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A comparative study of a hybrid nanofluid on a melting stretching surface using different nanoparticle shapes

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Abstract

This article is motivated by the effect of nanoparticle shapes on fluid motion and heat transmission across melting heat-stretchable impermeable surfaces. Thus, the impact of three different nanoparticle shapes (sphere, cylinder and lamina) at different volume fractions for two nanoparticles, i.e., \({\text{Fe}}_{3} {\text{O}}_{4}\) and \({\text{MgO}}\), in the presence of three base fluids (\({\text{H}}_{2} {\text{O}}\), \({\text{methanol}}\), \({\text{engine}}\;{\text{oil}}\)) is investigated. The system of nonlinear partial differential equations (PDEs) is reduced to a set of ordinary differential equations (ODEs) using suitable local similarity variables. To validate the theoretical findings of this investigation, the Runge–Kutta–Fehlberg method is used and MATLAB’s inbuilt program bvp4c is employed through which graphical outputs are deliberated to show the impact of nanoparticles on momentum and energy domain. This study shows that the lamina shape of \({\text{MgO}} - {\text{Fe}}_{3} {\text{O}}_{4} /{\text{engine}}\;{\text{oil}}\) has a major impact on \(\Theta \left( \xi \right)\) with increasing \(\varphi_{1} ,\varphi_{2}\). Due to the stronger thermal conductivity of \({\text{MgO}}\) lamina-shaped nanoparticles compared to other nanoparticle shapes within the flow region, the velocity profile increases with the augmentation of \(\varphi_{1}\, \text{and}\, \varphi_{2}\) . \({\text{MgO}} - {\text{Fe}}_{3} {\text{O}}_{4} /{\text{H}}_{2} {\text{O}}\) exhibits a more significant impact than the others.

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Abbreviations

\(A\) :

Velocity ratio parameter/–

\(B,B_{0}\) :

Applied magnetic field/\({\text{N}}\,{\text{m}}^{ - 1} \,{\text{A}}^{ - 1}\)

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

Coefficient of skin friction/–

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

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

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

Heat capacity of solid surface\(/{\text{J}}\,{\text{kg}}^{ - 1} \,{\text{K}}^{ - 1}\)

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

Eckert number/–

\(f,f^{\prime } ,F\) :

Non-dimensional velocity/–

\(M\) :

Magnetic number/–

\(m\) :

Flow behavior index parameter/–

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

Melting parameter/–

\({\mathbb{N}}_{ux}\) :

Nusselt number/–

\(\Pr\) :

Prandtl number/–

\(Q_{0}\) :

Volumetric heat coefficient\(/{\text{J}}\,{\text{K}}^{ - 1} \,{\text{m}}^{ - 3}\)

\(Q\) :

Heat source/sink/–

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

Radiation parameter/–

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

Heat flux/\({\text{W}}\,{\text{m}}^{ - 2}\)

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

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

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

Heat flux/\({\text{W}}\,{\text{m}}^{ - 2}\)

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

Local Reynolds number/–

\(a\) :

Wall thickness parameter

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

Hybrid nanofluid

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

Nanofluid

\(f\) :

Fluid

\(T\) :

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

\(T_{\infty }\) :

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

\(T_{{\text{m}}}\) :

Melting surface temperature/\({\text{K}}\)

\(T_{0}\) :

Reference temperature/\({\text{K}}\)

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

Surface velocity/\({\text{m}}\,{\text{s}}^{ - 1}\)

\(U_{\infty } ,U_{{\text{e}}}\) :

Free stream velocity/\({\text{m}}\,{\text{s}}^{ - 1}\)

\(u,\,v\) :

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

\(\kappa^{ * }\) :

Rosseland mean absorption\(/{\text{m}}^{ - 1}\)

\(\alpha\) :

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

\(\lambda\) :

Latent heat \(/{\text{J}}\;{\text{Kg}}^{ - 1}\)

\(\mu\) :

Dynamic viscosity/\({\text{kg}}\,{\text{m}}^{ - 1} \;{\text{s}}^{ - 1}\)

\(\rho\) :

Fluid density/\({\text{kg}}\,{\text{m}}^{ - 3}\)

\(\nu\) :

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

\(\theta ,\Theta\) :

Dimensionless temperature/–

\(\Theta_{{\text{r}}}\) :

Temperature ratio parameter

\(\beta\) :

Slip parameter/–

\(\beta^{ * }\) :

Slip coefficient\(/{\text{m}}\)

\(\varphi_{1} ,\varphi_{2}\) :

Volume fraction of 1st and 2nd nanoparticles/–

\(\sigma^{ * }\) :

Stefan–Boltzmann constant\(/{\text{Wm}}^{ - 2} \;{\text{K}}^{ - 4}\)

\(\eta ,\xi\) :

Similarity variable/–

\(\sigma\) :

Electrical conductivity/\({\text{simens}}\,.\,{\text{m}}^{ - 1}\)

\(\kappa\) :

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

\(\psi\) :

Stream function/–

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Authors and Affiliations

  1. Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Chandralekha Mahanta

  2. Department of Mechanical Engineering, National Institute of Technology Arunachal Pradesh, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Ram Prakash Sharma

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Mahanta, C., Sharma, R.P. A comparative study of a hybrid nanofluid on a melting stretching surface using different nanoparticle shapes. J Therm Anal Calorim 148, 13655–13677 (2023). https://doi.org/10.1007/s10973-023-12621-3

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