In this paper we investigate numerically the hydromagnetic boundary layer flow and heat transfer characteristics of a nanofluid using three types of nanoparticles (copper, aluminium oxide and titanium dioxide) having various shapes (spherical, cylindrical, arbitrary, etc) by considering three kinds of base fluids (water, ethylene glycol and engine oil) over a nonlinear inclined stretching surface, taking into account the effect of convective surface condition. Using similarity transformations, the governing nonlinear partial differential equations of the physical model are transformed into non-dimensional ordinary differential equations which are solved for local similar solutions using the very robust computer algebra software, Maple 13. The numerical simulation is carried out to investigate the role of the pertinent parameters on the flow and temperature fields as well as on the rate of heat transfer and on the rate of shear stress. The results show that the addition of nanoparticles to the base fluid may not always increase the rate of heat transfer. It depends significantly on the surface convection, type of base fluid and nanoparticles.  The finding of this study will open a gate for better understanding of nanofluid characteristics.

Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.