Analytical Analysis of Squeezing Flows

Abstract

This thesis covers the investigation of axisymmetric squeezing flows under slip and no slip boundary conditions. In the process, the flow of a fluid in a porous medium between two parallel plates approaching each other symmetrically has also been studied. The stream functions u r ( r , z , t )  1   1   and u z ( r , z , t )   r  z r  r and the transformation function  ( r , z )  r 2 F ( z ) were used to transfer the Navier-Stockes equations into an ordinary nonlinear differential equation along with the boundary conditions. To solve these nonlinear problems, different analytical methods that are; the Adomian decomposition method (ADM), the new iterative method (NIM), the homotopy perturbation method (HPM), the optimal homotopy asymptotic method (OHAM) and the differential transform method (DTM) are applied and velocity profiles for various parameters of Newtonian fluids are obtained. The velocity of plates and its effects on fluid velocity are established. The above mentioned methods are based on Taylor’s series but their line of action is different and one may face serious problems of convergence in their application. In this case, the convergence of the approximating series solution is discussed and the mathematica built-in code NDSolve is used to validate the results of analytical solutions. The results show that OHAM gives a better approximation under the conditions on which the research is premised.