Analyses of pseudo-similarity and boundary layer thickness for non-Newtonian falling film flow

Abstract

One aim of this paper is to provide an extensive study on pseudo-similarity solutions of thermal boundary layer in falling film flow with non-Newtonian power-law fluids. The related mathematical models and solution approach are systematically presented. Another aim of this work is to further investigate the momentum boundary layer and the thermal boundary layer. Based on a newly defined “local Prandtl number”, the dependence of the thickness of the momentum boundary layer and thermal boundary layer on the power-law index is discussed. It is found that the momentum boundary layer thickness decreases monotonically with power-law index; while the thermal boundary layer thickness decreases slightly with power-law index and increases significantly with the decrease of the “local Prandtl number”. This study shows that the adopted pseudo-similarity approach is capable of solving the problem of non-similarity thermal boundary layer in the falling film of a non-Newtonian power-law fluid.