Effects of variable fluid properties on unsteady thin-film flow over a non-linear stretching sheet

摘要

The effects of the variation of viscosity and surface tension with temperature on unsteady flow of a thin viscous liquid film over a heated horizontal stretching surface are analyzed considering general form of the stretching velocity and the temperature distribution. Using perturbation technique, an evolution equation is derived from the governing equations and this evolution equation (non-linear PDE) is solved numerically by using a combination of modified Euler method, the Newton-Kantorovich method, and the finite difference method. This leads to a five-parameter problem for some representative value of the parameters. It is shown that the film thickness decreases with the decrease of viscosity of the fluid as temperature increases and more or less heat flows out of the liquid through the stretching surface. Film thins faster both for thermo-capillary force and decrease of viscous force provided temperature decreases along the stretching direction. Physical explanations are furnished where it is necessary to justify the results.