Computer-extended series solution for laminar flow between a fixed impermeable disk and a porous rotating disk

The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid.

The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method.

The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15.

The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.