Travelling-Wave Similarity Solutions For Unsteady Thin-Film Flows
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Date
2016-12
Authors
Abas, Siti Sabariah
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The study of the thin-film flows have developed rapidly in the recent years for various
applications, for example, lava flow, in coating process and in electronic devices.
This thesis aims to study the travelling-wave similarity solution for unsteady threedimensional
flows of thin films of Newtonian and non-Newtonian power-law fluids
on an inclined plane. Specifically, flow around slender dry patch and flow of slender
rivulet are considered. The flow is driven by gravity or shear stress at the free surface in
the case of weak and strong surface-tension effects. The lubrication approximation is
applied to the Navier-Stokes equations and continuity equation subject to the boundary
conditions of no slip and no penetration, the balances of normal and tangential stress
together with the kinematic condition to yield a governing partial differential equation.
A similarity transformation, namely a travelling-wave similarity solution is used to
reduce the governing partial differential equation into the ordinary differential equation.
The differential equation is then solved numerically using a shooting method via
Mathematica 9:0 software. This study has provided the significant contribution in the
investigation of the unsteady thin-film flow of Newtonian and non-Newtonian powerlaw
fluids, particularly for the flow around the slender dry patch and the flow of slender
rivulet on an inclined plane.
Description
Keywords
Travelling-wave similarity solutions , unsteady thin-film flows