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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 8
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Original Articles

Heat transfer augmentation of a quasi-two-dimensional MHD duct flow via electrically driven vortices

, &
Pages 847-869 | Received 28 Apr 2016, Accepted 23 Jun 2016, Published online: 20 Sep 2016
 

ABSTRACT

The fluid dynamics and heat transfer characteristics of magnetohydrodynamic duct flow often degrade the laminarization caused by the magnetic field. The present work evaluates the performance of a system featuring alternating current injection from a point electrode as a vortex promoter for enhancement of the thermal-hydraulic characteristics. It is found that the vortices generated by the current injection alone generally induce a greater thermal-hydraulic performance with a significantly smaller additional pressure loss than configurations featuring a physical obstacle. A maximum overall efficiency index of 1.83 was recorded within the parameter space investigated.

Nomenclature

a=

duct height (out-of-plane)

B=

uniform out-of-plane magnetic field strength

Cp=

constant pressure specific heat capacity

CD=

cylinder drag coefficient

Ec=

Eckert number

f=

vortex shedding frequency

ff=

current injection frequency

f0=

natural vortex shedding frequency

h=

vortex street lateral spacing

H=

friction parameter

Ha=

Hartmann number

HR*=

overall heat transfer enhancement ratio

I=

current injection amplitude

l=

vortex street longitudinal spacing

ly=

transverse electrode position

L=

half duct width

Ld=

length of downstream flow region

Lw=

length of heated wall

2=

integral of velocity magnitude throughout the domain

n=

number of Hartmann layers

N=

interaction parameter

Nu=

time averaged Nusselt number

=

Nu for the same duct in the absence of a current injection and a cylinder

=

local instantaneous Nusselt number

p=

pressure

Δp=

time-averaged pressure drop

=

time-averaged pressure drop for a base case with no cylinder

=

overall net power enhancement

Pheat=

heat power

Pflow=

pumping power

PR*=

overall pressure penalty ratio

Pe=

Peclet number

Pr=

Prandtl number

ReL=

Reynolds number based on half duct width

St=

Srouhal number

t=

time

u=

x-direction velocity component

u=

velocity projected onto (x,y) plane

u0=

force vector field

U0=

peak fluid velocity at duct inlet

Uξ=

wake advection velocity

x=

streamwise coordinate

y=

transverse coordinate

z=

spanwise coordinate

α=

duct aspect ratio

β=

blockage ratio

δS=

Shercliff boundary layer thickness

η*=

overall efficiency index

κT=

thermal diffusivity

ν=

fluid kinematic viscosity

ρ=

density

σ=

electrical conductivity

θ=

temperature

τ=

current injection pulse width

ξp=

peak vorticity

ωf=

current forcing frequency

Nomenclature

a=

duct height (out-of-plane)

B=

uniform out-of-plane magnetic field strength

Cp=

constant pressure specific heat capacity

CD=

cylinder drag coefficient

Ec=

Eckert number

f=

vortex shedding frequency

ff=

current injection frequency

f0=

natural vortex shedding frequency

h=

vortex street lateral spacing

H=

friction parameter

Ha=

Hartmann number

HR*=

overall heat transfer enhancement ratio

I=

current injection amplitude

l=

vortex street longitudinal spacing

ly=

transverse electrode position

L=

half duct width

Ld=

length of downstream flow region

Lw=

length of heated wall

2=

integral of velocity magnitude throughout the domain

n=

number of Hartmann layers

N=

interaction parameter

Nu=

time averaged Nusselt number

=

Nu for the same duct in the absence of a current injection and a cylinder

=

local instantaneous Nusselt number

p=

pressure

Δp=

time-averaged pressure drop

=

time-averaged pressure drop for a base case with no cylinder

=

overall net power enhancement

Pheat=

heat power

Pflow=

pumping power

PR*=

overall pressure penalty ratio

Pe=

Peclet number

Pr=

Prandtl number

ReL=

Reynolds number based on half duct width

St=

Srouhal number

t=

time

u=

x-direction velocity component

u=

velocity projected onto (x,y) plane

u0=

force vector field

U0=

peak fluid velocity at duct inlet

Uξ=

wake advection velocity

x=

streamwise coordinate

y=

transverse coordinate

z=

spanwise coordinate

α=

duct aspect ratio

β=

blockage ratio

δS=

Shercliff boundary layer thickness

η*=

overall efficiency index

κT=

thermal diffusivity

ν=

fluid kinematic viscosity

ρ=

density

σ=

electrical conductivity

θ=

temperature

τ=

current injection pulse width

ξp=

peak vorticity

ωf=

current forcing frequency

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