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

Abstract EN

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.