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Application of rotating circular obstacles in improving ferrofluid heat transfer in an enclosure saturated with porous medium subjected to a magnetic field

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Abstract

In this paper, the evaluation of the heat transfer rate and fluid flow in an enclosure with rotating circular obstacles has been studied. The enclosure is filled with a porous medium and subjected to the magnetic field. Fe3O4/water nanofluid has been used to simulate the effect of magnetism. The finite volume method has been applied to solve the equations. To velocity–pressure coupling, the SIMPLE algorithm has been applied. The influence of magnetism on the enclosure in the conductive and non-conductive boundaries along the magnetic field has been investigated. The streamlines and isotherm-lines contours in the conductive and non-conductive boundaries along the magnetic field, the dimensionless angular velocities of the circular obstacles, and their direction have been obtained. The results show that the different temperature cases of the circular obstacles and their direction play an essential role in the flow and heat transfer. The highest and lowest heat transfer rates occur in cold circular obstacles and hot circular obstacles, respectively. Also, the composition of the porous medium and the magnetic field show different behaviors at the heat transfer rate.

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Abbreviations

\(\vec{b}_{0}\) :

Induced field (T)

\(B_{0}\) :

Magnitude of magnetic field (T)

\(C_{\text{p}}\) :

Specific heat capacity (J kg−1 K−1)

\(\vec{F}\) :

Lorentz force vector (N m−3)

\(q^{\prime\prime}\) :

Mean heat flux (W m−2)

\(q^{\prime\prime}\left( x \right)\) :

Local heat flux (W m−2)

Da:

Darcy number

g :

Gravity (m s−2)

Gr:

Grashof number

h :

Inter-phase heat transfer coefficient (W m−2 K−1)

H :

Dimensionless inter-phase heat transfer coefficient

\(h\left( y \right)\) :

Local heat transfer coefficient (W m−2 K−1)

Ha:

Hartmann number

J :

Current density (A m−2)

k :

Thermal conductivity (W m−1 K−1)

K :

Permeability (m2)

L :

Length of the enclosure (m)

Nuave :

Average Nusselt number

\({\text{Nu}}\left( y \right)\) :

Local Nusselt number

p :

Pressure (Pa)

Pr:

Prandtl number

R :

Radius of rotating circular obstacles (m)

Re:

Reynolds number

Ri:

Richardson number

T :

Temperature (K)

U :

Dimensionless velocity in the x-direction

u :

Velocity in the x-direction (m2 s−1)

V :

Dimensionless velocity in y-direction

v :

Velocity in y-direction (m2 s−1)

x :

Coordinate component in the x-direction

X :

Dimensionless coordinate component in the x-direction

Y :

Dimensionless coordinate component in the y-direction

y :

Coordinate component in the y-direction

\(\beta\) :

Thermal expansion coefficient (1/K)

\(\varGamma\) :

Dimensionless thermal diffusivity

\(\gamma\) :

Dimensionless thermal conductivity of porous medium

\(\varepsilon\) :

Porosity

\(\theta\) :

Dimensionless temperature

\(\vartheta\) :

Kinematic viscosity (m2 s−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\rho\) :

Density (kg m−3)

\(\sigma\) :

Electrical conductivity (S m−1)

\(\varphi\) :

Volume fraction

\(\psi\) :

Dimensionless stream function

\(\omega\) :

Angular velocity (rad s−1)

\(\varOmega\) :

Dimensionless angular velocity

\(\alpha\) :

Thermal diffusivity (m2 s−1)

ave:

Average

c :

Cold

f :

Fluid

h :

Hot

LTE:

Local thermal equilibrium

LTNE:

Local thermal non-equilibrium

MHD:

Magnetohydrodynamics

nf:

Nanofluid

p :

Particle

s :

Solid

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Authors and Affiliations

  1. Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Pouya Barnoon

  2. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Davood Toghraie

  3. Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Arash Karimipour

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  1. Pouya Barnoon
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Correspondence to Arash Karimipour.

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Barnoon, P., Toghraie, D. & Karimipour, A. Application of rotating circular obstacles in improving ferrofluid heat transfer in an enclosure saturated with porous medium subjected to a magnetic field. J Therm Anal Calorim 145, 3301–3323 (2021). https://doi.org/10.1007/s10973-020-09896-1

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