New asymptotic heat transfer model in thin liquid films

Abstract

In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.

Keywords

Bibliographic record

BibTeX Citation

@article{Chhay2017asymptoticheat,
  author = {Chhay, M. and Dutykh, D. and Gisclon, M. and Ruyer-Quil, Ch.},
  title = {New asymptotic heat transfer model in thin liquid films},
  journal = {Appl. Math. Model.},
  year = {2017},
  volume = {48},
  pages = {844--859},
  doi = {10.1016/j.apm.2017.02.022},
  abstract = {In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.},
  keywords = {asymptotic modelling, thin liquid film, Heat transfer, long waves, Thermal dependency properties, Marangoni effect}
}