Computer extended series solution for flow in a narrow channel of varying gap

Abstract

The problem of steady two-dimensional laminar incompressible flow of a Newtonian fluid in a long narrow channel of varying gap is considered. The similarity transformation reduces the governing equations into nonlinear ordinary differential equation. The resulting equation is solved using long series with polynomial coefficients. Thirty-one effective terms in the perturbation series representing coefficients of pressure gradient for various cases of bearings are obtained. Analytic continuations of series solution unravel the rich spectrum of flow structure which could not be fully revealed in earlier asymptotic as well as pure numerical studies. The qualitative features obtained are comparable to pure numerical results besides this the present analysis enables to extend the study up to αRe = 50 to ∞. The variations of velocity profiles and pressure gradient for different boundary conditions as functions of αRe are analyzed.