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Electrohydrodynamic fluids possess extensive applications, spanning from the formation of magnetic fields in planets and stars to oil recovery. In this paper, a variational principle for an electrohydrodynamic fluid is presented, and formulated through the semi-inverse method. The Ritz method is utilized to derive an approximate solution. Furthermore, the potential application of this principle to optimal control problems constrained by an electrohydrodynamic fluid is explored.

The unsteady flow over a continuously shrinking sheet with wall mass suction in a nanofluid is numerically studied. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations by using similarity transformation. The resulting similarity equations are then solved by the shooting method for three types of nanofluid: copper-water, alumina-water and titania-water to investigate the effect of nanoparticle volume fraction parameter ɸ to the flow in nanofluid. The skin friction coefficient and velocity profiles are presented and results show that dual solutions exist for a certain range of unsteadiness parameter A. It is also found that the nanoparticle volume fraction parameter ɸ and types of nanofluid play an important role to significantly determine the flow behaviour.

A number of nanofluids have been prepared to study the effect of lubrication properties of nanofluids on stainless steels taking Kaolin and Boron Nitride (BN) as the lubricant particles and Sodium Dodecyl Sulfate (SDS), Cetyl Trimethyl Ammonium Bromide (CTAB), Sodium Hexa Meta Phosphate (SHMP) as dispersants in the same liquid medium i.e. water. A pin on disc tribometer is being used to access the tribological behaviour of the prepared nanofluids. The particle size of these particle dispersions are examined with a nanoparticle size analyzer. It has been found that the use of dispersants significantly control the particle size and tribological behavior of the nanofluids as for Boron Nitride particle with Sodium Dodecyl Sulfate (SDS) as dispersant has got a very low value of coefficient of friction being equal to 0.142 while without dispersant the value is 0.498. Similarly, in case of Kaolin water with SDS as dispersant the value of coefficient of friction obtained is 0.161 and without dispersant it is 0.333. Sodium Dodecyl Sulfate (SDS) as dispersant has resulted a very low coefficient of friction compared to other dispersants tested even though it doesn’t always assure a least particle size. The role of SDS in yielding the lowest friction has pursued significant attention for further investigation.