Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film

Yu O. Kabova, V. V. Kuznetsov, O. A. Kabov

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14 Citations (Scopus)


Theoretical and numerical investigations of the heat transfer and hydrodynamics in a liquid film flowing along an inclined substrate under the action of gravity with a local heat source have been performed. A two-dimensional model, based on the thin layer approximation, has been developed describing deformations of the film interface. Equation of a non-isothermal thin-film flow with linear dependence of viscosity and surface tension on temperature is derived. A generalized analytical formula for the film thickness as a function of liquid flow-rate is obtained. Marangoni flow, due to local temperature changes, opposes the gravitationally driven film flow and forms a horizontal bump near the upper edge of the heater. Attention is paid to the viscosity effect on the shape of the bump and the film thinning on the local heaters. A second order deformation of the free surface before the bump up to flow may exist. The criterion for the appearance of this deformation is found analytically.

Original languageEnglish
Pages (from-to)1271-1278
Number of pages8
JournalInternational Journal of Heat and Mass Transfer
Issue number4
Publication statusPublished - 31 Jan 2012



  • Falling liquid film
  • Local heaters
  • Thermocapillarity
  • Variable viscosity

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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