Analytical Solution Of Two-dimensional Viscous Flow Between Slowly Expanding Or Contracting Walls With Weak Permeability

Abstract

In this article the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability is presented and Homotopy Perturbation Method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Comparisons are made between the Numerical solution (NM) and the results of the He's Homotopy Perturbation Method (HPM).

A New Technique to Solve Two-Dimensional Viscous Fluid Flow Among Slowly Expand or Contract Walls

“…Also, for all levels of suction or injection, if the wall is contracting (α<0), increase α lead to the axial velocity becomes low close to the center and high near the wall, the reason that the velocity becomes larger close to the wall because the flow towards the wall becomes larger. Moreover, from the comparison between the new method [4,15,16], we note that this method is effective and powerful, also its results agree well with the results of these methods. Although there is an agreement between the methods, the new technique is preferred.…”

“…Figure 7 shows the comparison of results between the new method and VPM [15] at Re=5 and α=0.5 for h(ζ) and h'(ζ), respectively for the state of expansion combined with injection. On another note, Figure 8 explains the comparison of the results between, YTHPM, RK-4 th order, and HPM [16] for α=0.5 and Re=1 for h(ζ) and h'(ζ), respectively. After we find the flow field, the remaining important properties of the flow like the pressure and shear stress can be found as follows: The gradient of pressure can be found by putting the components of velocity in Eq.…”

“…In ref. [16], results are obtained from the 4 th iteration and in ref. [15] from the 15 th iteration.…”