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Hydromagnetic transport of iron nanoparticle aggregates suspended in water

  • M Marin
  • M M Maskeen
  • A Zeeshan
  • O U Mehmood
  • M Hassan
Original Paper
  • 14 Downloads

Abstract

The current communication is reports about the transport phenomenon of iron metal (Fe) nanoparticle aggregates in water under the impact of an external imposed magnetic field over a stretching cylinder. The governed problem modeled using nonlinear coupled ordinary differential equations which are then tackled by the Mathematica software package bvph 2.0 based on the homotopy scheme. The impact of chemical dimension (dl), fractal dimension (df) and radius of gyration (Rg) on flow and temperature profiles are presented through graphs. Numerical results are computed for the skin friction coefficient and heat transfer coefficients corresponding to the sundry parameters. It is concluded from the results that by increasing the number of particles in the back bone the heat transfer rate is improved, while by increasing the dead end particles the wall shear stress is improved but the heat transfer rate is decreased.

Keywords

Particles aggregates Nanofluid Stretching cylinder MHD 

List of symbols

e

Aspect ratio of the ellipsoid (–)

dl

Chemical dimensions (–)

u, v

Velocity in x and r direction (ms−1)

ε

Curvature parameter (–)

ρ

Density (kg m−3)

T

Dimensional temperature (K)

θ

Dimensionless temperature (–)

f

Dimensionless velocity (–)

μ

Dynamic viscosity (kg m−1 s−1)

Ec

Eckert number (–)

df

Fractal dimensions (–)

M11, M33

Geometrical factors (–)

Gr

Grashof number (–)

q

Heat flux (J s−1)

Ak

Kapitza radius (m)

ν

Kinematic viscosity (m2 s−1)

B0

Magnetic field strength (T)

M

Magnetic number (–)

σ

Magnetic permeability (NA−2)

λ

Mixed convection parameter (–)

ϕint

Nanoparticles volume fraction within an aggregate (–)

ϕ

Nanoparticles volume fraction (–)

Nint

Number of particles within an aggregate (–)

N

Number of particles (–)

Nu

Nusselt number (–)

Pr

Prandtl number (–)

Rg

Radius of gyration (m)

\( a^{*} \)

Radius of primary particle (m)

Re

Reynolds number (–)

τ

Shear stress (kg s−2 m−1)

η

Similarity variable (–)

Cf

Skin friction coefficient (–)

cp

Heat capacity (m2 s−2 K−1)

b

Stretching rate (s−1)

k

Thermal conductivity (W m−1 K−1)

β

Thermal expansion coefficient (K−1)

ϕ

Volume fraction of nanoparticles (–)

Uw

Wall velocity (ms−1)

Subscript

a

Aggregate

Ambient

c

Backbone

nc

Dead end

f

Fluid

nf

Nanofluid

s

Solid nanoparticles

w

Wall

max

Maximum

PACS Nos.

51.30.+i 51.35.+a 81.10.Bk 

Notes

Compliance with ethical standards

Conflict of interest

The authors declared that they have no potential conflicts of interest concerning the authorship, research and publication of current article.

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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Department of Mathematics and StatisticsInternational Islamic UniversityIslamabadPakistan
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologyWah CanttPakistan
  4. 4.Department of MathematicsCOMSATS Institute of Information TechnologyLahorePakistan

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