Table of Contents
International Journal of Engineering Mathematics
Volume 2014, Article ID 485431, 12 pages
http://dx.doi.org/10.1155/2014/485431
Research Article

Process Parameter Identification in Thin Film Flows Driven by a Stretching Surface

1Department of Mathematics, National Institute of Technology Calicut, Kerala 673601, India
2Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
3Department of Mathematics, University of Ruhuna, 81000 Matara, Sri Lanka

Received 25 January 2014; Revised 10 June 2014; Accepted 12 June 2014; Published 21 July 2014

Academic Editor: Francisco Chinesta

Copyright © 2014 Satyananda Panda et al. 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

The flow of a thin liquid film over a heated stretching surface is considered in this study. Due to a potential nonuniform temperature distribution on the stretching sheet, a temperature gradient occurs in the fluid which produces surface tension gradient at the free surface of the thin film. As a result, the free surface deforms and these deformations are advected by the flow in the stretching direction. This work focuses on the inverse problem of reconstructing the sheet temperature distribution and the sheet stretch rate from observed free surface variations. This work builds on the analysis of Santra and Dandapat (2009) who, based on the long-wave expansion of the Navier-Stokes equations, formulate a partial differential equation which describes the evolution of the thickness of a film over a nonisothermal stretched surface. In this work, we show that after algebraic manipulation of a discrete form of the governing equations, it is possible to reconstruct either the unknown temperature field on the sheet and hence the resulting heat transfer or the stretching rate of the underlying surface. We illustrate the proposed methodology and test its applicability on a range of test problems.