### Engineering Mathematics

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### Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane

In this study, two highly accurate and simple analytical methods (known as semi exact solutions), the variational iteration method (VIM) and Adomian’s decomposition method (ADM) are applied for illustrating transient condition of viscous fluid flow over oscillating plane and also oscillating viscous fluid flow over stationary plane. The flow of an incompressible viscous fluid, caused by the oscillation of a flat wall and also the flow of an oscillating fluid flow over stationary wall are considered by Navier-Stokes equations and are subjected to the behavior of fluid flow in boundary layer at transient condition. The main purpose of this article is to solve transient Navier-Stokes first and second equations in new mathematical solving method which is called semi exact solutions where in each case, the velocity of viscous fluid is determined as a function of time and also vertical distance from plane in boundary layer at transient condition. Results reveal the boundary layer thickness and also the transient fluid flow velocity in boundary layer and even more it shows that the (VIM) and (ADM) methods are very effective and accurate in comparison with the exact solution results. The results demonstrate the velocity of fluid in boundary layer as a function of displacement and time and it is shown that in different time, the value of velocity obtained by “VIM” and “ADM” solving methods is almost equal to velocity which is derived from exact or numerical solutions. So the main background and reason of applying the mentioned methods is to verify the accuracy of “VIM” and “ADM” in solving different fluid mechanics equations especially Navier-Stokes equations.

Analytical Methods, VIM, ADM, Viscous Flow, Oscillating Wall, Stationary Wall, Transient Condition, Stokes Equation

APA Style

Edris Ghonoodi, Davood Domeiri Ganji. (2021). Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane. Engineering Mathematics, 5(2), 13-21. https://doi.org/10.11648/j.engmath.20210502.11

ACS Style

Edris Ghonoodi; Davood Domeiri Ganji. Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane. Eng. Math. 2021, 5(2), 13-21. doi: 10.11648/j.engmath.20210502.11

AMA Style

Edris Ghonoodi, Davood Domeiri Ganji. Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane. Eng Math. 2021;5(2):13-21. doi: 10.11648/j.engmath.20210502.11