@Article{IJNAMB-3-285,
author = {MATHIEU SELLIER AND SATYANANDA PANDA},
title = {Inverse Temperature Reconstruction in Thermocapillary-Driven Thin Liquid Films},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2012},
volume = {3},
number = {3},
pages = {285--296},
abstract = {A thin liquid film subject to a temperature gradient undergoes thermocapillary convection because of the non-uniform surface tension at the free surface. This induced flow perturbs the
film free surface and generate a free surface velocity field. These observable consequences can be
thought of as the &#147signature&#148 of the imposed temperature field and this work investigates whether
the temperature field can be reconstructed from this signature for general three-dimensional flows.
Using a model based on the lubrication approximation, we show that one can explicitly formulate
the partial differential equation which governs this inverse problem. This equation is solved using
finite differences. We illustrates the feasibility of this reconstruction exercise on a set of &#147artificial&#148
experimental data obtained by first solving the direct problem which consists in computing the
free surface deformation and free surface velocity field for a given applied temperature field.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/284.html}
}