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Heated falling films

Published online by Cambridge University Press:  14 November 2007

P. M. J. TREVELYAN ,
B. SCHEID ,
C. RUYER-QUIL  and
S. KALLIADASIS
P. M. J. TREVELYAN*
Affiliation:
Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK
B. SCHEID*
Affiliation:
Service de Chimie-Physique E.P., Université Libre de Bruxelles, C.P. 165/62, 1050 Brussels, Belgium
C. RUYER-QUIL
Affiliation:
Laboratoire FAST, UMR 7608, CNRS, Universités P. et M. Curie et Paris Sud, Bât. 502, Campus Universitaire, 91405 Orsay Cedex, France, ptrevely@ulb.ac.be; bscheid@ulb.ac.be, ruyer@fast.u-psud.fr; s.kalliadasis@imperial.ac.uk
S. KALLIADASIS
Affiliation:
Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK
*
†Present address: Centre for Nonlinear Phenomena and Complex Systems, CP 231, Université Libre de Bruxelles, 1050 Brussels, Belgium.
‡Present address: Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
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Abstract

We present new insights and results for the problem of a film falling down a heated wall: (i) treatment of a mixed heat flux boundary condition on the substrate; (ii) development of a long-wave theory for large Péclet numbers; (iii) refined treatment of the energy equation based on a high-order Galerkin projection in terms of polynomial test functions which satisfy all boundary conditions; (iv) time-dependent computations for the free-surface height and interfacial temperature; (v) numerical solution of the full energy equation; (vi) demonstration of the existence of a thermal boundary layer at the front stagnation point of a solitary pulse; (vii) development of models that prevent negative temperatures and are in good agreement with the numerical solution of the full energy equation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 295 - 334
Copyright
Copyright © Cambridge University Press 2007

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References

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