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

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: Navie...

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Bibliographic Details
Published in:Journal of fluid mechanics 2010-09, Vol.658, p.279-293
Main Authors: TRAORÉ, PH, PÉREZ, A. T., KOULOVA, D., ROMAT, H.
Format: Article
Language:English
Subjects:
cavities
Computational fluid dynamics
Computer simulation
Convection
Dielectrics
Energy equation
Engineering Sciences
Exact sciences and technology
Flow velocity
Fluid dynamics
Fluid flow
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Heat transfer
Hydrodynamic stability
Injection
instability
Liquids
Magnetohydrodynamics and electrohydrodynamics
Mathematical analysis
Mathematical models
MHD and electrohydrodynamics
Navier-Stokes equations
Nonlinearity (including bifurcation theory)
Physics
Stability
Temperature gradients
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112010001709