This paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.

This article is presented the surface tension effect on the two-dimensional blade section of the partially submerged propeller (PSP). In this regard, blade is entered to the water that causes to splash the water due to the impact and free surface. Also, because of the blade's angle of attack suction side is vented by air and pressure side is wetted and gripped the water to generate thrust. The Reynolds-Averaged Navier-Stokes (RANS) method is used in order to predict the hydrodynamic flow from entering to the exit. Present paper is numerically investigated the effect of free surface and surface tension i.e. related to the Weber number. So, many numerical results are presented and discussed that are included volume fraction, ventilation zones, pressure distributions, vertical and horizontal forces at various Weber numbers.