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Thermophysical properties of Maxwell Nanofluids via fractional derivatives with regular kernel

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Abstract

The researchers have diverted their mind to improve the thermophysical properties of convective heat transfer analysis. The studies on nanofluids have been reported because these systems display an anomalous enhancement of convective heat transfer. In this paper, we made a comparative analysis of Maxwell nanofluid with nanoparticles suspended in ethylene glycol through modern approaches of fractional differentiations. The governing equations of Maxwell nanofluid for velocity and temperature are fractionalized in terms of Atangana–Baleanu and Caputo–Fabrizio operators and then solved analytically by invoking Laplace transform to generate series solutions. The general solutions of temperature and velocity field are established in terms of Mittag–Leffler and Fox-H functions, respectively. Modern approaches of fractional differentiations have been analyzed for memory effects on the Maxwell nanofluid for improving the thermophysical properties. The impacts of rheological parameters are underlined for the volume fraction of nanoparticles, relaxation time and single- and multi-walled carbon nanotubes suspended in ethylene glycol. A graphical illustration is depicted to disclose the physical aspects of the problem based on the functionality of modern approaches of fractional differentiations. Our results suggest that thermal conductivity of Maxwell nanofluid increases when nanoparticle’s volume fraction increases.

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Abbreviations

T(y, t):

Temperature distribution

V(y, t):

Velocity field

\(\lambda _1\) :

Relaxation time of nanofluid

\(\rho _{\mathrm{nf}}\) :

Density of nanofluid

\(k_{\mathrm{nf}}\) :

Thermal conductivity of nanofluid

\((c_{\text{p}}\rho )_{\mathrm{nf}}\) :

Heat capacitance of nanofluid

\((\beta )_{\mathrm{nf}}\) :

Thermal expansion coefficient of nanofluid

\(\mu _{\mathrm{nf}}\) :

Dynamic viscosity of nanofluid

t :

Time variable

y :

Spatial variable

\(T_\infty\) :

Constant wall temperature

\(T_w\) :

Temperature rise up

\(\mathfrak {R}_1-\mathfrak {R}_5\) :

Functional parameters

\(\xi _1-\xi _2\) :

Fractional parameters

\(\beta _1-\beta _18\) :

Letting parameters

CF :

Caputo–Fabrizio fractional differential operator

AB :

Atangana–Baleanu fractional differential operator

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Acknowledgements

The author Kashif Ali Abro is highly thankful and grateful to Mehran University of Engineering and Technology, Jamshoro, Pakistan, for generous support and facilities of this research work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

    Kashif Ali Abro & Abdon Atangana

  2. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro & Mehwish Soomro

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Abdon Atangana

  4. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca Morelos, México

    J. F. Gómez-Aguilar

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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to J. F. Gómez-Aguilar.

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Abro, K.A., Soomro, M., Atangana, A. et al. Thermophysical properties of Maxwell Nanofluids via fractional derivatives with regular kernel. J Therm Anal Calorim 147, 449–459 (2022). https://doi.org/10.1007/s10973-020-10287-9

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