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Simulating natural convection and entropy generation of a nanofluid in an inclined enclosure under an angled magnetic field with a circular fin and radiation effect

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Abstract

Natural convection and radiation heat transfer of alumina (Al2O3)–water nanofluid are assessed in an enclosure under a magnetic field in different angles. The enclosure is a cavity at an angle of 45° with respect to the horizon, and a circular quadrant fin with the temperature Th is placed at the bottom corner of the cavity. The right wall is considered at the temperature Tc, and the rest of the walls are defined as adiabatic. The governing equations of flow are solved using algebraic finite volume method and the SIMPLE algorithm. In this work, the entropy generation is also evaluated other than heat transfer. The parameters in the present work include Rayleigh and Hartmann numbers, radiation parameter, magnetic field angle, nanoparticles volume fraction and aspect ratio. The results indicate higher Nusselt number and entropy generation and a lower Bejan number for a higher Rayleigh number and a lower Hartmann number. Addition of 6% of the nanoparticles causes an increase of 10% in the heat transfer rate and 11% in the entropy generation in the absence of radiation. The addition of the radiation mechanism to the enclosure leads to an increase in the heat transfer rate and entropy generation. It is also demonstrated that the vertical magnetic field is more intense than the horizontal magnetic field in the enclosure. With an increase in the fin aspect ratio from 0.3 to 0.7, the rate of heat transfer and entropy generation increases by 36 and 27%, respectively.

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Abbreviations

AR:

Aspect ratio

B 0 :

Magnetic field strength

Be :

Bejan number

C p :

Specific heat transfer coefficient (J kg−1 K−1)

G :

Gravity (m s−2)

h :

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

Ha :

Hartmann number \(\left( {Ha = B_{0} l\sqrt {\frac{{\sigma_{{\rm f}} }}{{\rho_{{\rm f}} \vartheta_{{\rm f}} }}} } \right)\)

k :

Thermal conductivity (W m−1 K−1)

l :

Enclosure length (m)

L :

Non-dimensional enclosure length

Nu :

Nusselt number

Nu Y :

Local Nusselt number

Nu M :

Average Nusselt number

p :

Pressure (Pa)

P :

Non-dimensional pressure \(\left( {\bar{P}l^{2} /\rho_{{\rm nf}} \alpha_{{\rm f}}^{2} } \right)\)

Pr :

Prandtl number \((\vartheta_{{\rm f}} /\alpha_{{\rm f}} )\)

r :

Radius of fin (m)

R :

Non-dimensional radius of fin

Rd :

Radiation parameter \(\left( {Rd = \frac{{4\sigma_{{\rm e}} T_{{\rm c}}^{3} }}{{k_{{\rm f}} \beta_{{\rm R}} }}} \right)\)

Ra :

Rayleigh number \(\left( {g\beta_{{\rm f}} l^{3} (T_{{\rm h}} - T_{{\rm c}} )/\alpha_{{\rm f}} \vartheta_{{\rm f}} } \right)\)

S Total :

Total entropy generation

T :

Temperature (K)

u, v :

Velocity components (m s−1)

U, V :

Velocity component \(\left( {U = ul/\alpha_{{\rm f}} , V = vl/\alpha_{{\rm f}} } \right)\)

x, y :

Cartesian coordinates in different directions (m)

X, Y :

Coordinates \(\left( {X = x/l,Y = y/l} \right)\)

β :

Expansion coefficient (1 K−1)

α :

Fluid thermal diffusivity (m2 s−1)

φ :

Volume fraction

ζ :

Irreversibility distribution ratio \(\left( {\zeta = \frac{{\mu_{{\rm nf}} T_{0} }}{{k_{{\rm f}} }}\left( {\frac{{\alpha_{{\rm f}} }}{{L\left( {T_{{\rm h}} - T_{{\rm C}} } \right)}}} \right)^{2} } \right)\)

ω :

Angle of magnetic field (°)

θ :

Temperature

μ :

Dynamic viscosity (W m−1 K−1)

ϑ :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Electrical conductivity (Ω m)

γ :

Cavity angle (°)

ψ :

Stream function (m2 s−1)

Ψ:

Dimensionless stream function

c :

Cold

h :

Hot

f :

Pure fluid

nf:

Nanofluid

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Acknowledgements

This research is partially supported by the National Key Research and Development Program (2016YFB0100903), the National Science Foundation of China (61503284), the Tianjin Key R&D Program (18YFZCGX00380), and Tianjin Science and Technology Major Project for Artificial Intelligence (17ZXRGGX00070).

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Authors and Affiliations

  1. School of Automotive and Transportation, Tianjin University of Technology and Education, Tianjin, 300222, China

    Rui Zhang

  2. Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Ali Ghasemi

  3. Cihan Scientific Research Centre, Cihan University-Erbil, Erbil, Kurdistan Region, Iraq

    Azeez A. Barzinjy

  4. Physics Department, College of Education, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq

    Azeez A. Barzinjy

  5. Department of Technical and Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran

    Maliheh Zareei

  6. Computer Department, Cihan University-Erbil, Erbil, Iraq

    Samir M. Hamad

  7. Scintific Research Center, Soran University, Soran, Kurdistan Region, Iraq

    Samir M. Hamad

  8. Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Masoud Afrand

  9. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Masoud Afrand

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  1. Rui Zhang
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  2. Ali Ghasemi
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  3. Azeez A. Barzinjy
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Correspondence to Masoud Afrand.

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Zhang, R., Ghasemi, A., Barzinjy, A.A. et al. Simulating natural convection and entropy generation of a nanofluid in an inclined enclosure under an angled magnetic field with a circular fin and radiation effect. J Therm Anal Calorim 139, 3803–3816 (2020). https://doi.org/10.1007/s10973-019-08729-0

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