An Analytic Solution of the Unsteady Flow Between Two Coaxial Rotating Disks

摘要

In this study, analytical solutions are obtained for the unsteady flow of a viscous, incompressible fluid between two coaxial rotating disks of infinite dimensions, using the homotopy analysis method (HAM). Using similar variables, we first simplify the exact Navier-Stokes equation to highly coupled nonlinear partial differential equations. Upon application of the HAM these equations are replaced by a system of linear and uncoupled ordinary differential equations and solutions effective throughout the entire temporal and spatial domains are obtained. The nature of the flow fields is discussed under the influence of the same or opposite direction of rotation, Reynolds number, etc. Physically interesting quantities, such as radial and tangential shear stresses, are also obtained, and are valid throughout the temporal domain. To the best of our knowledge, no such series solution is available in the literature for the problem under consideration.