Gravity-driven film flow with variable physical properties

Abstract

The laminar flow and heat transfer in an accelerating thin liquid film are considered with the view to examine the influence of variable density and transport properties. A new similarity transformation is proposed which exactly transforms the hydrodynamic and thermal boundary layer equations for vertically falling film flow into a coupled set of ordinary differential equations. The resulting two-point boundary value problem is integrated numerically with empirical data for the physical properties of water. For given inflow conditions, the temperature-dependency of the dynamic fluid viscosity makes both the hydrodynamic and thermal boundary layers thinner with increasing wall temperature. The expected thickening of the thermal boundary layer due to the increasing thermal diffusivity is therefore more than outweighed by the decreasing viscosity. The nonlinear variation of the physical properties makes these effects more pronounced at the lower inflow temperature.