On the purely analytic computation of laminar boundary layer flow over a rotating cone

Abstract

The fundamental purpose of the present research is to obtain analytical expressions for the solution of the steady laminar flow of an incompressible viscous Newtonian fluid over a rotating cone. Using a proper similarity transformation akin to the classical one of Von Karman the nonlinear equations of motion are reduced to a boundary value problem whose solution is then derived in terms of a series of exponentially-decaying functions for the full range of cone half-angle ϕ characterizing the conical flow structure. The exact numerical method is found to improve as the cone half-angle is decreased. The effects of the cone half-angle on the physically significant relevant parameters, such as the wall shears, the torque and the vertical suction are clarified. Purely explicit analytical expressions for the solution of governing equations to support the numerically evaluated solutions are also obtained via the homotopy analysis method.