Abstract
The studies of classical nanofluids are restricted to models described by partial differential equations of integer order, and the memory effects are ignored. Fractional nanofluids, modeled by differential equations with Caputo time derivatives, are able to describe the influence of memory on the nanofluid behavior. In the present paper, heat and mass transfer characteristics of two water-based fractional nanofluids, containing nanoparticles of CuO and Ag, over an infinite vertical plate with a uniform temperature and thermal radiation, are analytically and graphically studied. Closed form solutions are determined for the dimensionless temperature and velocity fields, and the corresponding Nusselt number and skin friction coefficient. These solutions, presented in equivalent forms in terms of the Wright function or its fractional derivatives, have also been reduced to the known solutions of ordinary nanofluids. The influence of the fractional parameter on the temperature, velocity, Nusselt number, and skin friction coefficient, is graphically underlined and discussed. The enhancement of heat transfer in the natural convection flows is lower for fractional nanofluids, in comparison to ordinary nanofluids. In both cases, the fluid temperature increases for increasing values of the nanoparticle volume fraction.
Highlights
Natural convection flows have been extensively studied due to their multiple engineering applications
Our interest here is to provide exact solutions for the temperature and velocity fields corresponding to the radiative natural convection flow of fractional nanofluids over an infinite vertical plate with heat and mass transfer, and to investigate the enhancement of heat transfer in such a flow, utilizing the fractional model
In order to bring to light the influence of the fractional parameter on the heat and mass transfer in the natural convection flow of the above-mentioned fractional nanofluids, and to obtain some physical insight into the present results, some numerical calculations have been carried out for different values of the fractional parameter α, radiation parameter Nr, and the nanoparticle value fraction φ
Summary
Natural convection flows have been extensively studied due to their multiple engineering applications. Interesting exact solutions have been obtained by Turkyilmazoglu and Pop [13], for the velocity and temperature fields corresponding to the natural convection flow of some nanofluids, past an infinite vertical plate with radiation effects. Our interest here is to provide exact solutions for the temperature and velocity fields corresponding to the radiative natural convection flow of fractional nanofluids over an infinite vertical plate with heat and mass transfer, and to investigate the enhancement of heat transfer in such a flow, utilizing the fractional model. The influence of the fractional parameter on the thermal and hydrodynamic response of physical interest, is graphically underlined and discussed
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