Pulsatile Flow Through a Curved Pipe – An Analytical Study

In this paper, the unsteady flow of Newtonian fluid through a curved pipe due to a pulsatile pressure gradient has been considered. The flow is three dimensional and the partial differential equations governing the flow are highly coupled and non-linear. Approximate analytical solutions of the governing partial differential equations have been obtained without neglecting any term containing the curvature ratio. Perturbation series in terms of curvature ratio has been used for obtaining the solutions. It is interesting to note that the solutions are valid for large as well as small values of Womersley number. The effect of different parameters such as, Reynolds number, Womersley number and curvature ratio on the flow through curved pipe is discussed in this paper. It is found that the axial velocity is qualitatively periodic in nature, as expected. The Reynolds number and curvature ratio are found to shift the axial velocity towards the outer boundary of the curved pipe.