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Magneto-hydrothermal performance of hybrid nanofluid flow through a non-Darcian porous complex wavy enclosure

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Abstract

The present work elucidates the hydrothermal characteristics within a non-Darcian porous complex wavy enclosure saturated with \(\hbox {Al}_{2}\hbox {O}_{3}\)–Cu–\(\hbox {H}_{2}\hbox {O}\) hybrid nanofluid considering a uniform magnetic field. The left sidewall of the enclosure is wavy and heated isothermally, whereas the other sidewall is maintained at ambient temperature, all other walls are insulated. The Forchheimer–Brinkman-extended Darcy model is implemented to analyze the flow through porous media. The dimensionless transport equations are numerically solved following the finite volume-based in-house computational code with successive staggered non-uniform mesh distribution. The hydrothermal behaviors are investigated meticulously changing the dimensionless variables like undulation amplitude (\(\lambda \)), Hartmann number (Ha), Darcy number (Da), and modified-Rayleigh number (\(\hbox {Ra}_{\mathrm{m}}\)). The remarkable results reveal that enhancing the heating surface area by heightening the amplitude of the undulation always leads to higher heat transfer, but does not always favor the growth of the flow strength. The heightening of the flow strength with amplitude is noted for higher \(\hbox {Ra}_{\mathrm{m}}\) only. The flow intensity, as well as heat transfer, increases with the growing \(\hbox {Ra}_{\mathrm{m}}\). The same decreases with increasing Da and Ha. Local distribution of heat transfer characteristics shows complex behavior depending on the amplitude of the undulations and associated dimensionless numbers.

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Abbreviations

B :

Strength of magnetic field (\(\hbox {N A}^{-1\, }\hbox {m}^{-2}\))

Da:

Porous medium Darcy number

\(F_{c}\) :

Forchheimer coefficient

g :

Gravitational acceleration (\(\hbox {m s}^{-2}\))

H :

Cavity height (m)

Ha:

Hartmann number

K :

Porous layer permeability (\(\hbox {m}^{2}\))

n :

Number of wall undulations

Nu:

Nusselt number (average)

P :

Pressure (dimensionless)

Pr:

Prandtl number

Ra:

Fluid-based Rayleigh number

\(\hbox {Ra}_{\mathrm{m}}\) :

Modified-Rayleigh number

\(\hbox {Re}_{\mathrm{m}}\) :

Magnetic Reynolds number

t :

Time (s)

T :

Temperature (K)

u,v :

Components of velocities (\(\hbox {m s}^{-1}\))

U, V :

Components of velocities (dimensionless)

x, y :

Cartesian coordinates (m)

X, Y :

Cartesian coordinates (dimensionless)

\(\alpha \) :

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

\(\beta \) :

Thermal expansion coefficient (\(\hbox {K}^{-1}\))

\(\varepsilon \) :

Porosity

\(\theta \) :

Temperature (dimensionless)

\(\lambda \) :

Surface waviness amplitude

\(\mu \) :

Dynamic viscosity (\(\hbox {Nms}^{-2}\))

\(\nu \) :

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

\(\rho \) :

Density of fluid (\(\hbox {kg m}^{-3}\))

\(\tau \) :

Time (dimensionless)

\(\varphi \) :

Hybrid nanoparticle concentration

\(\psi \) :

Stream function (dimensionless)

\(_\mathrm{{a}}\) :

Ambient

\(_\mathrm{{c}}\) :

Cold

\(_\mathrm{{f}}\) :

Base fluid

\(_\mathrm{{h}}\) :

Hot

max:

Maximum

\(_\mathrm{{s}}\) :

Solid

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering and Management, Kolaghat, 721171, India

    Dipak Kumar Mandal

  2. Department of Power Engineering, Jadavpur University, Salt Lake, Kolkata, 700106, India

    Nirmalendu Biswas

  3. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Nirmal K. Manna

  4. Department of Aeronautics and Astronautics, Air Force Institute of Technology, Dayton, OH, 45433, USA

    Rama Subba Reddy Gorla

  5. Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait

    Ali J. Chamkha

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  1. Dipak Kumar Mandal
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Mandal, D.K., Biswas, N., Manna, N.K. et al. Magneto-hydrothermal performance of hybrid nanofluid flow through a non-Darcian porous complex wavy enclosure. Eur. Phys. J. Spec. Top. 231, 2695–2712 (2022). https://doi.org/10.1140/epjs/s11734-022-00595-6

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