Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 7
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Original Articles

Analysis of the electro-thermo-convection induced by a strong unipolar injection between two concentric or eccentric cylinders

, , , &
Pages 789-804 | Received 08 Dec 2016, Accepted 03 Mar 2017, Published online: 27 Apr 2017
 

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

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