The instability of liquid films with temperature-dependent properties flowing down a heated incline
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 stabil...
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| Published in | AIMS mathematics Vol. 4; no. 6; pp. 1700 - 1720 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
AIMS Press
01.01.2019
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| Subjects | |
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| Abstract | 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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| AbstractList | 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. |
| Author | D’Alessio, Serge Pascal, Jean-Paul Rubaida Zafar, Syeda |
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| CitedBy_id | crossref_primary_10_1016_j_ijheatmasstransfer_2020_119700 crossref_primary_10_1016_j_physd_2022_133404 crossref_primary_10_1088_1742_6596_2090_1_012114 |
| Cites_doi | 10.1016/0094-4548(75)90002-8 10.1016/j.ijengsci.2013.05.003 10.1017/S0022112003005809 10.1017/S0022112057000373 10.1063/1.1706737 |
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| References | 1 23 2 14 T. B. Benjamin (3) C.-S. Yih (4) J. P. Pascal, N. Gonputh and S. J. D. D'Alessio (17) S. Lin (12) S. Kalliadasis, E. A. Demekhin, C. Ruyer-Quil (8) |
| References_xml | – ident: 12 article-title: i>Stability of a liquid flow down a heated inclined plan publication-title: Lett. Heat Mass Transfer doi: 10.1016/0094-4548(75)90002-8 – ident: 17 article-title: i>Long-wave instability of flow with temperature</i> dependent fluid properties down a heated inclin publication-title: Intl J. Eng. Sci. doi: 10.1016/j.ijengsci.2013.05.003 – ident: 8 article-title: t al. Thermocapillary instability and wave formation on a film flowing down a uniformly heated plan publication-title: </i> J. Fluid Mech. doi: 10.1017/S0022112003005809 – ident: 1 article-title: P. L. Kapitza, Wave flow of thin layers of a viscous – ident: 14 article-title: D. A. Goussis and R. A. Kelly, Effects of viscosity on the stability of film flow down heated or cooled inclined – ident: 2 article-title: P. L. Kapitza and S. P. Kapitza, Wave flow of thin layers of a viscous – ident: 3 article-title: i>Wave formation in laminar flow down an inclined plan publication-title: J. Fluid Mech. doi: 10.1017/S0022112057000373 – ident: 4 article-title: i>Stability of liquid flow down an inclined plan publication-title: Phys. Fluids doi: 10.1063/1.1706737 – ident: 23 article-title: N. Gonputh, J. P. Pascal and S. J. D. D'Alessio, Inclined flow of a heated fluid film with temperature dependent fluid properties, |
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| SubjectTerms | colloacation method inclined flow linear stability analysis thermocapillary marangoni effect variable fluid properties |
| Title | The instability of liquid films with temperature-dependent properties flowing down a heated incline |
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