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Numerical simulation of double-diffusive natural convection in an enclosure in the presence of magnetic field with heat-conducting partition using lattice Boltzmann method

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Abstract

In the present study, the effect of magnetic field on double-diffusive natural convection in an enclosure with heat-conducting partition is studied. Constant temperatures and concentrations are imposed along the left and right walls, and horizontal walls are insulated. The lattice Boltzmann method is used to solve the dimensionless governing equations. Streamlines, isotherms, isoconcentrations, and average Nusselt and Sherwood number for various values of thermal Rayleigh number (103 ≤ Ra ≤ 105), Hartmann number (0 ≤ Ha ≤ 100), the partition thickness (0.05 ≤ W ≤ 1.0), the partition location (0.25 ≤ Lx ≤ 0.75), partition length (0.25 ≤ Lf ≤ 1.0), magnetic field angle (0° ≤ ϕ ≤ 90°), and buoyancy ratio (− 5 ≤ N ≤ 5) are obtained. The results indicate that the heat and mass transfer mechanisms are influenced by Hartmann number. The flow pattern are significantly depend on the magnetic field angle. In addition, there is an optimal magnetic field angle of 90° at which the stable and maximum heat and mass transfer rates is obtained. Moreover, the correlations of the average Nusselt and Sherwood number are also fitted.

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Abbreviations

A :

Two-dimensional cavity aspect ratio

C :

Mass concentration (%)

C p :

Specific heat at constant pressure (J kg−1 K−1)

D :

Mass diffusivity (m2 s)

f i(x, t):

Velocity distribution function

g :

Gravity (m s−2)

g i(x, t):

Temperature distribution function

H :

Height of cavity (m)

Ha:

Hartmann number

He:

Dimensionless heat generation parameter

h i(x, t):

Concentration distribution function

Kr:

Thermal conductivity ratio

L :

Width of cavity (m)

Le:

Lewis number = Le = α/D

L x :

The partition location

L f :

The partition length

N :

Buoyancy ratio

Nu:

Nusselt number

p :

Pressure (N m−2)

P :

Dimensionless pressure

Pr:

Prandtl number = Pr = ν/α

Q :

Heat generation parameter

RaS :

Solutal Rayleigh number = gβΔTL3/ν2

Ra:

Thermal Rayleigh number = gβΔTL3/να

S :

Dimensionless concentration

Sh:

Local Sherwood number

T :

Local temperature (K)

u :

X direction velocity of fluid (m s−1)

v :

Y direction velocity of fluid (m s−1)

U :

Dimensionless velocity in X direction

V :

Dimensionless velocity in Y direction

x, y :

Dimensional coordinates (m)

X, Y :

Dimensionless coordinates

W :

The partition thickness

α :

Thermal diffusivity coefficient (m2 s)

β T :

Coefficient of thermal expansion (K−1)

β C :

Coefficient of mass expansion (m3 kg−1)

θ :

Dimensionless temperature

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

av:

Average

c:

Cold

h:

Hot

ϕ:

Magnetic field angle

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Acknowledgements

This work is supported by the Natural Science Foundation of Jiangsu Province (No. BK20180732), China Postdoctoral Science Foundation (No. 2018M632332), and the Natural Science Research of Colleges and Universities of Jiangsu Province (No. 18KJB470017).

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Authors and Affiliations

  1. School of Energy and Mechanical Engineering, Nanjing Normal University, Nanjing, China

    Shihua Lu, Boyu He, Weiwei Chen & Xinjun Li

  2. School of Energy and Power Engineering, Nanjing Institute of Technology, Nanjing, China

    Dongyan Gao

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  1. Shihua Lu
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Correspondence to Boyu He.

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Lu, S., He, B., Gao, D. et al. Numerical simulation of double-diffusive natural convection in an enclosure in the presence of magnetic field with heat-conducting partition using lattice Boltzmann method. J Therm Anal Calorim 146, 699–716 (2021). https://doi.org/10.1007/s10973-020-10044-y

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