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The instability of liquid films with temperature-dependent properties flowing down a heated incline

1 Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada
2 Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Special Issues: Applied and Industrial Mathematics in Canada and Worldwide

We investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral collocation method. Comparisons with nonlinear simulations are also made and the agreement is good.
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Keywords inclined flow; thermocapillary Marangoni effect; variable fluid properties; linear stability analysis; colloacation method

Citation: Jean-Paul Pascal, Serge D’Alessio, Syeda Rubaida Zafar. The instability of liquid films with temperature-dependent properties flowing down a heated incline. AIMS Mathematics, 2019, 4(6): 1700-1720. doi: 10.3934/math.2019.6.1700


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This article has been cited by

  • 1. Nicolas Cellier, Christian Ruyer-Quil, A new family of reduced models for non-isothermal falling films, International Journal of Heat and Mass Transfer, 2020, 154, 119700, 10.1016/j.ijheatmasstransfer.2020.119700

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