Gravity-driven laminar film flow of power-law fluids along vertical walls |
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| Affiliation: | 1. Department of Theoretical Mechanics, Faculty of Mechanics and Mathematics, Tomsk State University, 634050 Tomsk, Russia;2. Institute of Power Engineering, Tomsk Polytechnic University, 634050 Tomsk, Russia;3. Department of Applied Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania;1. Department of Fluid Machinery and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, No. 28 West Xianning Rood, Xi’an 710049, Shaanxi, PR China;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK;1. Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy;2. Dipartimento di Ingegneria Industriale e dell''Informazione, Seconda Università degli Studi di Napoli, via Roma, 29, 81031 Aversa CE, Italy;1. Department of Mining Machinery Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India;2. Department of Automobile Engineering, PSG College of Technology, Coimbatore, 641 004, India;3. Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India;1. B. Verkin Institute for Low Temperature Physics & Engineering NASU, Kharkiv 61103, Ukraine;2. Lehrstuhl für Physikalische Chemie II TUM, Garching b., Munich 85747, Germany |
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| Abstract: | A theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory. The upper part of the film, which consists of a developing viscous boundary layer and an external inviscid freestream, is treated separately from the viscous dominated part of the flow, thereby taking advantage of the distinguishing features of each flow region. It is demonstrated that the film boundary layer developing along a vertical wall can be described by a generalized Falkner-Skan type equation originally developed for wedge flow. An exact similarity solution for the velocity field in the film boundary layer is thus made available.Downstream of the boundary layer flow regime the fluid flow is completely dominated by the action of viscous shear, and fairly accurate solutions are obtained by the Von Karman integral method approach. A new form of the velocity profile is assumed, which reduces to the exact analytic solution for the fully-developed film. By matching the downstream integral method solution to the upstream generalized Falkner-Skan similarity solution, accurate estimates for the hydrodynamic entrance length are obtained. It is also shown that the flow development in the upstream region predicted by the approximate integral method closely corresponds to the exact similarity solution for that flow regime. An analytical solution of the resulting integral equation for the Newtonian case is compared with previously published results. |
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