Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.
Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Mar. 3, 2002; final revision, Apr. 23, 2003. Associate Editor: D. A. Siginer. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Usha , R., and Uma, B. (January 5, 2004). "Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane ." ASME. J. Appl. Mech. November 2003; 70(6): 915–923. https://doi.org/10.1115/1.1631592
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