Application of Differential Transform Method for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Two Parallel Plates

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow and the axisymmetric flow, are investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation using similarity transformation. This highly nonlinear equation is solved analytically subject to the relevant boundary conditions by employing the differential transform method (DTM). Graphical results are presented to investigate the influence of the squeeze number S on the velocity, skin friction, and pressure gradient. It is concluded that the present analysis using the DTM is capable of studying the squeezing flow behavior up to and even beyond the squeeze number S=60. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge–Kutta scheme.