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Synthesis of entropy generation in Cu–Al2O3 water-based thin film nanofluid flow

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Abstract

In this research communication, assessment of entropy in the MHD flow of a hybrid nanofluid (Cu–Al2O3 /H2O) and a mono-nanofluid (Cu–H2O) of a thin film across an elongated plane with radiative heat is explored. Computational solutions of the equations describing the model are derived employing scaling analysis followed by RKF-45-based shooting technique with MATLAB software. A parametric analysis pertaining to the impressions of diverse physical parameters on the flow features is deliberated. The quantitative differences of the outcomes between the Cu–Al2O3 /H2O and Cu–H2O are brought out. Validation of the derived results of the current investigation ascertains a greater accuracy of the numerical code adopted in comparison with those results available in the literature. The temperature and the rate of thermal diffusion of the hybrid nanofluid are more prominent than those in the Cu–H2O case. Blade-shaped particles yield a temperature enhancement of 42.8% higher than the case of spherical-shaped particles in hybrid nanofluid, while the mono-nanofluid experiences a 22.2% enhancement. Free surface temperature of Cu–H2O with blade-shaped nanomaterials is 32.2% more than that in the spherical-shaped particles, while it is doubled in Cu–Al2O3 /H2O. Radiative emission has a diminishing impact on the entropy generation in both nanofluids.

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Abbreviations

(b, c):

Positive constants [s−1]

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

Brinkman number \(= \frac{{\mu_{{\text{f}}} U^{2} }}{{k_{{\text{f}}} \left( {T_{{\text{s}}} - T_{0} } \right)}}\)

\(B_{0}\) :

Constant magnetic strength [Wb m−2]

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

Specific heat at constant pressure [J kg−1 K−1]

\(f\) :

Dimensionless stream function

\(k\) :

Thermal conductivity of the fluid [W m−1 K−1]

\(k^{*}\) :

Absorption coefficient [m−1]

\(M\) :

Magnetic field parameter \(= \frac{{\sigma_{{\text{f}}} B_{0}^{2} }}{{b\rho_{{\text{f}}} }}\)

Nr:

Thermal radiation parameter \(= \frac{{16\sigma^{*} T_{0}^{3} }}{{3k_{{\text{f}}} k^{*} }}\)

\({\text{Pr}}\) :

Prandtl number \(= \frac{{\left( {\mu C_{{\text{p}}} } \right)_{{\text{f}}} }}{{k_{{\text{f}}} }}\)

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

Reynolds number \(= \frac{{{\text{Ux}}}}{{\nu_{{\text{f}}} }}\)

\(S\) :

Unsteadiness parameter \(= \frac{c}{b}\)

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

Shape factor

\(S_{0}\) :

Characteristic entropy generation rate \(= \frac{{k_{{\text{f}}} \left( {T_{{\text{s}}} - T_{0} } \right)^{2} }}{{x^{2} T_{0}^{2} }}\)

T :

Fluid Temperature [K]

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

Constant reference temperature [K]

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

Stretching sheet’s temperature [K]

\(T_{\infty }\) :

Ambient fluid temperature [K]

\(T_{0}\) :

Temperature at the slit [K]

\(u, v\) :

Velocity components along x, y-axis [m s−1

\(\mu\) :

Dynamic viscosity [kg m−1 s−1]

\(\nu\) :

Kinematic viscosity [m2 s−1]

\(\rho\) :

Fluid density [kg m−3]

\(\sigma\) :

Electrical conductivity [S m−1]

\(\sigma^{*}\) :

Stefan-Boltzmann constant [W m−2 K−4]

\(\phi_{1}\) :

Volume fraction of copper

\(\phi_{2}\) :

Volume fraction of alumina

\(\theta\) :

Dimensionless temperature

\(\xi\) :

Film thickness

\(\psi\) :

Stream function

\(\Omega\) :

Dimensionless temperature ratio \(= \frac{{\left( {T_{{\text{s}}} - T_{0} } \right)}}{{T_{0} }}\)

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

Nanofluid

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

Hybrid nanofluid

\(f\) :

Fluid

\(s_{1}\) :

Copper

\(s_{2}\) :

Alumina

\(^{\prime}\) :

Differentiation with respect to \(\eta\)

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Acknowledgements

The authors acknowledge the constructive suggestions received from the Reviewers and the Editor which led to definite improvement in the paper. Also, the authors thanks are due to Professor M. Taylor for reading the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam, Tirupati, India

    K. Sreelakshmi, G. Sandhya & G. Sarojamma

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    K. Vajravelu

  3. Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait

    AJ Chamkha

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  1. K. Sreelakshmi
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Correspondence to G. Sarojamma.

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Sreelakshmi, K., Sandhya, G., Sarojamma, G. et al. Synthesis of entropy generation in Cu–Al2O3 water-based thin film nanofluid flow. J Therm Anal Calorim 147, 13509–13521 (2022). https://doi.org/10.1007/s10973-022-11540-z

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