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Simultaneous use of non-uniform magnetic field and porous medium for the intensification of convection heat transfer of a magnetic nanofluid inside a tube

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Abstract

This paper investigates the influence of a magnetic field on the ferrofluid forced convection characteristics in a semi-porous tube by applying the finite volume method and the Darcy–Brinkman–Forchheimer model. Two-phase simulation is performed by taking into account the effects of Brownian motion, thermophoresis, and magnetophoresis of nanoparticles. Two cases are considered for this: case 1 with a porous medium at the center of the tube and case 2 with a porous layer in the vicinity of the wall. Some influential parameters, including magnetic and Darcy numbers, thickness, and thermal conductivity of porous medium, are studied in the pressure drop and heat transfer enhancement in both cases. Results indicate that in case 1, the applied magnetic field (with \(Mn = 1 \times 10^{6}\)) can only lead to an increase of about 78% while a porous medium (with \(Da = 10^{ - 4}\)) causes a 78% improvement alone. The effect of both techniques simultaneously will, however, result in an approximately 120% enhancement in the heat transfer rate.

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Availability of data and material

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

c :

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

C F :

Form drag coefficient (−)

D :

Tube diameter (m)

Da :

Darcy number (−)

D B :

Brownian diffusivity (m2s−1)

d p :

Particle diameter (m)

D T :

Thermophoretic diffusivity (m2s−1)

f :

Fanning friction factor

H :

Intensity of magnetic field (Am−1)

J p :

Mass flux vector of nanoparticle (kg m−2 s−1)

K :

Permeability of porous medium (m2)

k B :

Boltzmann’s constant (JK−1)

Mn :

Magnetic number (−)

m p :

Magnetic moment of nanoparticles (Am2)

M r :

Reference magnetization (Am−1)

Num :

Mean Nusselt number (−)

q* :

Non-dimensional heat flux (−)

r :

Radial coordinate (m)

Re:

Reynolds number (−)

T :

Temperature (K)

\({T}_{b}\) :

Mean fluid temperature (K)

V z ,V r :

Velocity components (ms−1

μ B :

Bohr magneton (9.274 × 10−24 Am2)

μ o :

Vacuum permeability (4π × 10−7 TmA−1)

ε :

Porosity (-)

\(\xi\) :

Langevin parameter (-)

ρ :

Density (kgm−3)

\(\phi\) :

Volume fraction of particles (−)

bf :

Base fluid

mnf:

Magnetic nanofluid

in:

Inlet

np:

Nanoparticle

p :

Porous

w :

Wall

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Authors and Affiliations

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

    Hossein Soltanipour

  2. Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

    Farzad Pourfattah

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  1. Hossein Soltanipour
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HS: Data collection, Analysis, Methodology, Validation, Writing—Editing. Farzad P: Data curation, Conceptualization, Writing—review & editing.

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Correspondence to Hossein Soltanipour.

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Soltanipour, H., Pourfattah, F. Simultaneous use of non-uniform magnetic field and porous medium for the intensification of convection heat transfer of a magnetic nanofluid inside a tube. J Braz. Soc. Mech. Sci. Eng. 43, 459 (2021). https://doi.org/10.1007/s40430-021-03174-3

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