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Investigation of MHD effect on nanofluid heat transfer in microchannels

An incompressible lattice Boltzmann approach

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Abstract

An incompressible preconditioned lattice Boltzmann method (IPLBM) is proposed to investigate the fluid flow and heat transfer characteristics of nanofluid in microchannel with hydrophilic or superhydrophobic walls and partially under the influence of transverse magnetic field as well as a heat flux. The modified IPLBM is shown to overcome the velocity inaccuracy in developing regime under partial magnetic field with respect to standard LBM. Then, the method is utilized to resolve the velocity and temperature fields at Re = 100 and various volume fractions of nanoparticles (0 ≤ φ ≤ 0.2%), Hartmann numbers (0 ≤ Ha ≤ 30) and slip coefficients (0 ≤ B ≤ 0.1). Superhydrophobic walls are shown to reduce the wall shear stress at B = 0.1 of up to 38.4, 58.5 and 70%, respectively, for Ha = 0, 15 and 30. Ignoring the temperature jump in modeling overestimates the Nusselt number with an error that culminates at B = 0.1 and φ = 0.2% to 19.6, 22.7 and 25%, respectively, for Ha = 0, 15 and 30. It is concluded that with magnetic field presence and realistic temperature jump, the surface material of superhydrophobic walls should be chosen properly to avoid inevitable and uncontrolled reduction in heat transfer, such that the highest hydrophobicity is not always the best choice. Reasonable agreements are achieved by comparing our results with credible analytic and numerical solutions and also with an experimental study.

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Abbreviations

\({\vec{\mathbf{a}}}\) :

Acceleration vector of transverse magnetic field (m s−2)

a x :

Acceleration component in x direction, (m s−2)

a y :

Acceleration component in y direction, (m s−2)

B = β/H C :

Dimensionless slip coefficient

B 0 :

Magnetic field intensity [T]

\(\vec{c}\) :

Microscopic lattice velocity vector

\(\overline{{{\mathbf{C}}_{{\mathbf{f}}} }}\) :

Friction factor

C p :

Specific heat capacity (J kg−1 K−1)

C S :

Lattice speed of sound

f :

Density distribution function

F :

Source term

g :

Dimensionless temperature distribution function

Ha = B 0 H C(σnf/ µ nf)0.5 :

Hartmann number

H C :

Height of the microchannel (μm)

k :

Thermal conductivity coefficient (W m−1 K−1)

Ma = u/C S :

Mach number

Nu :

Nusselt number

\(\overline{Nu}\) :

Average Nusselt number

Pr = ν/α :

Prandtl number

q″:

Heat flux (W m−2)

Re = U in H c/ν nf :

Reynolds number

T :

Temperature (K)

u :

Horizontal velocity (m s−1)

\({\vec{\mathbf{V}}}\) :

Velocity vector (m s−1)

v :

Vertical velocity (m s−1)

W :

Weight function

x, y :

Horizontal and vertical coordinates (m)

α :

Thermal diffusivity coefficient (m2 s−1)

β :

Slip coefficient [μm]

γ :

Adjustable parameter for PLBM

Γ :

Ratio of specific heat capacity

ζ :

Temperature jump coefficient

θ :

Dimensionless temperature

θ FD :

Dimensionless fully developed temperature

θ jump :

Dimensionless temperature jump

µ :

Dynamic viscosity [Pa.s]

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Electrical conductivity (siemens m−1)

τ f :

Relaxation time for f

τ g :

Relaxation time for g

\(\bar{\tau }_{\text{w}}\) :

Averaged wall shear stress (Pa)

φ :

Volume fraction of nanoparticles

w :

Weight coefficient

eq:

Equilibrium

f:

Pure fluid

FD:

Fully developed

in:

Inlet of channel

k:

Direction of lattice links

nf:

Nanofluid

*:

Dimensionless

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    Ali Alipour Lalami

  2. Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Babol, Islamic Republic of Iran

    Hamid Hassanzadeh Afrouzi

  3. ANZAC Research Institute, The University of Sydney, Sydney, NSW, 2139, Australia

    Abouzar Moshfegh

  4. Faculty of Medicine and Health Sciences, Macquarie University, Sydney, NSW, 2109, Australia

    Abouzar Moshfegh

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  1. Ali Alipour Lalami
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  2. Hamid Hassanzadeh Afrouzi
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  3. Abouzar Moshfegh
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Correspondence to Hamid Hassanzadeh Afrouzi.

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Alipour Lalami, A., Hassanzadeh Afrouzi, H. & Moshfegh, A. Investigation of MHD effect on nanofluid heat transfer in microchannels. J Therm Anal Calorim 136, 1959–1975 (2019). https://doi.org/10.1007/s10973-018-7851-1

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