Thin film development on a double layer of fluids over a stretching sheet

Abstract

Abstract The thin film development on a double layer of fluids in which the first layer is Newtonian and the second layer is of second-grade fluid on a stretching sheet is analyzed in this paper. The governing equations describing the flow are solved using the Long-wave perturbation method. The coupled partial differential equations thus obtained are solved numerically by the finite volume approach where the spatial derivatives are approximated using the upwind difference scheme and the time derivatives are by forward difference. The study focuses on analyzing the impact of surface tension parameters, viscosity ratio parameters, and Reynolds numbers on the flow dynamics. From the analysis, it is observed that the film height decreases for higher surface tension parameters and Reynolds numbers of both fluid layers and the viscosity ratio parameter $m>1$.