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Marangoni convection in a hybrid nanofluid-filled cylindrical annular enclosure with sinusoidal temperature distribution

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Abstract

The current research numerically investigates the Marangoni convection in a cylindrical annulus filled with hybrid nanofluid saturated porous media. The interior and exterior walls are subjected to spatially varying sinusoidal thermal distributions with various amplitude ratios and phase deviations. The limits at the top and bottom are adiabatic. To solve the system of non-dimensional governing equations, the finite difference approach is applied. The main objective of the ongoing study is to investigate the impact of the Marangoni number, nanoparticle volume fraction and the radii ratio on the amplitude ratio and phase deviation. Also, the fluid flow, thermal characteristics, local and average Nusselt numbers are analysed in the hybrid nanofluid-filled vertical cylindrical annulus with magnetic effects. The findings indicate that the sinusoidal temperature promotes multicellular flow in the porous annular region. In the annulus with sinusoidal boundaries, the Marangoni number underperforms while the nanoparticle volume fraction outperforms.

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Data availability statement

No data associated in the manuscript.

Abbreviations

A :

Aspect ratio (L/D)

\(A_\textrm{l}\) :

Amplitude at left wall (m)

\(A_\textrm{r}\) :

Amplitude at right wall (m)

\(B_{0}\) :

Magnetic field strength

D :

annulus gap (m)

Da:

Darcy number

g :

Gravitational acceleration \((\textrm{m}/\textrm{s}^{2})\)

\(h_{\textrm{nl}}\) :

Thickness of nanolayer

Ha:

Hartmann number

k :

Thermal conductivity \((\textrm{W}/\textrm{mk})\)

K :

Permeability of the porous medium \((\textrm{m}^2)\)

L :

Height of the annulus (m)

Ma:

Marangoni number

Nu:

Nusselt number

p :

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

Pr:

Prandtl number

r, x :

Dimensional coordinates

R, X :

Dimensionless coordinates

\(r_{\textrm{p}}\) :

Radius of nanoparticles (nm)

\(r_{0}\) :

Radius of the outer cylinder (m)

\(r_{\textrm{i}}\) :

Radius of the inner cylinder (m)

Ra:

Rayleigh number

\(T_{\textrm{l}}, T_{\textrm{r}}\) :

Dimensional temperature at left and right walls

U, V :

Dimensionless velocity components

u, v :

Dimensional velocity components (m/s)

\(\alpha \) :

Thermal diffusivity \((\textrm{m}^2/\textrm{s})\)

\(\beta \) :

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

\(\epsilon \) :

Amplitude ratio

\(\delta \) :

Porosity of the porous medium \((\textrm{m}^2)\)

\(\eta \) :

Dimensionless vorticity

\(\gamma \) :

Phase deviation

\(\lambda \) :

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

\(\mu \) :

dynamic viscosity (kg/ms)

\(\nu \) :

kinematic viscosity \((\textrm{m}^2/\textrm{s})\)

\(\Omega \) :

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

\(\phi \) :

Solid volume fraction of nanoparticles

\(\psi \) :

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

\(\Psi \) :

Dimensionless stream function

\(\rho \) :

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

\(\sigma \) :

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

\(\sigma ^{*}\) :

Surface tension parameter

\(\tau \) :

Time (s)

\(\theta _{\textrm{l}},\theta _{\textrm{r}}\) :

Dimensionless temperatures at left and right walls (K)

c:

Cold wall

f:

Properties associated with fluid

hnf:

Properties associated with hybrid nanofluid

l:

Left wall

r:

Right wall

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Authors and Affiliations

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

    B. Kanimozhi & M. Muthtamilselvan

  2. Department of Mathematical Sciences, United Arab Emirates University, 15551, Al-Ain, United Arab Emirates

    Qasem Al-Mdallal

Authors
  1. B. Kanimozhi
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  2. M. Muthtamilselvan
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  3. Qasem Al-Mdallal
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All authors contributed equally.

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Correspondence to M. Muthtamilselvan.

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Kanimozhi, B., Muthtamilselvan, M. & Al-Mdallal, Q. Marangoni convection in a hybrid nanofluid-filled cylindrical annular enclosure with sinusoidal temperature distribution. Eur. Phys. J. E 46, 1 (2023). https://doi.org/10.1140/epje/s10189-022-00253-8

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