Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

In this research, the author investigated two-dimensional incompressible, laminar and steady boundary-layer flow past a stretching/shrinking sheet which is in a water-based nanofluid containing metallic and nonmetallic nanoparticles; namely, silver, copper, alumina and titania. Theoretical exact solutions for the dimensionless stream function and dimensionless temperature were obtained. Hence, a detailed analysis of the existence of those solutions was effectively deduced for the stretching/shrinking sheet conditionally in order with the values of permeability, magnetic and suction/injection parameters. Via many tables and graphs, the effects of various physical parameters included in dimensionless profiles for the stream function, velocity and temperature were studied. These parameters include the solid volume fraction, magnetic, permeability, radiation, surface convection, stretching/shrinking sheet, reduced skin friction coefficient and reduced Nusselt number. On comparing the present results with those in the literature, a very good agreement was obtained in some special cases for different values of the investigated parameters. In addition, it was shown that the effective electrical conductivity considerably and remarkably affects the nanofluids' flow and, hence, it is mandatory to take this into account and not to ignore it as in some recent papers, especially with its presence in the solutions' conditions, otherwise, a spurious physical sight is to be obtained. It was therefore indicated that the included parameters have to be re-investigated and we must not depend on the published results that dropped this term. Further, the critical values and curves for obtaining one solution (dual solutions) were successfully secured for a stretching sheet (shrinking sheet). For a stretching/shrinking sheet, profiles of the velocity decrease as the solid volume fraction increases in the region (0, 0.2], then, they increase as this parameter increases when its value lies in the region (0.2, 0.4]. (C) 2016 Elsevier B.V. All rights reserved.