Comparative study for heat transfer characteristics of many graphene hybrid nanofluids flow over a shrinking sheet

In this work, steady two-dimensional boundary layer flow of an electrically conductive hybrid nanofluids past a shrinking sheet, along with magnetic field, thermal radiation, suction/injection, heat source/sink and velocity slip model, has been investigated. Particularly, eight mixed hybrid graphene nanofluids of copper, silver, aluminium oxide and titanium dioxide were studied and compared with the classical graphene–water nanofluid. Appropriate similarity transformations have been used to convert the governing PDEs into a set of non-linear ODEs, then, we deduced exact solutions of the flow and temperature. In addition, possibility of obtaining no, unique and dual solutions for these functions were introduced as critical values and regions via graphs. Moreover, validation of the present solutions with those in the literature has been tabulated. Furthermore, asymptotic expression and local extremum for the most important equation were studied.

On comparing with those results in the literature at some special values of the included parameters, excellent agreements were gotten. It was mentioned that two conditions have to be simultaneously applied to result the temperature dual solution with restrictions on choosing values of specific parameters. Further, in the injection case, the temperature distributions are larger by about 66.7% on comparing with those in the suction case, for all almost the investigated parameters. To get the highest temperature, it was deduced that the copper is to be firstly added to the water and then mixed with the graphene to produce the hybrid nanofluid. Graphene–copper/water employs as a heater on increasing the Eckert number, shrinking parameter and second velocity slip (for $N<0$). Furthermore, it acts as cooler with an increase of magnetic field, $|$heat source/sink parameter$|$, suction/injection parameter, solid volume fraction, first velocity slip and second velocity slip (for $N>0$).