Abstract
To answer the questions on the behavior of liquid flows under complicatedly combined actions of stresses, evaporation and temperature-dependent surface tension effects, thin liquid layers flowing under gravity down an inclined plane uniformly heated from below are considered There may be two thermal boundary conditions on the hot plate, i e , either constant heat flux or fixed temperature By using long-wave approximation, the nonlinear evolution equations governing the two-dimensional surface waves have been derived upto O(ε2) and O(ε) for the constant heat flux and the fixed temperature case, respectively Here the small parameter ε(l) is the ratio of the characteristic length scale parallel to the flow to the initial basic film thickness The linear and the nonlinear stability analyses are also performed by using numerical calculations Consequently, the flow subjected to the constant heat flux can be marked as a more stable system than the flow mechanism at a fixed-tem-perature boundary condition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benjamin, T. B., “Wave Formation in Laminar Flow Down an Inclined Plane,”J. Fluid Mech.,2,554 (1957).
Benny, D. J., “Long Waves on Liquid Films,”J. Math. Phys.,45, 150 (1966).
Burelbach, J. P., Bankoff, S. G. and Davis, S. H., “Nonlinear Stability of Evaporating/Condensing Liquid Films,”J. Fluid Mech.,195,463(1988).
Chang, H.-C, “Onset of Nonlinear Waves on Falling Films,”Phys. Fluids A,1(8), 1314(1989).
Delhaye, J. M., “Jump Conditions and Entropy Sources in Two Phase Systems: Local Instant Formulation,”Int. J. Multiphase Flow,1,395 (1974).
Gjevik, B., “Occurrence of Finite-Amplitude Surface Waves on Falling Liquid Films,”Phys. Fluids,13,1918 (1970).
Joo, S. W, Davis, S. H. and Bankoff, S. G., “Long-wave Instabilities of Heated Falling Films: Two-dimensional Theory of Uniform Layers,”J. FluidMech.,230,117 (1991).
Kim, H., Bankoff, S. G. and Miksis, M. J., “Electrostatic Field Effects on a Rotating Liquid Film Conical Radiator,”AIAA J. Propulsion and Power,9, 245 (1993).
Kim, H., Bankoff, S. G. and Miksis, M. J., “The Cylindrical Electrostatic Liquid Film Radiator for Heat Rejection in Space,”J. Heat Transfer,116,986 (1994).
Kim, H., Bankoff, S. G. and Miksis, M. J., “The Effect of an Electrostatic Field on Film Flow Down an Inclined Plane,”Phys. Fluids A,4,2117 (1992).
Kim, H., “Long-Wave Instabilities of Film Row under an Electrostatic Field: Two-Dimensional Disturbance Theory,”Korean J. Chem. Eng.,14,41 (1997).
Lin, S.-P., “Finite Amplitude Side-Band Stability of a Viscous Film,”J. FluidMech.,63,417 (1974).
Palmer, H. J., “The Hydrodynamic Stability of Rapidly Evaporating Liquids at Reduced Pressure,”J. Fluid Mech.,75, 487 (1976).
Yih, C.-S., “Stability of Liquid Flow Down an Inclined Plane,”Phys. Fluids,5, 321 (1963).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, H. Stability analysis of heated thin liquid-film flows with constant thermal boundary conditions. Korean J. Chem. Eng. 16, 764–773 (1999). https://doi.org/10.1007/BF02698349
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02698349