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Mixed convection in a nanofluid-filled sloshing porous cavity including inner heated rose

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Abstract

In this paper, study of the heat transfer by mixed convection in sloshing enclosures heated from inside by an inner rose and filled with a porous medium using nanofluids is carried out. The Hazen–Dupain–Darcy model is applied to represent the porous medium, while the nanofluids are investigated using the one-phase model. The governing equations are converted to the dimensionless form and then solved numerically using the finite volume method. The controlling parameters in this simulation are numbers of the rose petals k, lengths of the rose petals a, the Richardson number Ri, the sloshing cavity amplitude A, the resonance frequency ω, the nanoparticle volume fraction ϕ and the Darcy number Da. It is found that rate of the heat transfer in case of the even number of the rose petals is greater than that of the odd number case. Also, the increase in either the sloshing cavity amplitude A or lengths of the rose petals a enhances the local Nusselt number, while as the resonance frequency ω increases, the average Nusselt number around the rose is reduced.

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Abbreviations

\(A\) :

Wavy amplitude

b, c :

Ergun’s constants

\(C_{\text{p}}\) :

Specific heat

\({\text{Da}}\) :

Darcy parameter

\(d_{\text{P}}\) :

Average particle size

\(F\) :

Forchheimer coefficient

\({\text{Gr}}\) :

Grashof number

\(g\) :

Gravitational acceleration \(\left( {{\text{m s}}^{-2} } \right)\)

\(K\) :

Permeability \(( {\text{m}}^{2} )\)

\(k\) :

Thermal conductivity \(({\text{W}}\,{\text{m}}^{ - 1} {\text{K}}^{ - 1} )\)

\({\text{Nu}}\) :

Nusselt number

\(P\) :

Pressure \(({\text{N m}}^{-2})\)

\({ \Pr }\) :

Prandtl number

\({\text{Re}}\) :

Reynolds number

\({\text{Ri}}\) :

Richardson parameter

\(T\) :

Temperature \(({\text{K}})\)

\(t\) :

Time (s)

\(\varvec{u}\) :

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

\(u, v\) :

Dimension velocity components \(({\text{m s}}^{-1})\)

\(U, V\) :

Dimensionless velocity components

\(x, y\) :

Cartesian coordinates (m)

\(X, Y\) :

Dimensionless coordinates

\(\alpha\) :

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

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\varepsilon\) :

Porosity

\(\phi\) :

Solid volume fraction

\(\mu\) :

Viscosity

\(\nu\) :

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

\(\rho\) :

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

\(\sigma\) :

Capacity ratio

\(\tau\) :

Dimensionless time

\(\omega\) :

Resonance frequency

f:

Fluid

nf:

Nanofluid

p:

Porous medium

np:

Dispersed nanoparticles

s:

Solid porous matrix

eff:

Porous medium with nanofluid

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under grant number (G.R.P./51/41).

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Correspondence to Abdelraheem M. Aly.

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Ahmed, S.E., Aly, A.M. Mixed convection in a nanofluid-filled sloshing porous cavity including inner heated rose. J Therm Anal Calorim (2020) doi:10.1007/s10973-019-09216-2

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Keywords

  • Mixed convection
  • Nanofluid
  • Porous medium
  • Sloshing enclosure
  • Rose shape