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Forced convection Fe3O4/water nanofluid flow through a horizontal channel under the influence of a non-uniform magnetic field

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Abstract

The problem of forced convection ferrofluid flow inside rectangular channel under the influence of a non-uniform magnetic field was numerically studied. The magnetic field was created by placing four magnetic sources in vicinity of four heaters, located at the bottom wall of the channel. The governing equations which are take account of the ferrohydrodynamic effect were solved by the finite volume method with the prediction-projection scheme. The effects of magnetic number, Reynolds number, volume fraction of nanoparticles and magnetic sources locations on the flow and heat transfer behaviors were examined. Results show the formation of vortices near the magnetic sources in the presence of magnetic field. The skin friction coefficient increases by increasing the magnetic field strength; however it decreases by augmenting the Reynolds number and the volume fraction of nanoparticles. The heat transfer rate increases by increasing magnetic number, Reynolds number and volume fraction of nanoparticles. An optimum position of magnetic sources was obtained giving maximum heat transfer rate. In the absence of magnetic field, the effect of nanoparticles gives an enhancement of heat transfer of 23%. It can be enhanced up to 228% under the effect of the magnetic field only. The coupled effects of both nanoparticles and magnetic field enhance the heat transfer up to 300%.

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Abbreviations

c p :

Specific heat (J/Kg K)

C f :

Local skin friction coefficient

C f m :

Average skin friction coefficient

Ec, :

Eckert number, \(\rho_{{{\text{bf}}}} u_{0}^{2} /\left( {\rho C_{{\text{P}}} } \right)_{{{\text{bf}}}} \Delta T\)

h :

Heat transfer coefficient (W/m2K)

\(\vec{H}\) :

Magnetic field vector

H :

Height of channel (m)

I :

Electric current (A)

k :

Thermal conductivity (W/mK)

L :

Length of the channel (m)

\(l\) :

Heater length (m)

\(M\) :

Magnetization

Mn :

Magnetic number, \(\mu_{0} H_{0}^{2} K^{\prime}\Delta T/\rho_{bf} u_{0}^{2}\)

Nu :

Local Nusselt number

Nu m :

Average Nusselt number

P :

Non-dimensional pressure, p/ρbf \(u_{0}^{2}\)

p :

Pressure (Pa)

Pr :

Prandtl number, \(\mu_{bf} c_{p,bf} /k_{bf}\)

Re :

Reynolds number, \(\rho_{bf} u_{0} h/\mu_{bf}\)

t :

Time (s)

T :

Temperature (K)

u 0 :

Inlet velocity (m/s)

\(\vec{v}\) :

Velocity vector

\(\vec{V}\) :

Dimensionless velocity vector, \(\vec{v}/u_{0}\)

x, y :

Coordinates (m)

X,Y :

Dimensionless coordinates, x/H, y/H

\(x_{S}\) :

Abscissa of magnetic sources (m)

\(X_{S}\) :

Dimensionless modified abscissa of magnetic sources, \(X_{S} = (x_{S} - x_{i} )/l\)

μ :

Dynamic viscosity (Kg/ms)

ρ :

Density (Kg/m3)

θ :

Dimensionless temperature, (T-TC)/(TH−TC)

φ :

Volume fraction of nanoparticles

τ :

Dimensionless time, tu0/H

bf :

Base fluid

C :

Cold

H :

Hot

m :

Average

nf :

Nanofluid

p :

Particles

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  1. Laboratory of Energy, Heat and Mass Transfer (LETTM), Faculty of Sciences of Tunis, Tunis El Manar University, Tunis, Tunisia

    Zouhaier Mehrez & Afif El Cafsi

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  1. Zouhaier Mehrez
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Correspondence to Zouhaier Mehrez.

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Mehrez, Z., El Cafsi, A. Forced convection Fe3O4/water nanofluid flow through a horizontal channel under the influence of a non-uniform magnetic field. Eur. Phys. J. Plus 136, 451 (2021). https://doi.org/10.1140/epjp/s13360-021-01410-2

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