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Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with a Linearly Heated Wall Using Nanofluid

  • Research Article - Mechanical Engineering
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Abstract

In this paper, Lattice Boltzmann simulation of natural convection in a square cavity with a linearly heated wall which is filled by nanofluid has been investigated. The fluid in the cavity is a water-based nanofluid containing various nanoparticles such as copper (Cu), cupric oxide (CuO) or alumina (Al2O3). This study has been conducted for Rayleigh numbers of 103 to 105, while solid volume fraction (φ)varied from 0 to 16 %. The effects of nanopartcles are displayed on streamlines, isotherms counters, local and average Nusselt number. Copper nanoparticle enhances heat transfer more than other nanoparticles, while the lowest heat transfer is demonstrated by alumina (Al2O3) nanoparticles. In addition, the increment of Rayleigh number causes the effect of the nanoparticles to increase.

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Abbreviations

c :

Lattice speed

c i :

Discrete particle speeds

c p :

Specific heat at constant pressure

F :

External forces

f :

Density distribution functions

f eq :

Equilibrium density distribution functions

g :

Internal energy distribution functions

g eq :

Equilibrium internal energy distribution functions

G :

Gravity

k :

Thermal conductivity

L :

Enclosure height

M :

Lattice numbers

Ma :

Mach number

Nu :

Nusselt number

Pr :

Prandtl number

R :

Constant of the gases

Ra :

Rayleigh number

T :

Temperature

x, y :

Cartesian coordinates

ω i :

Weighted factor for flow (D2Q9)

β :

Thermal expansion coefficient

φ :

Volume fraction

τ c :

Relaxation time for temperature

τ v :

Relaxation time for flow

ρ :

Density

μ :

Dynamic viscosity

ϑ :

Kinematic viscosity

Δx :

Lattice spacing

Δt :

Time increment

\({\omega^{ '} _{i}}\) :

Weighted factor for temperature (D2Q4)

avg:

Average

C:

Cold

f:

Fluid

H:

Hot

nf:

Nanofluid

s:

Solid

*:

Normalized

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Authors and Affiliations

  1. School of Computer Science, Engineering and Mathematics, Flinders University, GPO Box 2100, Adelaide, SA, 5001, Australia

    GH. R. Kefayati

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  1. GH. R. Kefayati
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Correspondence to GH. R. Kefayati.

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Kefayati, G.R. Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with a Linearly Heated Wall Using Nanofluid. Arab J Sci Eng 39, 2143–2156 (2014). https://doi.org/10.1007/s13369-013-0748-1

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  • DOI: https://doi.org/10.1007/s13369-013-0748-1

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