Application Of Optimal Homotopy Asymptotic Method For Non- Newtonian Fluid Flow In A Vertical Annulus.

In this paper, the flow of an incompressible non Newtonian fluid in a vertical annulus is considered. The fluid is governed by Sisko fluid model and is assumed to flow upwards under the influence of the pressure gradient and gravity. The non linear momentum equation is then solved using the optimal Homotopy asymptotic method (OHAM). The effect of the power index n, the material parameter η and the pressure gradient on the velocity and the stress are explored and presented. It is well known that the momentum flux changes its sign at the same value of the non dimensional radius for which the velocity is maximum. The same has been observed in the present study for Sisko fluids. Further, it is also observed that for negative pressure gradient, the influence of g is more on the shear thinning fluids than that of Newtonian and shear thickening fluids. Thus the second degree approximation of the solution obtained using OHAM is suffice to find analytical solutions to the above mentioned category of problems. [ABSTRACT FROM AUTHOR]