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Numerical investigation of ZnO–MWCNTs/ethylene glycol hybrid nanofluid flow with activation energy

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Abstract

The hybrid nanofluids are finding applications in advanced heat transfer technologies and heat exchangers due to their enhanced thermal conductivity and economic efficiency compared to the monotype nanofluids. In the present article, the heat and mass exchange in the chemically reactive unsteady boundary layer flow of ZnO–MWCNTs/ethylene glycol hybrid nanofluid in the hydromagnetic environment is examined by employing a non-Newtonian flow model and taking into account the Arrhenius activation energy. The flow governing equations are coupled PDEs of highly nonlinear nature, which are solved by shooting strategy. The numerical results for the hybrid nanofluid temperature, Nusselt number, Sherwood number, and skin friction are presented in graphs and discussed comprehensively to understand the impact of various thermofluidic parameters on heat, mass, and flow characteristics of the ZnO–MWCNTs/ethylene glycol hybrid nanofluid. A comparative analysis among Nusselt number profiles of ZnO–MWCNTs/ethylene glycol, TiO2–MWCNTs/ethylene glycol, Al2O3–MWCNTs/ethylene glycol, and Fe3O4–MWCNTs/ethylene glycol is also performed. Numerical results reveal that the maximum enhancement in heat transport rate occurs in the case of ZnO–MWCNTs/EG hybrid nanofluid. The presence of concentration slip and the chemical reaction stimulated by the activation energy augment the mass exchange rate in ZnO–MWCNTs/ethylene glycol hybrid nanofluid.

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Abbreviations

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

Temperature at the surface of stretching sheet (K)

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

Stretching sheet velocity (m s−1)

\(u_{\infty }\) :

Ambient fluid velocity (m s−1)

\(T_{\infty }\) :

Temperature of the ambient fluid (K)

\(u,v\) :

Velocities in x and r direction respectively (m s−1)

\(\kappa\) :

Thermal conductivity (W m−1 K−1)

\(\sigma\) :

Electrical conductivity (S m−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\rho\) :

Density (kg m−3)

\(k_{1}\) :

Second-grade fluid coefficient

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

Chemical reaction rate

\(K\) :

Boltzmann constant

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

Activation energy

\(m\) :

Fitted rate constant

\(D_{0}\) :

Mass diffusivity coefficient

\(m_{1}\) :

Thermal slip factor

\(m_{2}\) :

Concentration slip factor

\(\Pr\) :

Prandtl number \(\left( { = \frac{{\mu_{{\text{f}}} \left( {c_{{\text{p}}} } \right)_{{\text{f}}} }}{{\kappa_{{\text{f}}} }}} \right)\)

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

Eckert number \(\left( { = \frac{{u_{{\text{w}}}^{2} }}{{\left( {c_{{\text{p}}} } \right)_{{\text{f}}} (T_{{\text{w}}} - T_{\infty } )}}} \right)\)

\(A\) :

Unsteadiness parameter \(\left( { = \frac{c}{a}} \right)\)

\({\text{Sc}}\) :

Schmidt number \(\left( { = \frac{{v_{{\text{f}}} }}{{D_{0} }}} \right)\)

\(S\) :

Suction parameter \(\left( { = \frac{{v_{0} }}{{\sqrt {a\nu } }}} \right)\)

\(b^{*}\) :

Second-grade fluid parameter \(\left( { = \frac{{k_{1} a}}{{\mu_{{\text{f}}} (1 - ct)}}} \right)\)

\(M\) :

Magnetic number \(\left( { = \sqrt {\frac{\sigma }{{\rho_{{\text{f}}} a}}} B_{0} } \right)\)

\(d_{1}\) :

Thermal slip parameter \(\left( { = m_{1} \sqrt {\frac{a}{\nu (1 - ct)}} } \right)\)

\(d_{2}\) :

Concentration slip parameter \(\left( { = m_{2} \sqrt {\frac{a}{\nu (1 - ct)}} } \right)\)

\(\delta\) :

Temperature difference parameter \(\left( { = \frac{{T_{{\text{w}}} - T_{\infty } }}{{T_{\infty } }}} \right)\)

\(k^{*}\) :

Chemical reaction rate parameter \(\left( { = \frac{{k_{r}^{2} }}{a}} \right)\)

\(E^{*}\) :

Activation energy parameter \(\left( { = \frac{{E_{{\text{a}}} }}{{KT_{\infty } }}} \right)\)

\(\eta\) :

Non-dimensional space variable

\(\theta\) :

Non-dimensional temperature

\(\phi\) :

Nanoparticle volume fraction

\(\phi_{1}\) :

Volume fraction of ZnO nanoparticles

\(\phi_{2}\) :

Volume fraction of MWCNTs

EG:

Ethylene glycol

SWCNTs:

Single-walled carbon nanotubes

DWCNTs:

Double-walled carbon nanotubes

MWCNTs:

Multi-walled carbon nanotubes

\(\infty\) :

For ambient fluid

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

For surface of the sheet

hnf:

For hybrid nanofluid

nf:

For nanofluid

f:

For base fluid

\({\text{s}}\) :

For zinc oxide nanoparticles

\({\text{CNTs}}\) :

For multi-walled carbon nanotubes

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Acknowledgements

The authors owe their deep sense of gratitude to the honorable Vice-Chancellor of Defence Institute of Advanced Technology (Deemed University) for constant encouragement and support in the current research. Also, Miss Preeti is thankful to the Defence Research and Development Organization (DRDO), Government of India, for supporting this work under the Senior Research Fellowship (F-16-52-08).

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  1. Department of Applied Mathematics, Defence Institute of Advanced Technology (Deemed to be University), Pune, 411025, India

    Preeti Prashar & Odelu Ojjela

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  1. Preeti Prashar
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Correspondence to Odelu Ojjela.

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Prashar, P., Ojjela, O. Numerical investigation of ZnO–MWCNTs/ethylene glycol hybrid nanofluid flow with activation energy. Indian J Phys 96, 2079–2092 (2022). https://doi.org/10.1007/s12648-021-02132-y

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