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FREE-SURFACE DYNAMICS OF THIN SECOND-GRADE FLUID OVER AN UNSTEADY STRETCHING SHEET

Part of: Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  05 November 2018

S. PANDA Open the ORCID record for S. PANDA [Opens in a new window] ,
K. K. PATRA Open the ORCID record for K. K. PATRA [Opens in a new window]  and
M. SELLIER Open the ORCID record for M. SELLIER [Opens in a new window]
S. PANDA*
Affiliation:
Department of Mathematics, National Institute of Technology Calicut, NIT (P.O.)-673601, Kerala, India email satyanand@nitc.ac.in, kirankumar_p140033ma@nitc.ac.in
K. K. PATRA
Affiliation:
Department of Mathematics, National Institute of Technology Calicut, NIT (P.O.)-673601, Kerala, India email satyanand@nitc.ac.in, kirankumar_p140033ma@nitc.ac.in
M. SELLIER
Affiliation:
Department of Mechanical Engineering, The University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand email mathieu.sellier@canterbury.ac.nz
*
✉satyanand@nitc.ac.in
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Abstract

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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.

Keywords

thin liquid filmstretching sheetsecond-grade fluidfree-surface flowlong-wave theoryfinite-volume method

MSC classification

Primary: 76A20: Thin fluid films
Secondary: 76A05: Non-Newtonian fluids
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 2 , October 2018 , pp. 249 - 268
Copyright
© 2018 Australian Mathematical Society 

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