de Electrónica y Electromagnetismo, Facultad de Física, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
D. KOULOVA
Affiliation:
Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
H. ROMAT
Affiliation:
Laboratoire d'Etudes Aérodynamiques, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we solve numerically the entire set of equations associated with the electro-thermo-convective phenomena that take place in a planar layer of dielectric liquid heated from below and subjected to unipolar injection. For the first time the whole set of coupled equations is solved: Navier–Stokes equations, electrohydrodynamic (EHD) equations and the energy equation. We first validate the numerical simulation by comparing the electro-convection stability criteria with ones obtained with a stability approach. The numerical solution of the electro-thermo-convection problem is then presented entirely with a detailed analysis of stability parameters. In particular, the relation between fluid velocity, non-dimensional electrical parameter T, Rayleigh number Ra and Prandtl number Pr is given. An analytical model is presented in order to understand the flow behaviour at some critical conditions. The way that the onset of motion passes from purely electrical convection to purely thermal convection is, in particular, investigated and explained in detail. Finally, a result on the heat transfer enhancement due to electro-convection is exhibited and compared with data from experimental works available in this field.

JFM classification

Instability: Instability MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 279 - 293
Copyright
Copyright © Cambridge University Press 2010

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References

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