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Numerical Solutions for Radiative Heat Transfer in Ferrofluid Flow due to a Rotating Disk: Tiwari and Das Model

  • M. Mustafa EMAIL logo , Junaid Ahmad Khan , T. Hayat and A. Alsaedi
Published/Copyright: January 11, 2018

Abstract

In this paper, we explore the von-Kármán infinite disk problem for the situation where ferrofluid resides in the space above the rotating disk. Furthermore, flow field is influenced by axial magnetic field. In this study, we treat water as the base fluid which consists of homogeneous suspensions of Fe3O4 ferromagnetic particles. The main motivation here is to resolve heat transfer problem in the existence of non-linear radiative heat transfer. With the aid of von-Kármán relations, the equations of fluid motion and heat transfer are changed into a set of self-similar differential equations. These equations are dealt by an implicit finite-difference method with high precision. The results reveal that wall heat transfer rate can be improved by increasing solid volume fraction of ferromagnetic particles. Drag coefficient at the disk and heat transfer rate are increased as the strength of Lorentz force is enhanced. Viscous dissipation effect has an important part in improving heart transfer process which is vital in some applications. The results demonstrate that cooling capability of magnetite–water nanofluid is much superior to the conventional coolants. An excellent correlation of present results with the previous published articles is found in the all the cases.

Nomenclature

r,φ,z

Cylindrical coordinate system

u,v,w

velocity components along the r–, φ–, z– directions

B0

uniform magnetic field

T

fluid temperature

R

radius of rotating disk

Ω

angular velocity

M

Hartman number

cp

specific heat capacity

F,G,H

dimensionless function along radial, azimuthal and axial direction

Pr

Prandtl number

Cf

skin friction coefficient

aR

mean absorption coefficient

Nur

local Nusselt number

q''

wall heat flux

k

thermal conductivity

Re

local Reynolds number

Rd

Radiation parameter

Ec

Eckert number

1st order derivative with respect to η

2nd order derivative with respect to η

Greek symbols
v

kinematic viscosity

α

thermal diffusivity

θ

dimensionless temperature

η

similarity variable

σ

electrical conductivity

σ*

Stefan–Boltzman constant

τr,τφ

wall shear stress along r –and φ– direction

ρ

density

ϕ

nanoparticle volume fraction

μ

dynamic viscosity

Ω

angular velocity

θw

temperature ratio parameter

Subscripts
nf

nanofluid

w

condition at the wall

condition at infinity

f

fluid phase

s

solid phase

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Received: 2015-12-26
Accepted: 2017-12-5
Published Online: 2018-1-11
Published in Print: 2018-2-23

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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