Water Evaporation and Condensation in Air with Radiation: The Self-Similar Spalding Model

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Several simple ways of improving the accuracy of Spalding model predictions over common textbook conventions for air/water evaporation/condensation problems are illustrated using open-literature examples. First is the choice of thermodynamic reference state for enthalpy evaluation. The common practice of choosing the steam table reference point (0.01 °C) with water-vapor enthalpy of hfg (2501 kJ/kg) and air enthalpy of zero introduces an enthalpy mismatch between air and water vapor that unnecessarily compromises accuracy. Choosing the air/water interface temperature as the reference point and setting both air and water-vapor enthalpies at this point to the same numerical value gives the most accurate results of several methods tried. Second is judicious choice of the blowing factor in high-rate mass transfer situations. The laminar boundary layer blowing factor is more accurate than the common stagnant-film (Couette flow) blowing factor for flat-plate flow and may be more accurate for a cylinder in crossflow under laminar conditions, as illustrated by the example of air leak effect on steam condenser tube performance. Third is radiation modeling, often a problematic or ignored feature in this type of problem. Two common, but opposite, assumptions about radiation participation in water - transparent interface and opaque interface - are shown to be equivalent for most purposes. A methodology is introduced for modeling true interfacial absorption/emission associated with phase change if/when the amount of this effect becomes known well enough to justify its inclusion. The importance of including radiation is illustrated by several examples: cloud droplet evaporation-condensation, sweat cooling, and the wet-bulb psychrometer. Fourth is inaccuracy introduced by unnecessarily setting Lewis number to unity.

Original languageEnglish (US)
Article number081501
JournalJournal of Heat Transfer
Issue number8
StatePublished - Aug 1 2017


  • Spalding formulation
  • air-water
  • condensation
  • evaporation
  • radiation

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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