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Koo–Kleinstreuer–Li correlation for simulation of nanofluid natural convection in hollow cavity in existence of magnetic field

  • Yuan Ma
  • Rasul MohebbiEmail author
  • M. M. RashidiEmail author
  • Zhigang Yang
Article

Abstract

The lattice Boltzmann method is used to study natural convection of a CuO/water nanofluid in a hollow cavity. The hollow walls are fixed at a uniform temperature, and the effect of an applied magnetic field is examined. The Koo–Kleinstreuer–Li model, which accounts for nanoparticle’s Brownian motion, is used to gain the nanofluid effective thermal conductivity and nanofluid viscosity. The mechanisms how the inclination angle of magnetic field, Hartmann number, Rayleigh number, hollow width and nanoparticle volume fraction affect the streamlines, isotherms and rate of heat transfer are also studied. The results show that the average Nusselt number is increased by incrementing the nanoparticle volume fraction, Ra, magnetic field inclination angle and hollow width, but decreased by the Ha. For L = 0.4, the value of Ra where the dominant mechanism of heat transfer is changed from conduction to convection is larger than 105. But for L = 0.48 or 0.56, the turning point of the dominant heat transfer mechanism is at Ra < 105. Besides, at L = 0.4 or 0.48, the average Nusselt numbers in hot walls are higher than those in cold wall, but the opposite trend is found at L = 0.56.

Keywords

LBM Nanofluid Hollow cavity Magnetic field KKL correlation 

List of symbols

a

Length of the hollow

c

Gap between two ribs

H

Height of the cavity

ei

Discrete lattice velocity

f

Density distribution function

feq

Equilibrium density distribution function

Ha

Hartmann number

Nu

Nusselt number

U, V

Non-dimensional velocity components

Pr

Prandtl number

b

Height of the rib

W

Length of the enclosure

θ

Orientation of the magnetic field

cs

Speed of sound in Lattice scale

g

Energy distribution function

geq

Equilibrium energy distribution function

kB

Boltzmann constant

T

Fluid temperature

k

Thermal conductivity

Ra

Rayleigh number

Greek symbols

ωi

Weight function in direction i

ϕ

Volume fraction

τc

Relaxation time for temperature

α

Thermal diffusivity

ρ

Density

τv

Relaxation time for flow

β

Thermal expansion coefficient

μ

Dynamic viscosity

Subscripts

loc

Local

S

Solid particles

nf

Nanofluid

c

Cold

ave

Average

f

Fluid

h

Hot

i

Move direction of single particle

Notes

Acknowledgements

This work was supported by the Shanghai Automotive Wind Tunnel Technical Service Platform (16DZ2290400). The computing facility of Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems is gratefully acknowledged.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Shanghai Automotive Wind Tunnel CenterTongji UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsShanghaiChina
  3. 3.School of EngineeringDamghan UniversityDamghanIran
  4. 4.Beijing Aeronautical Science & Technology Research InstituteBeijingChina

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