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Mixed thermomagnetic convection of ferrofluid in a porous cavity equipped with rotating cylinders: LTE and LTNE models

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Abstract

In the present study, the impressions of the MHD and porous medium on mixed convection of Fe3O4-water nanofluid in a cavity with rotating cylinders in three different temperature cases with local thermal equilibrium and local thermal non-equilibrium approaches were studied. The effect of the presence of cylinders in three different temperature cases to improve the heat transfer rate was investigated. A finite volume method was used to solve equations. The Richardson, Hartmann, and Darcy numbers ranges are 1 ≤ Ri ≤ 100, 0 ≤ Ha ≤ 30, 0.001 ≤ Da ≤ 0.1, respectively. The volume fraction of nanoparticles varies in the range of 0–3%. The results show that the use of porous media has a beneficial effect on increasing the heat transfer rate, but the combination of the porous medium and the magnetic field can increase or decrease the heat transfer. Also, the most effective and highest heat transfer rate was occurred at Da = 0.01 and Da = 0.1, respectively. In addition, when the cylinders are cold or hot, the highest and lowest heat transfer rates occur, respectively. Finally, it was concluded that the magnetic field could control the fluid flow inside the cavity.

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Abbreviations

Da:

Darcy number

Gr:

Grashof number

H :

Dimensionless inter-phase heat transfer coefficient

Ha:

Hartmann number

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

Local Nusselt number

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

Ri:

Richardson number

U :

Dimensionless velocity in the x-direction

V :

Dimensionless velocity in y-direction

X :

Dimensionless coordinate component in the x-direction

Y :

Dimensionless coordinate component in the y-direction

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

Induced field (T)

\( B_{0} \) :

Magnitude of magnetic field (T)

\( C_{p} \) :

Specific heat capacity (J kg−1 K−1)

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

Mean heat flux (W m−2)

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

Local heat flux (W m−2)

\( \vec{F} \) :

Lorentz force vector (N m−3)

g :

Gravity (m s−2)

h :

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

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

Local heat transfer coefficient (W m−2 K)

J :

Current density (A m−2)

k :

Thermal conductivity (W m−1 K−1)

K :

Permeability (m−2)

L :

Length of the cavity (m)

p :

Pressure (Pa)

R :

Radius of cylinders (m)

T :

Temperature (K)

u :

Velocity in the x-direction (m s−2)

v :

Velocity in y-direction (m s−2)

x :

Coordinate component in the x-direction

y :

Coordinate component in the y-direction

\( \beta \) :

Thermal expansion coefficient (1 K−1)

\( \Gamma \) :

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)

\( \Omega \) :

Dimensionless angular velocity

\( \alpha \) :

Thermal diffusivity (m2 s−1)

AC:

Adiabatic cylinders

ave:

Average

c:

Cold

CC:

Cold cylinders

f:

Fluid

h:

Hot

HC:

Hot cylinders

LC:

Lower cylinder

LTE:

Local thermal equilibrium

LTNE:

Local thermal non-equilibrium

nf:

Nanofluid

p:

Particle

s:

Solid

UC:

Upper cylinder

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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

    Pouya Barnoon, Davood Toghraie & Mohammad Salarnia

  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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  2. Davood Toghraie
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Correspondence to Arash Karimipour.

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Barnoon, P., Toghraie, D., Salarnia, M. et al. Mixed thermomagnetic convection of ferrofluid in a porous cavity equipped with rotating cylinders: LTE and LTNE models. J Therm Anal Calorim 146, 187–226 (2021). https://doi.org/10.1007/s10973-020-09866-7

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