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Numerical simulations of solid particles dispersion during double-diffusive convection of a nanofluid in a cavity with a wavy source

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Abstract

This study attempts to address the dispersion of the solid particles in nanofluid flow throughout the double-diffusive convection under the impacts of buoyancy ratio, magnetic field and three different boundary conditions. The main target of this study is to examine the mixing processes between solid particles and nanofluid flow at natural convection flow. An incompressible scheme of smoothed particle hydrodynamics (ISPH) is applied to study the dispersion processes of solid particles through the nanofluid flow. The mesh-free nature of ISPH method is helpful in handling the interactions between solid and fluid particles in an easy way. The sidewalls are wavy walls, and the solid particles are embedded in an open circular cylinder positioned in the cavity center. The numerical simulations are performed for various values of buoyancy ratio \(\left( { - 2 \le N \le 2} \right)\), Hartman parameter \(\left( {0 \le {\text{Ha}} \le 100} \right)\), Lewis number \(\left( {0 \le {\text{Le}} \le 50} \right)\), nanoparticles parameter \(\left( {0 \le \phi \le 0.1} \right)\), wave amplitude \(\left( {0.05 \le A \le 0.15} \right)\) and wave undulation number \(\left( {2 \le \kappa \le 10} \right)\). Results show that the variations on the boundary conditions of heat and mass differentiate dramatically the direction of solid particles dispersion in a cavity. Buoyancy ratio is playing a main role in direction of the solid particles dispersion, and Hartman parameter reduces the solid particles dispersion.

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Abbreviations

\(A\) :

Wave amplitude

\(a\) :

Length of a wavy shape (m)

\({\mathbf{B}}\) :

Magnetic field vector

\(B_{0}\) :

Magnitude of magnetic field

\(C\) :

Concentration

\(C_{p}\) :

Heat capacity

\(D\) :

Mass diffusivity (m2/s)

Ha:

Hartman parameter

g :

Gravitational acceleration (m/s2)

\(k\) :

Thermal conductivity (W/m K)

\(L\) :

Cavity length

\(L_{\text{w}}\) :

Total length of a wavy shape

Le:

Lewis number

\(N\) :

Buoyancy ratio parameter

\({\mathbf{n}}\) :

Normal vector

\(\kappa\) :

Undulation number

\(\overline{\text{Nu}}_{w}\) :

Average Nusselt number

\(np\) :

Total number of particles

\(m\) :

Mass (kg)

\(P\) :

Dimensionless pressure

\(p\) :

Dimensional pressure (N/m2)

Pr:

Prandtl number

Ra:

Rayleigh number

\(r_{\text{c}}\) :

Radius of the circular cylinder

\(\overline{\text{Sh}}_{w}\) :

Average Sherwood number

\(T\) :

Temperature (K)

\(t\) :

Time (s)

\(u, v\) :

Dimension velocity components (m/s)

\(W\) :

Kernel function

\(W_{\text{G}}\) :

Width of a circular cylinder gate

\(U, V\) :

Dimensionless velocity components

\(x, y\) :

Cartesian coordinates (m)

\(X, Y\) :

Dimensionless coordinates

\(\alpha\) :

Thermal diffusivity (m2/s)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\gamma\) :

Kernel renormalization factor

\(\Phi\) :

Dimensionless concentration

\(\phi\) :

Solid volume fraction

\(\mu\) :

Dynamic viscosity

\(\psi\) :

Stream function

\(\lambda\) :

Phase deviation

\(\rho\) :

Density (kg/m3)

\(\tau\) :

Dimensionless time

\(\theta\) :

Dimensionless temperature

\(\sigma\) :

Electrical conductivity

\(\zeta\) :

Hot source length

f:

Fluid

nf:

Nanofluid

h:

Hot

C:

Cold

i:

Target particle

j:

Neighbor particle

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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 the research groups program under Grant Number (R.G.P2/17/42).

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Khalid University, Abha, 6141, Saudi Arabia

    Abdelraheem M. Aly

  2. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    Abdelraheem M. Aly

  3. Electrical Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University, Wadi Addwasir, 11991, Saudi Arabia

    Ehab Mahmoud Mohamed

  4. Electrical Engineering Department, Faculty of Engineering, Aswan University, Aswan, 81542, Egypt

    Ehab Mahmoud Mohamed

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Correspondence to Ehab Mahmoud Mohamed.

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Aly, A.M., Mohamed, E.M. Numerical simulations of solid particles dispersion during double-diffusive convection of a nanofluid in a cavity with a wavy source. Arch Appl Mech 91, 2089–2108 (2021). https://doi.org/10.1007/s00419-020-01871-4

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