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Comparative study of computational frameworks for magnetite and carbon nanotube-based nanofluids in enclosure

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Abstract

Multi-wall carbon nanotubes (MWCNTs) characterize innovative nanoparticles that progress the thermal characteristics of base fluids, compelling them appropriate for utilizing in renewable energy, heat exchanger, and automotive engineering. In this analysis, the buoyancy-driven flow in a superposed spherical enclosure packed with amalgamated porous (Fe3O4-MWCNTs/H2O) hybrid nanofluid layers was explored by employing the procedure of Levenberg–Marquardt with backpropagated artificial neural networks (LMB-ANN) for two temperature models. The exterior wall of enclosure was kept at a constant frigid condition, while the inner surface received partial heating to create a heat flux. The flow situation within the porous cavity was modeled using the Darcy–Boussinesq model. To evaluate the model equations, the control volume-based finite element method (CVFEM) was adopted. The results obtained from numerical method explain the reference data of LMB-ANN for several situations of porous cavity by modifying model variables. By varying the model parameters within the scope of the present numerical approach, a set of proposed data LMB-ANN is generated for cases. The proposed model has equaled for perfection after the numerical findings of various instances have been evaluated using the LMB-ANN train, test, and validating strategy. Several error graphs and statistical visualizations focused on mean square errors, error histogram, and regression assessment are designed to support the proposed methodology (LMB-NN). The proposed approach (LMB-ANN) has been verified based on the correlation of the suggested and benchmark (numerical) outputs, with a validity level ranging from 10–02 to 10–09. Also, the principal findings revealed that elevating the Rayleigh and Darcy numbers improves energy transmission inside the enclosure.

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Abbreviations

MWCNT:

Multi-wall carbon nanotubes

MHD:

Magnetohydrodynamics

ML:

Multi-layer

ANN:

Artificial neural network

LMB:

Levenberg–Marquardt backpropagated

MSE:

Mean squared error

CVFEM:

Control volume finite element method

AE:

Absolute error

\(X,Y\) :

Space coordinates

\(B\) :

Magnetic field [Tesla]

\(p\) :

Pressure

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

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

\(q_{{{\text{Hnfs}}}}\) :

Interface heat transfer coefficient

\(c,d\) :

Major- and minor-axis elliptic cylinder

\(e_{1}\) :

Eccentricity

\(T_{{\text{c}}} ,T_{{\text{h}}}\) :

Temperature of cool and hot surface

\(T\) :

Temperature of liquid (K)

\(k\) :

Thermal conductivity (\({\text{Wm}}^{ - 1} \;{\text{K}}^{ - 1}\))

\(g\) :

Gravitational acceleration

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

Specific heat \(\left( {{\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1} } \right)\)

\({\text{{\rm N}u}}_{{{\text{Loc}}}}\) :

Local Nusselt number

\({\text{{\rm N}u}}_{{{\text{Avg}}}}\) :

Average Nusselt number

\({\text{Ha}}\) :

Hartmann number

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

Rayleigh number

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

Darcy number

\(Q\) :

Surface heat transmission coefficient

\(\delta_{{\text{h}}}\) :

Ratio of modified thermal conductivity

\(f\) :

Activation function

\(W\) :

Mass of neuron

\(\mu\) :

Dynamic viscosity \(\left( {{\text{mPa}}} \right).\)

\(\beta\) :

Thermal expansion

\(\rho\) :

Nanofluid density \(\left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right).\)

\(\psi\) :

Stream function

\(\sigma\) :

Electrical conductivity

\(\phi\) :

Volume fraction of nanoparticle

\(\Theta\) :

Dimensional heat profiles

\(\lambda\) :

Porosity

hnf:

Hybrid nanofluid

nf:

Nanofluid

bf:

Base fluid

s:

Solid nanoparticles

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Acknowledgements

The authors acknowledge the financial support from Khalifa University of Science and Technology through the Grant. RC2-2018-024.

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Authors and Affiliations

  1. Mechanical & Nuclear Engineering Department, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates

    Saleem Nasir & Abdallah S. Berrouk

  2. Center for Catalysis and Separation (CeCas), Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, United Arab Emirates

    Saleem Nasir & Abdallah S. Berrouk

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Nasir, S., Berrouk, A.S. Comparative study of computational frameworks for magnetite and carbon nanotube-based nanofluids in enclosure. J Therm Anal Calorim 149, 2403–2423 (2024). https://doi.org/10.1007/s10973-023-12811-z

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