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Applications of lattice Boltzmann method for double-diffusive convection in the cavity: a review

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Abstract

Over the years, the lattice Boltzmann method (LBM) has been evolved as a substitute and efficient numerical tool to mimic the single/multiphase fluid flow and transport problems. LBM has been mainly advantageous in multi-physics and multiphase flow applications. On the other hand, double-diffusive convection has extensive occurrence in domestic and industrial activities. The type of convection in which the combined effect of temperature and concentration gradients (resulting in the density variation) on fluid's hydrodynamic and thermal characteristics is called double-diffusive convection (DDC). The importance of DDC has been recognized in various engineering applications, and it has thoroughly been investigated experimentally, theoretically, and numerically. This paper is proposed to deliver a brief review of double-diffusive convection by computational approach (mainly lattice Boltzmann method and Navier–Stokes equation-based solvers). This review explores the illustration of some of the practical applications of DDC, studies of DDC in various heated cavities. The paper also gives insights into LBM formulation of DDC under various external force conditions. A table compromising various empirical correlations of the average Nusselt numbers and average Sherwood numbers as a function of different governing parameters has been discussed.

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Abbreviations

A R :

Aspect ratio, dimensionless

Da :

Darcy number, dimensionless

N :

Buoyancy ratio

F :

External force, N

B :

Magnetic field, Tesla = N/Am2

D :

Mass diffusivity, \({\mathrm{m}}^{2}/\mathrm{s}\)

Ma :

Mach number

Bi :

Biot number, dimensionless

Sc :

Schmidt number, dimensionless

\(f\) :

Flow field distribution function

\({g}_{y}\) :

Gravitational acceleration \(\left(\mathrm{m}/{\mathrm{s}}^{2}\right)\)

\(\overline{Nu}\) :

Average Nusselt number, dimensionless

\(\overline{Sh}\) :

Average Sherwood number, dimensionless

Nu :

Local Nusselt number, dimensionless

Sh :

Local Sherwood number, dimensionless

g :

Distribution function for the temperature field

h :

Distribution function for the concentration field

e k :

Discrete lattice in an ith direction

w k :

Mass factor in the respective direction

Le :

Lewis number, dimensionless

Ra :

Rayleigh number, dimensionless

Re :

Reynold number, dimensionless

Pr :

Prandtl number, dimensionless

Ri :

Richardson number, dimensionless

Gr :

Grashof number, dimensionless

Ha :

Hartmann number, dimensionless

Da :

Darcy number, dimensionless

Be :

Bejan number, dimensionless

Ec :

Eckert number, dimensionless

T :

Temperature, K

C :

Dimensional concentration, mol/m3

M :

Nodal number

\(\sigma\) :

Electrical conductivity, s/m

n :

Power-law-index, dimensionless

\({D}_{f}\) :

Dufour parameter, dimensionless

Sr :

Soret parameter, dimensionless

x, y :

Cartesian coordinates, m

t :

Time, sec

p :

Pressure, Pa

u :

Velocity in the x-direction, m s−1

v :

Velocity in the y-direction, m s−1

\(\theta\) :

Dimensioless temperature

S :

Dimensionless concentration

U :

Dimensionless velocity

P :

Dimensionless pressure

\(\beta_{T}\) :

Thermal expansion coefficient, K−1

\(\beta_{C}\) :

Concentration expansion coefficient, m3 kg−1

\(\omega\) :

Relaxation parameter

\(\rho\) :

Fluid density, kg m−3

\(\upsilon\) :

Kinematic viscosity, m2 s−1

\(\alpha\) :

Thermal diffusivity, m2 s−1

\(\Omega\) :

Collision operator

\(\tau\) :

Relaxation time

\(\omega_{f}\) :

Relaxation factor for fluid field

\(\omega_{g}\) :

Relaxation factor for thermal field

\(\omega_{h}\) :

Relaxation factor for concentration field

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Authors and Affiliations

  1. Department of Chemical Engineering, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Sudhanshu Kumar & Krunal M. Gangawane

  2. Department of Mechanical Engineering, Technology Faculty, Firat University, Elazig, 23100, Turkey

    Sudhanshu Kumar & Hakan F. Oztop

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  1. Sudhanshu Kumar
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Kumar, S., Gangawane, K.M. & Oztop, H.F. Applications of lattice Boltzmann method for double-diffusive convection in the cavity: a review. J Therm Anal Calorim 147, 10889–10921 (2022). https://doi.org/10.1007/s10973-022-11354-z

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