Long series analysis of laminar flow through parallel and uniformly porous walls of different permeability

Abstract

The steady two-dimensional laminar flow of a viscous incompressible fluid in a channel due to non-uniform suction or injection through its uniformly porous parallel walls is considered. A solution valid for large suction/injection Reynolds numbers comprising various cases is presented. Following Terrill [5], the governing equations reduce to nonlinear ordinary differential equation. The resulting equation is solved using a long series with polynomial coefficients. The analysis involves recasting the series representing physical parameters into new forms, series with Legendre polynomials as coefficients, divergent but asymptotic series, application of Pade' approximants, reversion of series, Euler transformation, etc. These techniques contribute considerably to obtaining larger regions of validity of the series.