Free-surface dynamics of thin second-grade fluid over an unsteady stretching sheet

Satyananda Panda, Kiran Kumar Patra, Mathieu Sellier

Abstract


We derive an evolution equation for the free-surface dynamics of a thin film of a
second-grade fluid over an unsteady stretching sheet using long-wave theory. For the
numerical investigation of the viscoelastic effect on the thin-film dynamics, a finite-volume
approach on a uniform grid with implicit flux discretization is applied. The
present results are in excellent agreement with results available in the literature for a
Newtonian fluid. We observe that the fluid thins faster with the rapid stretching rate of
the sheet, but the second-grade parameter delays the thinning behaviour of the liquid
film.

doi:10.1017/S1446181118000251

Keywords


thin liquid film, stretching sheet, second-grade fluid, free-surface flow, long-wave theory, finite-volume method.



DOI: http://dx.doi.org/10.21914/anziamj.v60i0.12091



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.