Two layer film flow on an unsteady stretching cylinder

Abstract

Most of the earlier research works related to the thin film flow over a stretching cylinder are primarily limited to the boundary layer flow of a single liquid. Whereas, multilayer film coating is commonly used to coat microelectronic chips, circuits, etc. This scenario motivated us to investigate the thin double-layer liquid film development over a stretching cylinder. In the present work, the above limitations of earlier models have been removed to investigate the two-layer film flow over a stretching cylinder by considering a full set of momentum equations. The governing set of equations is transformed into a system of nonlinear partial differential equations (PDEs) by applying appropriate similarity transformation. The analytical solutions are obtained by using the asymptotic analysis method for smaller values of Reynolds number (i.e. Re1<<1). Whereas numerical solutions are obtained by implicit finite difference method for smaller as well as moderate values of Re1. It is found that the film thinning rate enhanced for both the liquid layers with raising values of the cylinder’s radius (A) and density ratio (m). It is further seen that both the liquid layers thin faster with a decreasing initial thickness ratio of both liquid layers (δ). It is also observed that the variation of film height for the first layer is very small in comparison to the second layer for increasing values of viscosity ratio parameter (n). The film height for both the liquid layers decreases very fast for a smaller Reynolds number (Re1) at the initial time but a reverse trend is noticed at large time.