Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions

Abstract

We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions $u_r\left(r,z,t\right)=\left(1/r\right)\left(\partial \psi /\partial z\right)$ and $u_z\left(r,z,t\right)=-\left(1/r\right)\left(\partial \psi /\partial r\right)$ and a transformation $\psi \left(r,z\right)=r^{2}F\left(z\right)$. The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.