Analytical solution of flow of second-order non-Newtonian fluids through annular pipes

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 smaller value for a given Hc. 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.