Series analysis for the flow between two stretchable disks

Abstract

In this paper, we present the semi-analytical/semi-numerical solution of an axis-symmetric flow between two coaxial infinite stretching disks. The governing momentum equations in cylindrical co-ordinates are reduced to fourth order nonlinear ordinary differential equation (NODE) with the relevant boundary conditions. The resulting nonlinear boundary value problem is solved by using Computer Extended Series Solution (CESS) and Homotopy Analysis Method (HAM). The effects of Reynolds number R and disk stretching parameter γ are discussed in detail. The resulting solutions are compared with the earlier numerical findings. The above methods admit a desired accuracy and the results are presented in the form of graphs. The validity of the series solution is extended to a much larger values of R up to infinity. Further, the variations of shear stress and pressure parameter as a functions of R and γ are analyzed. For very large R, the governing equation reduces to third order NODE with infinite boundary is solved by using Dirichlet series and the solution is compared with the numerical findings.

Keywords

• Stretchable disks
• Dirichlet series
• CESS
• Domb-Sykes plot
• HAM and Pade’ approximants
• Residual error