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Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field Using KKL Model

  • Research Article - Mechanical Engineering
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Abstract

In this paper, flow and heat transfer of a nanofluid in a square cavity with curve boundaries in presence of magnetic field is investigated numerically using lattice Boltzmann method. The base fluid in the enclosure is water containing Al2O3. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. This investigation when compared with other numerical methods was found to be in excellent agreement. The influence of the nanoparticle volume fraction, Rayleigh number and Hartmann number on flow and heat transfer is investigated. The results show that enhancement in heat transfer increases with increase of Hartmann number except for Ra = 104 in which Ha = 40 roles as a critical Hartmann number.

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Abbreviations

B :

Magnetic field

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

Gr :

Grashof number

g :

Internal energy distribution functions

g eq :

Equilibrium internal energy distribution functions

g y :

Gravitational acceleration (m s −2)

k :

Thermal conductivity

Ha :

Hartmann number \({(=LB\sqrt {\sigma /\mu} )}\)

L :

Height or width of the adiabatic wall

Nu :

Local Nusselt number

p :

Pressure (Pa)

Pr :

Prandtl number (= υ /α)

Ra :

Rayleigh number (= g β ΔTL 3/α υ)

R :

Radius of curve boundary

T :

Fluid temperature

(u, v):

Velocity components in (x, y) directions, respectively

(x,y):

Cartesian coordinates

(X, Y):

Dimensionless coordinates

α :

Thermal diffusivity (m2 s−1)

θ :

Dimensionless temperature

μ :

Dynamic viscosity (Pa s−1)

υ :

Kinematic viscosity (m2 s)

ζ :

Angle measured from the up point of curve boundary

σ :

Electrical conductivity

ρ :

Fluid density (kg m−3)

τ c :

Relaxation time for temperature

τ v :

Relaxation time for flow

θ M :

Direction of the magnetic field

β :

Thermal expansion coefficient (K−1)

ψ :

Stream function

c:

Cold

h:

Hot

nf:

Nanofluid

f:

Base fluid

s:

Solid particles

ave:

Average

loc:

Local

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    M. Sheikholeslami, M. Gorji-Bandpy & D. D. Ganji

Authors
  1. M. Sheikholeslami
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  2. M. Gorji-Bandpy
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  3. D. D. Ganji
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Corresponding author

Correspondence to M. Sheikholeslami.

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Sheikholeslami, M., Gorji-Bandpy, M. & Ganji, D.D. Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field Using KKL Model. Arab J Sci Eng 39, 5007–5016 (2014). https://doi.org/10.1007/s13369-014-1060-4

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  • DOI: https://doi.org/10.1007/s13369-014-1060-4

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