Table of Contents
Chinese Journal of Engineering
Volume 2013, Article ID 751909, 21 pages
http://dx.doi.org/10.1155/2013/751909
Research Article

Influence of Temperature Gradient on the Stability of a Viscoelastic Film with Gradually Fading Memory over a Topography with Ridges and Furrows

Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany

Received 28 June 2013; Accepted 22 August 2013

Academic Editors: K. Ariyur, B.-Y. Cao, and B. Sun

Copyright © 2013 Mohammed Rizwan Sadiq Iqbal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A long-wave evolution equation is derived using an asymptotic analysis, and the linear stability of a viscoelastic film flowing along the direction of parallel grooves over a uniformly heated topography is studied. A numerical approach adopting spectral collocation technique is used to demarcate the stable and unstable flow regimes. The combined influence of thermocapillarity and viscoelasticity on the films stability is analyzed. By accounting the bottom topography comprising longitudinal gutters, the possibilities of regulating the film dynamics under iso- and nonisothermal conditions and/or optimizing design structure of an apparatus for desirable flow outcomes have been focussed.