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Impact of the Shape Factor on Combined Buoyancy and Marangoni Convection in a Hybrid Nanofluid Filled Cylindrical Porous Annulus

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Abstract

The ongoing research numerically examines the impact of the nanoparticle shape factor on the coupled Marangoni and buoyancy convection in a cylindrical porous annular region saturated with Ag-MgO/water hybrid nanofluid with magnetic effects. The internal wall of the annulus is considered to be hot, while the external wall is believed to be cold. The inner cylinder is fitted with a thin circular heated disc. To solve the non-dimensional governing equations, the finite difference approach with ADI, central differencing, and SOR technique is used. The major goal of the current study is to analyze the impact of the various shape factors on the Marangoni convection, magnetic field and nanoparticle volume fraction in the cylindrical annulus. The current study reveals that the spherical shaped nanoparticle outperforms in all the cases and \(\overline{Nu}\) hikes with the Marangoni number and declines with Hartmann number.

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Data Availability

All data is available within the manuscript.

Abbreviations

A:

Aspect ratio (H/D)

D :

annulus gap (m)

Da :

Darcy number

g :

gravitational acceleration \((m/s^{2})\)

Ha :

Hartmann number

k :

thermal conductivity(W/mk)

K :

Permeability of the porous medium \((m^2)\)

L :

Location of the baffle (h/H)

m :

Sphericity

Ma :

Marangoni number

Nu :

Nusselt number

p :

Pressure \((N/m^{2})\)

Pr :

Prandtl number

r, x :

dimensional coordinates

R, X :

dimensionless coordinates

\(r_{0}\) :

Radius of the outer cylinder (m)

\(r_{i}\) :

Radius of the inner cylinder (m)

Ra :

Rayleigh number

T :

Dimensional temperature

U, V :

Dimensionless velocity components

u, v :

Dimensional velocity components (m/s)

\(\alpha\) :

thermal diffusivity \((m^2/s)\)

\(\beta\) :

thermal expansion coefficient \((K^{-1})\)

\(\epsilon\) :

Size of the baffle (l/D)

\(\delta\) :

Porosity of the porous medium \((m^2)\)

\(\eta\) :

Dimensionless vorticity

\(\lambda\) :

Radii ratio \((r_{0}/r_{i})\)

\(\mu\) :

dynamic viscosity (kg/ms)

\(\nu\) :

kinematic viscosity \((m^2/s)\)

\(\Omega\) :

Dimensional vorticity \((s^{-1})\)

\(\phi\) :

Solid volume fraction of nanoparticles

\(\psi\) :

dimensional stream function \((m^2/s^{1})\)

\(\Psi\) :

dimensionless stream function

\(\rho\) :

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

\(\sigma\) :

Electrical conductivity \((sm^{-1})\)

\(\sigma ^{*}\) :

Surface tension

\(\tau\) :

Time (s)

\(\theta\) :

Dimensionless Temperature

avg :

average

c :

cold wall

f :

Properties associated with fluid

hnf :

Properties associated with hybrid nanofluid

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Acknowledgements

The author would like to thank Deanship of Scientific Research at Majmaah University for supporting this work under project No. R-2023-522.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, Tamil Nadu, India

    B. Kanimozhi & M. Muthtamilselvan

  2. Department of Mathematics, Faculty of Sciences AlZulfi, Majmaah University, Majmaah, 11952, Saudi Arabia

    Ziyad A. Alhussain

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  1. B. Kanimozhi
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  2. M. Muthtamilselvan
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Correspondence to M. Muthtamilselvan.

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Kanimozhi, B., Muthtamilselvan, M. & Alhussain, Z.A. Impact of the Shape Factor on Combined Buoyancy and Marangoni Convection in a Hybrid Nanofluid Filled Cylindrical Porous Annulus. Microgravity Sci. Technol. 35, 41 (2023). https://doi.org/10.1007/s12217-023-10065-w

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