Thermophysical properties of Maxwell Nanofluids via fractional derivatives with regular kernel
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Thermophysical properties of Maxwell Nanofluids via fractional derivatives with regular kernel Kashif Ali Abro1,2 · Mehwish Soomro2 · Abdon Atangana1,3 · J. F. Gómez‑Aguilar4 Received: 17 May 2020 / Accepted: 21 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
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. Keywords Convective heat transfer · Carbon nanotubes · Ethylene glycol · Fractional differentiations · Maxwell nanofluid List of symbols T(y, t) Temperature distribution V(y, t) Velocity field 𝜆1 Relaxation time of nanofluid 𝜌nf Density of nanofluid knf Thermal conductivity of nanofluid (cp 𝜌)nf Heat capacitance of nanofluid (𝛽)nf Thermal expansion coefficient of nanofluid 𝜇nf Dynamic viscosity of nanofluid t Time variable * J. F. Gómez‑Aguilar [email protected] 1
Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa
2
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca Morelos, México
y Spatial variable T∞ Constant wall temperature Tw Temperature rise up ℜ1 − ℜ5 Functional parameters 𝜉1 − 𝜉2 Fractional parameters 𝛽1 − 𝛽1 8 Letting parameters Abbreviation CF Caputo–Fabrizio fractional differential operator AB Atangana–Baleanu fractional differential operator
Introduction Investigations of free convection hydromagnetic flows of
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