AN EXTENDED STUDY OF THE HYDRODYNAMICS OF GRAVITY-DRIVEN FILM FLOW OFPOWER-LAW FLUIDS

A new similarity transformation has been devised for extensive studies of accelerating non-Newtonian film flow. The partial differential equ ations governing the hydrodynamics of the How of a power-law fluid dow n along an inclined plane surface are transformed into a set of two or dinary differential equations by means of the dimensionless velocity c omponent approach. Although the analysis is applicable for any angle o f inclination alpha (0 less than or equal to alpha pi/2), the resultin g one-parameter problem involves only the power-law index n. Neverthel ess, physically essential quantities, like the velocity components and the skin-friction coefficient, do depend on a and relevant relationsh ips are deduced between the vertical and inclined cases. Accurate nume rical similarity solutions are provided for ii in the range from 0.1 t o 2.0. The present method enables solutions to be obtained also for hi ghly pseudo-plastic films, i.e. for it below 0.5. The mass flow rate e ntrained into the momentum boundary layer from the inviscid freestream is expressed in terms of a dimensionless mass flux parameter phi, whi ch depends on the dimensionless boundary layer thickness and the veloc ity components at the edge of the viscous boundary layer. phi, which i s thus an integral part of the similarity solution, turns out to decre ase monotonically with M. This parameter is of particular relevance in the determination of the streamwise position at which the entire free stream has been entrained and viscous stresses prevail all the way to the free surface of the film. A short-cut method to facilitate rapid a nd yet accurate estimates of the mass flux parameter is developed to t his end. (C) 1998 The Japan Society of Fluid Mechanics Incorporated an d Elsevier Science B.V. All rights reserved.