Computer extended series solution for unsteady flow in a contracting or expanding pipe

Unsteady flow in a semi-infinite contracting or expanding pipe is reinvestigated using long series analysis. The proposed series method is useful in analysing the problem for a moderately large constant α (α = aa/ν, where a = a(t), the radius of the pipe is a function of time, a(t) is the velocity of the wall, and ν is kinematic viscosity). For positive values of α (expansion of the pipe) accuracy of the series representing shear stress and pressure gradient is increased from α = 2.89 to α = 6.0 by extracting the singularity followed by completion of the series. For negative values of α (contraction of the pipe), we revert the series which results into the increase of the region of validity of the transposed series from α = -25.0 to α = -2.89. Later we use Padé approximants for summing them. Also, the asymptotic solution for large values of α is obtained and it agrees closely with pure numerical values of shear stress at the wall and pressure gradient.