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Numerical study of magnetic field effect on the ferrofluid forced convection and entropy generation in a curved pipe

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Abstract

This paper presents the effect of a magnetic field on the ferrofluid flow pattern, heat transfer and entropy generation in a curved pipe. A non-uniform magnetic field is applied to ferrofluid (water + 2% vol. Fe3O4 nanoparticles) flow and under the constant heat flux boundary condition. Governing equations are solved by the finite volume method and based on the SIMPLE algorithm. The major objective of this work is to illustrate the effects of circumferential angle \(\left( {0^\circ \le \phi \le 180^\circ } \right)\) and strengths of a magnetic field \(\left( {0 \le {\text{Mn}} \le 3 \times 10^{6} } \right)\) on the hydro-thermal behavior and entropy production rate. It is found that circumferential angle of the magnetic source plays an important role in hydro-thermal performance of a curved pipe. At low magnetic numbers, the optimal circumferential location of the magnetic source is \(\phi_{\text{opt}} = 180^\circ\) which leads to the maximum heat transfer enhancement and hydro-thermal performance and the minimal entropy generation rate. For high magnetic numbers, the optimal operating condition occurs at \(\phi = 0^\circ\) and \(\phi = 60^\circ\) depending on the magnetic number. Second law analysis reveals that the major source of entropy generation comes from heat transfer irreversibility which reduces significantly by applying a magnetic field. In the range of studied parameters, the maximum heat transfer enhancement is about 29% which occurs at \(\phi = 0^\circ\) and \({\text{Mn}} = 3 \times 10^{6}\).

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Abbreviations

C:

Specific heat at constant pressure (Jkg−1K−1)

d p :

Particle diameter (m)

Ec:

Eckert number (−)

H :

Magnetic field intensity (Am−1)

I :

Electric current (A)

K :

Thermal conductivity (Wm−1 K−1)

k B :

Boltzmann constant (1.380648 × 10−23J K−1)

Ms:

Saturation magnetization (Am−1)

Mn:

Magnetic number (−)

m p :

Magnetic moment of nanoparticles (Am2)

Nu:

Nusselt number(−)

P :

Pressure (Pa)

Pr:

Prandtl number (−)

q′′:

Heat flux (Wm−2)

q*:

Non-dimensional heat flux (−)

r :

Radial coordinate (m)

R c :

Radius of curvature (m)

Re:

Reynolds number (−)

S f :

Volumetric entropy generation rate due to friction (Wm−3 K−1)

S gen :

Total volumetric entropy generation rate (Wm−3 K−1)

S T :

Volumetric entropy generation rate due to heat transfer (Wm−3 K−1)

T :

Temperature (K)

u, v, w :

Velocity components (ms−1)

x, y, z :

Cartesian coordinates (m)

α :

Particle volume fraction (−)

μ :

Dynamic viscosity (Pa s−1)

μ B :

Bohr magneton (9.274 × 10−24 Am2)

μ o :

Vacuum permeability (Tm A−1)

ξ :

Langevin parameter (−)

ρ :

Density (kg m−3)

ϕ v :

Viscous dissipation function (s−1)

f:

Base fluid

ff:

Ferrofluid

in:

Inlet

p:

Nanoparticle

o:

Without magnetic field

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Authors and Affiliations

  1. Department of Mechanical Engineering, Urmia University of Technology, P.O.B. 57155-419, Urmia, Iran

    Hossein Soltanipour & Amirhossein Gharegöz

  2. Department of Mining and Metallurgical Engineering, Urmia University of Technology, Urmia, Iran

    Mehdi Bahmani Oskooee

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  1. Hossein Soltanipour
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  2. Amirhossein Gharegöz
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  3. Mehdi Bahmani Oskooee
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Correspondence to Hossein Soltanipour.

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Soltanipour, H., Gharegöz, A. & Oskooee, M.B. Numerical study of magnetic field effect on the ferrofluid forced convection and entropy generation in a curved pipe. J Braz. Soc. Mech. Sci. Eng. 42, 135 (2020). https://doi.org/10.1007/s40430-020-2218-5

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