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Darcy–Forchheimer MHD rotationally symmetric micropolar hybrid-nanofluid flow with melting heat transfer over a radially stretchable porous rotating disk

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Abstract

This study fills a gap in the literature by exploring the complex interplay between microrotation, magnetic fields, and temperature factors in hybrid nanofluids, improving our understanding of their behavior and potential usage. For hybrid nanofluids, this study examines their combined effect rather than individual components. The hybrid nanofluids, specially engineered mixture of base fluid, which is water, and two types of nanoparticles, titanium dioxide (TiO2) and iron oxide (Fe3O4), known for their remarkable energy transfer capabilities, are investigated. These fluids find applications in heat generation, micropower generation, and solar collectors. The research focuses on understanding the impact of various factors, including microrotation, inertial characteristics, thermal radiation, melting heat transfer, and Joule dissipation, on surface heating in the presence of a radially stretchable rotating disk. The governing equations are transformed into ordinary differential equations using similarity variables, and the study employs the homotopy analysis method for a semi-analytical solution. The results reveal how temperature, velocities, heat transmission rates, and skin-friction change under different material properties. This research has implications for magnetohydrodynamics in space propulsion, radiative heat transfer in high-temperature applications, and solar thermal systems. It also contributes to environmental engineering and automotive cooling systems.

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Data availability

The data that support the findings of the study are available from the corresponding author upon reasonable request.

Abbreviations

\(\eta\) :

Transformed coordinate, NA

\({\eta }^{*}\) :

Porosity parameter, NA

\(\alpha\) :

Thermal diffusivity, m2 S−1

\({\alpha }_{\text{hnf}}\) :

Thermal diffusivity of hybrid nanofluid, m2 s−1

\(\beta\) :

Heat generation absorption parameter, NA

\({B}_{0}\) :

Strength of the magnetic field, T (Tesla)

\({\text{Bi}}\) :

Thermal slip parameter, NA

\({\text{Br}}\) :

Brinkman number, NA

\({C}_{\text{b}}\) :

Drag force, N m−2

\({C}_{\text{fx}}\) :

Local skin-friction coefficient, NA

\({{\text{Cs}}}_{2}\) :

Heat capacity of the solid surface, J m−3 K−1

\({\text{Ec}}\) :

Eckert number, NA

\(F\) :

Coefficient of the porous medium, m s−1

\({F}_{\text{r}}\) :

Darcy–Forchheimer parameter, NA

\({H}_{0}\) :

Microrotation slip parameter, NA

\(K\) :

Effective thermal conductivity, W m−1 K−1

\({K}_{\text{f}}\) :

Thermal conductivity, W m−1 K−1

\({K}_{\text{hnf}}\) :

Effective thermal conductivity of hybrid nanofluid, W m−1 K−1

\({K}_{\text{nf}}\) :

Effective thermal conductivity of nanofluid, W m−1 K−1

\({L}_{0}\) :

Velocity slip parameter, NA

\({\text{Me}}\) :

Melting parameter, NA

\(M\) :

Magnetic parameter, NA

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

Heat capacitance, J m−3 K−1

\({\left(\rho {C}_{\text{p}}\right)}_{\text{f}}\) :

Heat capacitance, J m−3 K−1

\({\left(\rho {C}_{\text{p}}\right)}_{\text{hnf}}\) :

Heat capacitance of hybrid nanofluid, J m−3 K−1

\({\varphi }_{1},{\varphi }_{2}\) :

Volume concentration, NA

\(q\) :

Axial velocity in similarity coordinates, NA

\({q}_{{\text{w}}}\) :

Heat flux at the wall, W m−2

\(Q\) :

Heat generation/absorption coefficient, W m−3

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

Local Reynolds number, NA

\({\text{Rd}}\) :

Radiation parameter, NA

\(r, \Phi , z\) :

Cylindrical coordinates system, \(m, m, m\)

\({s}_{0}\) :

Microrotation slip parameter, NA

\(\sigma\),\({\sigma }_{\text{f}}\) :

Electric conductivity, S m−1

\({\sigma }_{\text{hnf}}\), \({\sigma }_{\text{nf}}\) :

Electric conductivity of hybrid nanofluid, nanofluid, S m−1

\(T\) :

Fluid temperature, K

\({T}_{m}\) :

Melting surface temperature, K

\({T}_{\infty }\) :

Ambient temperature, K

\({\tau }_{\text{wt}}\) :

Radial stress at the wall, N m−2

\({\tau }_{\text{w}\Phi }\) :

Transverse shear stress at the wall, N m−2

\({\rho }_{\text{hnf}}\) :

Density of hybrid nanofluid, kg m−3

\({\sigma }^{*}\) :

Stefan-Boltzmann constant, W m−2 K−4

\(\Omega\) :

Constant angular velocity, rad s−1

\(u, v, w\) :

Velocity components, m s−1

\({f}{\prime} (\eta ), f(\eta ), g(\eta )\) :

Radial, axial, and tangential velocity, respectively, NA

\({k}^{*}\) :

Rosseland absorption, W m−1 K−1

\(\mu\) :

Dynamic viscosity, Pa s

\(\nu\) :

Kinematic viscosity, m2 s−1

\(\rho\) :

Fluid density, kg m−3

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Acknowledgements

“This project was supported by Researchers Supporting Project Number. (RSP2024R411), King Saud University, Riyadh, Saudi Arabia”.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, 28420, Khyber Pakhtunkhwa, Pakistan

    Zahir Shah

  2. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, 43600, Pakistan

    Muhammad Sulaiman

  3. Department of Mathematics, Abdul Wali Khan University, Mardan, 25200, Khyber Pakhtunkhwa, Pakistan

    Abdullah Dawar

  4. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Mansoor H. Alshehri

  5. Department of Industrial Machines and Equipments, Faculty of Engineering, Lucian Blaga” University of Sibiu, 10 Victoriei Boulevard, Sibiu, Romania

    Narcisa Vrinceanu

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  1. Zahir Shah
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Shah, Z., Sulaiman, M., Dawar, A. et al. Darcy–Forchheimer MHD rotationally symmetric micropolar hybrid-nanofluid flow with melting heat transfer over a radially stretchable porous rotating disk. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-12986-z

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