Study of non-Newtonian fluid flow through a wavy channel using finite element technique

A theoretical study of non-Newtonian fluid bounded by a harmonically waved surface is made with the main objective being the calculation of fluid velocity using perturbation theory. The problem is formulated in terms of vorticity, stream function and appropriate rheological equations of state, P{sub ik} = P{prime}{sub ik} {minus} P{delta}{sub ik} in which P{sub ik} = total stress tensor, P{prime}{sub ik} = deformation induced stress tensor, P = arbitrary isotropic pressure, and {delta}{sub ik} = Kronecker delta. The flow considered is parallel in absence of waves and it is exemplified by a two dimensional boundary layer over a plane. The problem is ultimately reduced to a set of linear ordinary differential equations which are then properly combined to result a single fourth order ordinary differential equation. Then the resulting equation is then solved numerically by applying the finite element technique.