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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 4
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Original Articles

Magnetic field influence on double-diffusive natural convection in a square cavity – A numerical study

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Pages 448-475 | Received 02 Aug 2016, Accepted 28 Nov 2016, Published online: 09 Mar 2017
 

ABSTRACT

In this paper double diffusive natural convection in a square cavity in the presence of external magnetic field has been studied numerically by Galerkin’s weighted residual finite element method using velocity-vorticity formulation. Simulation results are reported for 0 < Ha < 200, buoyancy ratio, 2 < N < 2, 104 < Ra < 106 and field inclination angle varying from 00 to 3600 for different fluid systems, namely gas, water, and liquid Gallium. Results indicate that the streamline pattern is greatly influenced by the direction and intensity of magnetic field and at Ra = 1.0e5, the increase in Ha from 0 to 30 has resulted in a decrease in Nusselt number and Sherwood number by about 72% and 78% respectively. The inclination angle has played an important role in the suppression of heat and mass transfer, maximum suppression is experienced at Θ = 45 and 270 while minimum is recorded at Θ = 135 and 315. Liquid Gallium showed the least response to change in magnetic field intensity compared to other two fluids.

Nomenclature

C=

concentration of species, kg/m3

D=

binary diffusion coefficient, m2/s

g=

gravitational acceleration, m/s2

Gr=

Grashof number

Ha=

Hartmann number

N=

buoyancy ratio

Nu=

Nusselt number

Pr=

Prandtl number

Re=

Reynolds number

Ri=

Richardson number

Sc=

Schmidt number

Sh=

Sherwood number

t=

time, s

T=

temperature, K

u,v=

horizontal and vertical velocity components, m/s

U, V=

nondimensional velocity components

U0=

lid velocity, m/s

x, y=

horizontal and vertical coordinates, m

X, Y=

nondimensional coordinates

α=

thermal diffusivity, m2/s

βC=

concentration volumetric expansion coefficient, m3/kg

βT=

thermal volumetric expansion coefficient, K−1

μ=

dynamic viscosity, kg/s · m

υ=

kinematic viscosity, m2/s

ϕ=

nondimensional concentration of species

θ=

nondimensional temperature

Θ=

magnetic field inclination angle measure from horizontal anticlockwise

ρ=

density, kg/m3

τ=

nondimensional time

ω=

vorticity, s—1

Ω=

nondimensional vorticity

Δ=

difference

σ=

electrical conductivity, s/m

Subscripts=
c=

cold

h=

hot

Nomenclature

C=

concentration of species, kg/m3

D=

binary diffusion coefficient, m2/s

g=

gravitational acceleration, m/s2

Gr=

Grashof number

Ha=

Hartmann number

N=

buoyancy ratio

Nu=

Nusselt number

Pr=

Prandtl number

Re=

Reynolds number

Ri=

Richardson number

Sc=

Schmidt number

Sh=

Sherwood number

t=

time, s

T=

temperature, K

u,v=

horizontal and vertical velocity components, m/s

U, V=

nondimensional velocity components

U0=

lid velocity, m/s

x, y=

horizontal and vertical coordinates, m

X, Y=

nondimensional coordinates

α=

thermal diffusivity, m2/s

βC=

concentration volumetric expansion coefficient, m3/kg

βT=

thermal volumetric expansion coefficient, K−1

μ=

dynamic viscosity, kg/s · m

υ=

kinematic viscosity, m2/s

ϕ=

nondimensional concentration of species

θ=

nondimensional temperature

Θ=

magnetic field inclination angle measure from horizontal anticlockwise

ρ=

density, kg/m3

τ=

nondimensional time

ω=

vorticity, s—1

Ω=

nondimensional vorticity

Δ=

difference

σ=

electrical conductivity, s/m

Subscripts=
c=

cold

h=

hot

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