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ABSTRACT
A computational study has been performed to see the effects of electro-thermo-convection induced via a strong unipolar injection between two concentric or eccentric cylinders using the finite volume method. The parameters are taken in the range of radius ratio 0.1 ≤ Г ≤ 0.9, injection strength in the range of 1 ≤ C ≤ 20, mobility number changes in the range 4 ≤ M ≤ 150, electric Rayleigh number in the range of 100 ≤ T ≤ 800, and Rayleigh number changes in the range of 5000 ≤ Ra ≤ 25000. It is observed that the most important effective parameter is radius ratio, which affects both heat and fluid flow. Moreover, electrical Rayleigh numbers suppress the thermo-convection and in any case higher transfer is observed due to electric charge injection.
Nomenclature
| a | = | thermal diffusivity (m2/s) |
| C | = | injection strength |
| Cp | = | specific heat at constant pressure (J/kg.K) |
| E | = | electric fields (V/cm) |
| e | = | eccentricity |
| g | = | acceleration of gravity (m/s2) |
| j | = | electric current density (A/m2) |
| K | = | ionic mobility (m2/V.s) |
| M | = | mobility number |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | electric charge density (C/m3) |
| r | = | radius (m) |
| Ra | = | thermal Rayleigh number |
| T | = | electric Rayleigh number |
| t | = | time (s) |
| U | = | velocity (m/s) |
| V | = | electric potential (V) |
| (x,y) | = | Cartesian coordinates |
| β | = | coefficient of thermal expansion (1/K) |
| ε | = | permittivity of the fluid (F/m) |
| Γ = (re/ri) | = | radius ratio |
| (η,ϕ) | = | bicylindrical coordinates |
| θ | = | temperature (K) |
| λ | = | thermal conductivity (W/m.K) |
| μ | = | dynamic viscosity (Pa.s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| ψ | = | stream function (m2/s) |
| ω | = | vorticity (1/s) |
| Subscript | = | |
| i | = | inner cylinder |
| e | = | outer cylinder |
| Superscript | = | |
| * | = | dimensional variables |
Nomenclature
| a | = | thermal diffusivity (m2/s) |
| C | = | injection strength |
| Cp | = | specific heat at constant pressure (J/kg.K) |
| E | = | electric fields (V/cm) |
| e | = | eccentricity |
| g | = | acceleration of gravity (m/s2) |
| j | = | electric current density (A/m2) |
| K | = | ionic mobility (m2/V.s) |
| M | = | mobility number |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| q | = | electric charge density (C/m3) |
| r | = | radius (m) |
| Ra | = | thermal Rayleigh number |
| T | = | electric Rayleigh number |
| t | = | time (s) |
| U | = | velocity (m/s) |
| V | = | electric potential (V) |
| (x,y) | = | Cartesian coordinates |
| β | = | coefficient of thermal expansion (1/K) |
| ε | = | permittivity of the fluid (F/m) |
| Γ = (re/ri) | = | radius ratio |
| (η,ϕ) | = | bicylindrical coordinates |
| θ | = | temperature (K) |
| λ | = | thermal conductivity (W/m.K) |
| μ | = | dynamic viscosity (Pa.s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| ψ | = | stream function (m2/s) |
| ω | = | vorticity (1/s) |
| Subscript | = | |
| i | = | inner cylinder |
| e | = | outer cylinder |
| Superscript | = | |
| * | = | dimensional variables |