Computer extended series solution of the circular porous slider

Abstract

A fluid of constant density is forced through the porous bottom of a circular slider which is moving laterally on a flat plane. The radius of the slider is assumed to be much larger than gap width between the slider and the plane. The similarity transformations reduce the equations of motion to a set of nonlinear ordinary differential equations which are solved using a semi-analytical numerical technique for small as well as moderately large Reynolds numbers. In this method we develop the series expansion with polynomial coefficients of the solution function. We calculate few terms manually and invoke the series expansion (with polynomial coefficients) for obtaining a large number of terms in the perturbation series using a computer. This series expansion enables us to calculate a sufficiently large number of universal coefficient functions by delegating routine complex algebra to the computer. The region of the validity of the series representing drag and lift are further increased by reverting the corresponding series (by changing the role of dependent and independent variables). Use of Pade' approximants for summing the reverted series is found to accelerate the convergence of the series. Calculation of lift and drag agree favourably with available pure numerical results.