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Thermosolutal convection of NEPCM inside a curved rectangular annulus: hybrid ISPH method and machine learning

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Abstract

In this work, the incompressible smoothed particle hydrodynamics (ISPH) method is utilized to simulate thermosolutal convection in a novel annulus barred by NEPCMs. The novel annulus is formed between a horizontal curved rectangle connected to a vertical rectangle containing a vertical ellipse. It is the first attempt to investigate the heat and mass transmission of NEPCM in such a unique annulus. NEPCM’s sophisticated designs of closed domains during heat/mass transfer can be applied in energy savings, electrical device cooling, and solar cell cooling. The ISPH method solved the fractional time derivative of governing partial differential equations. The artificial neural network (ANN) is integrated with the ISPH results to predict the average Nusselt \(\overline{{\text{Nu}} }\) and Sherwood numbers \(\overline{{\text{Sh}} }\). The scales of physical parameters are Hartmann number (Ha = 0–80), buoyancy ratio parameter (N = − 10–20), Dufour/Soret numbers (Du = 0–0.4 & Sr = 0–0.8), Rayleigh number (Ra=103–105), fractional time derivative (α = 0.85–1), nanoparticle parameter (φ = 0–0.15), and fusion temperature (θf = 0.05–0.95). The main findings showed the importance of buoyancy ratio and Rayleigh number in enhancing the buoyancy-driven convection which accelerates the velocity field and strengths the isotherms and isoconcentration. The velocity field decreases according to an enhancement in Hartmann number and nanoparticle parameter. The exact agreement of the ANN model prediction values with the goal values demonstrates that the created ANN model can predict the \(\overline{{\text{Nu}} }\) and \(\overline{{\text{Sh}} }\) values properly. The complicity of a closed domain by carving the horizontal rectangle and inserting the ellipse inside a vertical rectangle can be utilized into cooling equipment, solar cells, and heat exchangers.

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Abbreviations

\(C\) :

Dimensional concentration

\({\text{Cr}}\) :

Heat capacity

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

Specific heat (J kg−1 K−1)

\({\text{g}}\) :

Acceleration of gravity (m s−2)

\(k\) :

Thermal conductivity (W m−1 K−1)

\({\text{Le}}\) :

Lewis number

\(p\) :

Pressure (\({\text{Pa}}\))

\(N\) :

Buoyancy ratio parameter

\(T\) :

Dimensional temperature (\({\text{K}}\))

\({\text{Pr}}\) :

Prandtl number

\({\text{Ra}}\) :

Rayleigh number

\(X,Y\) :

Cartesian coordinates

\(U, V\) :

Velocities components

\(\alpha \) :

Fractional time-derivative parameter

\(\beta \) :

Thermal expansion coefficient (K−1)

\(\varphi \) :

Nanoparticle volume fraction

\(\delta \) :

Temperature parameter (K)

\(\theta \) :

Dimensionless temperature

\(\Phi \) :

Dimensionless concentration

\({\rho }_{p}\) :

Density of NEPCM particles

\(\mu \) :

Viscosity (kg m−1 s−1)

\(\rho \) :

Density (kg m−3)

\(\tau \) :

Dimensionless time

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP. 2/38/45).

Funding

This study was funded by Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, under Grant Number (RGP. 2/38/45).

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Authors and Affiliations

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

    Abdelraheem M. Aly & Zehba Raizah

  2. School of Mechanical Engineering, University of Ulsan, Ulsan, South Korea

    Sang-Wook Lee & Nghia Nguyen Ho

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  1. Abdelraheem M. Aly
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Aly, A.M., Lee, SW., Ho, N.N. et al. Thermosolutal convection of NEPCM inside a curved rectangular annulus: hybrid ISPH method and machine learning. Comp. Part. Mech. (2024). https://doi.org/10.1007/s40571-024-00744-9

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