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Thermocapillary and buoyancy driven convection analysis for a hybrid nanofluids enclosed in a cavity with heated obstacle

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Abstract

Two-dimensional numerical simulations are performed to investigate the problem of thermocapillary, and buoyancy driven convection. A hybrid MWCTN-Fe\(_3\)O\(_4\)-thermal oil nanofluid was used in an enclosed cavity equipped with a hot obstacle. The entire set of equations associated with the convective heat transfer phenomena in a hybrid nanofluid layer with a free surface are solved numerically using the blocked-off region method of Patankar. A parametric study varying the position, the size of the obstacle, the Marangoni number, the Rayleigh number, the volume fraction of the nanofluid has been performed. The results concern the flow profile, the temperature profile and the evolution of the Nusselt number under different conditions. It was shown that an enhancement of the convective heat transfer of more than 170% can be achieved on the cold wall just by switching the position of the obstacle from the bottom to the top.

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Abbreviations

Ca:

Capillary number

Cp:

Specific heat capacity (J/kg C)

\({\overrightarrow{{g}}}\) :

Acceleration of gravity (m s\(^{-2})\)

h :

Obstacle height (m)

L :

Enclosure width (m)

m :

Nanoparticles shape factor

Ma:

Marangoni number

n :

Normal vector

Nu:

Nusselt number

Pr:

Prandlt number

Ra:

Thermal Rayleigh number

T :

Dimensionless temperature

t :

Time (s)

\({\overrightarrow{{U}}}\) :

Velocity (m s\(^{-1})\)

w :

Obstacle width (m)

x,y :

Cartesian coordinate (m)

\(\alpha \) :

Thermal diffusivity (m\(^{2}\) s\(^{-1})\)

\(\beta \) :

Coefficient of thermal expansion of fluid (K\(^{-1})\)

\(\lambda \) :

Thermal conductivity (W/m K)

\(\mu \) :

Dynamic viscosity (Pa s)

\(\nu \) :

Kinematic viscosity (m\(^{2}\) s\(^{-1})\)

\(\rho \) :

Density (kg m\(^{-3})\)

\(\sigma \) :

Surface tension (N m\(^{-1})\)

\(\phi \) :

Nanoparticles volume fraction (%)

\(\psi \) :

Stream function (m\(^{2}\) s\(^{-1})\)

\(\omega \) :

Vorticity (s\(^{-1})\)

ave:

Average

bf:

Fe\(_{3}\)O\(_{4\, }\)nanofluid

C:

Cold

f:

Fluid

H:

Hot

hnf:

Hybrid nanofluid

loc:

Local

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Acknowledgements

This research has been funded by Scientific Research Deanship at University of Ha’il—Saudi Arabia through project number RG-21 035.

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Authors and Affiliations

  1. Laboratory of Metrology and Energy Systems, University of Monastir, Monastir, Tunisia

    Walid Hassen

  2. Department of Mechanical Engineering, College of Engineering, Ha’il University, Ha’il, Saudi Arabia

    Lioua Kolsi, Wajdi Rajhi, Fuhaid Alshammari, Naif Alshammari & Nidhal Ben Khedher

  3. Mechanical Engineering Department, College of Engineering, Jouf University, P.O. Box 2014, Sakaka, Aljouf, Saudi Arabia

    Ahmed Ghazy

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  1. Walid Hassen
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Correspondence to Lioua Kolsi.

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Hassen, W., Kolsi, L., Rajhi, W. et al. Thermocapillary and buoyancy driven convection analysis for a hybrid nanofluids enclosed in a cavity with heated obstacle. Eur. Phys. J. Spec. Top. 231, 2669–2681 (2022). https://doi.org/10.1140/epjs/s11734-022-00598-3

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