New asymptotic heat transfer model in thin liquid films

Marx Chhay, Denys Dutykh, Marguerite Gisclon, Christian Ruyer-Quil

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In this article, we present a model of heat transfer occurring through a liquid 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 is obtained, 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.

Original languageBritish English
Pages (from-to)844-859
Number of pages16
JournalApplied Mathematical Modelling
StatePublished - Aug 2017


  • Asymptotic modeling
  • Heat transfer
  • Long waves
  • Marangoni effect
  • Thermal dependency properties
  • Thin liquid film


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