Shear-driven flows of locally heated liquid films

Elizaveta Ya Gatapova, Oleg A. Kabov

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater's upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of "ripples" on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas-liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid-gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.

Original languageEnglish
Pages (from-to)4797-4810
Number of pages14
JournalInternational Journal of Heat and Mass Transfer
Issue number19-20
Publication statusPublished - 1 Sep 2008


  • Evaporation
  • Gas flow
  • Liquid film
  • Marangoni force
  • Micro/minichannels
  • Non-uniform heating

ASJC Scopus subject areas

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

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