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On the hydrothermal features of radiative Fe3O4–graphene hybrid nanofluid flow over a slippery bended surface with heat source/sink

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Abstract

The present investigation concentrates on the hydrothermal features of both hybrid nanofluid and usual nanofluid flow over a slippery permeable bent structure. The surface has also been considered to be coiled inside the circular section of radius R. Ferrous and graphene nanoparticles along with the host fluid water are taken to simulate the flow. The existence of heat sink/source and thermal radiation are incorporated within the system. Resulting equations are translated into its non-dimensional form using similarity renovation and solved by the RK-4 method. The consequence of pertinent factors on the flow profile is explored through graphs and tables. Streamlines and isotherms for both hybrid nanofluid and usual nanofluid are depicted to show the hydrothermal variations. The result communicates that temperature is reduced for curvature factor, whereas velocity is found to be accelerated. Heat transfer is intensified for thermal Biot number, and the rate of increment is higher for hybrid nanosuspension. Velocity and temperature are intensified for enhanced nanoparticle concentration. The heat transport process is decreased for the heat source parameter, but the reduction rate is comparatively slower for hybrid nanofluid.

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Abbreviations

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

Velocity components (m s−1)

\(r,s \,\) :

Spatial coordinates (m)

\(a\) :

Stretching constant (s−1)

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

Stretching velocity (m s−1)

\(a\) :

Stretching rate (s−1)

\(R\) :

Radius of curvature (m)

\(T_{{\rm w}}\) :

Temperature of the surface (K)

\(T_{\infty }\) :

Temperature away from surface (K)

\(T\) :

Hybrid nanofluid temperature (K)

\(\rho\) :

Density (kg m−3)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\kappa\) :

Thermal conductivity (W m−1 K−1)

\(\rho C_{{\rm p}}\) :

Heat capacitance (J m−3 K−1)

\(\sigma\) :

Electrical conductivity (Ω−1 m−1)

\(B_{0}\) :

Magnetic field (Ω1/2 m−1 s−1/2 kg1/2)

\(q_{{\rm r}}\) :

Radiative heat flux (kg s−3)

\(\sigma^{*}\) :

Stefan Boltzmann constant (W m−2 K−4)

\(k^{*}\) :

Mean absorption coefficient (m−1)

\(L\) :

Velocity slip factor (m)

\(v_{{\rm w}}\) :

Suction/injection velocity (m s−1)

\(h\) :

Convective heat transport coefficient (W m−2 K−1)

\(\phi\) :

Nanoparticle volume fraction

\(Q\) :

Heat source or sink

\(K = \sqrt {\frac{a}{{\nu_{{\rm f}} }}} R\) :

Curvature parameter

\(L_{{\rm slip}} = L\sqrt {\frac{a}{{\nu_{{\rm f}} }}}\) :

Velocity slip parameter

\(\Pr = \frac{{\mu_{{\rm f}} \left( {\rho C_{{\rm p}} } \right)_{{\rm f}} }}{{\rho_{{\rm f}} \kappa_{{\rm f}} }}\) :

Prandtl number

\(M = \frac{{\sigma_{{\rm f}} B_{0}^{2} }}{{a\rho_{{\rm f}} }}\) :

Magnetic parameter

\(S = - \frac{{v_{{\rm w}} }}{{\sqrt {a\nu_{{\rm f}} } }}\) :

Suction/injection parameter

\({\text{Bi}} = \frac{{h_{{\rm f}} }}{{\kappa_{{\rm f}} }}\sqrt {\frac{{\nu_{{\rm f}} }}{a}}\) :

Biot number

\(N = \frac{{4\sigma^{*} T^{3}_{\infty } }}{{3k^{*} \kappa_{{\rm f}} }}\) :

Radiation parameter

\(\theta_{{\rm w}} = \frac{{T_{{\rm w}} }}{{T_{\infty } }}\) :

Temperature ratio parameter

\(\lambda = \frac{Q}{{a\left( {\rho c_{{\rm p}} } \right)_{{\rm f}} }}\) :

Heat source/sink parameter

Nu:

Nusselt number

\(C_{{\rm f}}\) :

Skin friction

\({\text{Nu}}_{{\rm r}}\) :

Reduced Nusselt number

\(C_{{\rm fr}}\) :

Reduced skin friction

\(\text{Re}_{{\rm s}} = \frac{{as^{2} }}{{\nu_{{\rm f}} }}\) :

Local Reynold’s number

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

Base fluid

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

Nanofluid

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

Hybrid nanofluid

\(1, \, 2\) :

First and second nanoparticle, respectively

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Acknowledgements

The authors wish to express their cordial thanks to the respected Editor in chief and honourable reviewers for their valuable suggestions and comments to improve the presentation of this article.

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  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Nilankush Acharya

  2. Department of Information Technology, Fanshawe College, London, ON, Canada

    Fazle Mabood

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Acharya, N., Mabood, F. On the hydrothermal features of radiative Fe3O4–graphene hybrid nanofluid flow over a slippery bended surface with heat source/sink. J Therm Anal Calorim 143, 1273–1289 (2021). https://doi.org/10.1007/s10973-020-09850-1

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