Liquid film flow over an unsteady moving surface with a new stretching velocity

Abstract

In this paper, the liquid film flow over an unsteady moving surface is investigated by considering a new surface moving velocity Uw = Ax/t. With this prescribed surface velocity, the governing Navier-Stokes (NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically for both two-dimensional and axisymmetric flow configurations. The results are an exact solution to the full NS equations. The flow characteristics are controlled by a wall moving parameter, namely, A. It is found that solutions only exist for a certain range of the wall moving parameter, i.e., A ≥ −1/2 for the two dimensional case and A ≥ −1/4 for the axisymmetric case. The dimensionless liquid film thickness (β) first increases with the increase in A in the solution domain, and then, it reaches a peak of βm = 1.3864 at A = 0.90 for the two-dimensional case and βm = 1.5836 at A = 0.53 for the axisymmetric case. For both flow configurations, the liquid film thickness increases with time and there exists flow reversal for a positive value of A. These new solutions can not only provide an exact solution to the NS equations but also be used to explain the liquid film flow occurring in practical applications.