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Statistical and numerical analysis of electrically conducting hybrid nanomaterial near the stagnation region

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Abstract

Regression analysis helps predict and understand the complex phenomena exhibited by fluids by examining the impact of independent variables on dependent variables. This article introduces a study that utilizes statistical analysis to explore the flow and heat transport behavior dynamics of a two-dimensional electrically conducting hybrid nanomaterial near the stagnation point. The innovation of this research lies in the novel synthesis method, which involves integrating molybdenum dioxide and aluminum oxide into a water-based fluid. The impacts of viscous dissipation, Joule heating (without an electric field), and convective boundary conditions are considered. This approach shows promise for practical applications across various industries. By comprehending and optimizing the behavior of hybrid nanofluids, potential benefits in the efficiency and performance of the system can be realized in areas such as electronics cooling and industrial heat exchangers. A significant aspect of this research involves the intelligent utilization of an external magnetic field oriented perpendicular to the flow direction. While this enhances energy flow, it also moderates the velocity profile of hybrid nanofluids. During regression analysis, it is observed that the effect of the Eckert number on the Nusselt number is greater than that of the Biot number.

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Abbreviations

\(\left( {u,\,v} \right)\) :

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

\(\left( {x,\,y} \right)\) :

Coordinates \(({\text{m}})\)

\(U_0\),\(U_\infty\) :

Reference stretching and free stream velocities \(({\text{m}}/{\text{s}})\)

\(T\) :

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

\(T_w\) :

Surface/wall temperature \(({\text{K}})\)

\(T_\infty\) :

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

\(U_\text{w} (x)\) :

Stretching velocity m s−1

\(ne_1\) :

Free electron density e m−3

\(e_1\) :

Electron charge \(({\text{C}})\)

\(h_1\) :

Heat transfer coefficient \(({\text{W}}\,{\text{m}}^{-2} \,{\text{K}^{-1}})\)

\(\tau_w\) :

Wall shear stress \(({\text{N}}\,{\text{m}}^{-2} )\)

\(B_0\) :

Magnetic field strength \(({\text{A}}\,{\text{m}^{-1}})\)

\(m^*\) :

Hall parameter \(({\text{m}}^3 \,{\text{C}^{-1}})\)

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

Reynolds number

\(\Pr\) :

Prandtl number

\(A\) :

Dimensionless velocity ratio

\(\frac{\partial f(\xi ,\eta )}{{\partial \eta }}\) :

Non-dimensional velocity

\(\theta (\xi ,\eta )\) :

Non-dimensional temperature

\(M^*\) :

Magnetic parameter

\(\gamma^*\) :

Biot number

\(Ec^*\) :

Eckert number

\(C_\text{f}\) :

Skin friction

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

Nusselt number

\({\text{MoS}}_2\) :

Molybdenum dioxide

\({\text{Al}}_2 {\text{O}}_3\) :

Aluminum oxide

\(\phi_\text{np1}\) :

\({\text{MoS}}_2\) Volume fraction

\(\phi_\text{np2}\) :

\({\text{Al}}_2 {\text{O}}_3\) Volume fraction

\(\mu_\text{hnf}\) :

Dynamic viscosity \(({\text{kg}}\,{\text{ms}^{-1}})\)

\(\mu_\text{bf}\) :

Base fluid dynamic viscosity \(({\text{kg}}\,{\text{ms}^{-1}})\)

\(\rho_\text{hnf}\) :

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

\(\rho_\text{bf}\) :

Base fluid density \(({\text{kg}}\,{\text{m}}^{-3} )\)

\(\alpha_\text{hnf}\) :

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

\(\alpha_\text{bf}\) :

Base fluid thermal diffusivity \(({\text{m}}^2 \,{\text{s}^{-1}})\)

\(\nu_\text{hnf}\) :

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

\(\nu_\text{bf}\) :

Base fluid kinematic viscosity \(({\text{m}}^2 \,{\text{s}^{-1}})\)

\(\sigma_\text{hnf}\) :

Electrical conductance \(({\text{S}}\,{\text{m}^{-1}})\)

\(\sigma_\text{bf}\) :

Base fluid electrical conductivity \(({\text{S}}\,{\text{m}^{-1}})\)

\(\kappa_\text{hnf}\) :

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

\(k_\text{bf}\) :

Base fluid thermal conductivity \((\text{W}\, \text{m}^{-1}\, \text{K}^{-1})\)

\(\kappa_\text{np1}\) :

\({\text{MoS}}_2\) Thermal conductivity \((\text{W}\, \text{m}^{-1}\, \text{K}^{-1})\)

\(\kappa_\text{np2}\) :

\({\text{Al}}_2 {\text{O}}_3\) Thermal conductivity \((\text{W}\, \text{m}^{-1}\, \text{K}^{-1})\)

\((c_\text{p} )_\text{hnf}\) :

Specific heat \(({\text{J}}\,{\text{kg}^{-1}}\, \text{K}^{-1})\)

\((c_\text{p} )_\text{bf}\) :

Base fluid specific heat \(({\text{J}}\,{\text{kg}^{-1}}\, \text{K}^{-1})\)

BVP:

Boundary value problem

BCs:

Boundary conditions

MHD:

Magnetohydrodynamic

ODE:

Ordinary differential equation

PDE:

Partial differential equation

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Acknowledgements

The authors would like to acknowledge Deanship of Graduate Studies and Scientific Research, Taif University for funding this work.

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Authors and Affiliations

  1. Department of Humanities and Sciences, School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Khursheed Muhammad

  2. Department of Computer Science, National University of Sciences and Technology (NUST), Balochistan Campus (NBC), Quetta, 87300, Pakistan

    Zahid Nisar

  3. Department of Physics, College of Sciences, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia

    Abdullah M. S. Alhuthali

  4. Department of Chemistry, Faculty of Science, King Khalid University, P.O. Box 9004, 61413, Abha, Saudi Arabia

    Mohamed Hussien

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Muhammad, K., Nisar, Z., Alhuthali, A.M.S. et al. Statistical and numerical analysis of electrically conducting hybrid nanomaterial near the stagnation region. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13095-7

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