Abstract: This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method.Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed.It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a_c nailer value for a given H_c.Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

Key words: integral transformation, shape factor, non-Newtonian coefficient, second-order fluids, annular pipes