Pseudo-Similarity and Boundary Layer Thickness for Non-Newtonian Falling Film Flow
The pseudo-similarity solutions of the thermal boundary layer of a falling film flow of power-law fluids are presented. Based on a proposed “local Prandtl number”, the dependence of the thickness of the momentum boundary layer and thermal boundary layer on the power-law index and local Prandtl number are discussed. Their variations with power-law index and local Prandtl number are also presented. The momentum layer thickness depends only on the power-law index, while the thermal boundary layer thickness depends both on the power-law index and the local Prandtl number. The momentum boundary layer thickness decreases significantly with the increase of the power-law index. While the thermal boundary layer thickness decreases slightly with increasing the power-law index and decreases with increasing the parameter local Prandtl number. With the introduction of the “local Prandtl number”, it is found that the heat transfer problem turned out to involve only two independent parameters, the power-law index and the local Prandtl number. The pseudo-similarity solution and the assumed true-similarity solution are presented for the investigation of non-similarity thermal boundary layer. The degree of non-similarity of thermal boundary layer has been determined for various values of power-law indices and local Prandtl numbers.
KeywordsBoundary Layer Boundary Layer Thickness Thermal Boundary Layer Boundary Layer Equation Film Flow
- 4.I. Pop, T. Watanabe, H. Konishi, Gravity-driven laminar film flow along a vertical wall with surface mass transfer. Int. Commun. Heat Mass Transf. 23(5), 685–695 (1996)Google Scholar
- 12.H.I. Andersson, F. Irgens, Film flow of power law fluids, in Encyclopaedia of Fluid Mechanics, vol. 9, ed. by N.P. Cheremisinoff, (Gulf Publishing Company, Houston, 1990), pp. 617–648Google Scholar