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Research Papers: Evaporation, Boiling, and Condensation

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

[+] Author and Article Information
M. Q. Brewster

Department of Mechanical
Science and Engineering,
University of Illinois,
Urbana, IL 61801
e-mail: brewster@illinois.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 23, 2016; final manuscript received February 17, 2017; published online April 11, 2017. Assoc. Editor: Amitabh Narain.

J. Heat Transfer 139(8), 081501 (Apr 11, 2017) (13 pages) Paper No: HT-16-1535; doi: 10.1115/1.4036075 History: Received August 23, 2016; Revised February 17, 2017

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.

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References

Spalding, D. B. , 1960, “ A Standard Formulation of the Steady Convective Mass Transfer Problem,” Int. J. Heat Mass Transfer, 1(2–3), pp. 192–207. [CrossRef]
Kays, W. M. , Crawford, M. E. , and Weigand, B. , 2013, Convective Heat and Mass Transfer, 4th ed., McGraw-Hill, New York.
Mills, A. F. , 2001, Mass Transfer, Prentice-Hall, Upper Saddle River, NJ.
Lienhard, J. H., IV , and Lienhard, J. H., V , 2015, A Heat Transfer Textbook, 4th ed., Phlogiston Press, Cambridge, UK.
Eckert, E. R. G. , and Drake, R. M., Jr. , 1959, Heat and Mass Transfer, McGraw-Hill, New York.
Wang, K. T. , and Brewster, M. Q. , 2010, “ Phase-Transition Radiation in Vapor Condensation Process,” Int. Commun. Heat Mass Transfer, 37(8), pp. 945–949. [CrossRef]
Moran, M. J. , Shapiro, H. N. , Boettner, D. D. , and Bailey, M. B. , 2014, Fundamentals of Engineering Thermodynamics, 8th ed., Wiley, New York.
Brewster, M. Q. , 2015, “ Evaporation and Condensation of Water Mist/Cloud Droplets With Thermal Radiation,” Int. J. Heat Mass Transfer, 88, pp. 695–712. [CrossRef]
Bird, R. B. , Stewart, W. E. , and Lightfoot, E. N. , 1960, Transport Phenomena, Wiley, New York.
Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2011, Fundamentals of Heat and Mass Transfer, 7th ed., Wiley, New York.

Figures

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Fig. 1

Thermodynamic state definitions and mass fluxes at water vapor–liquid interface

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Fig. 2

Energy fluxes at water vapor–liquid interface with grouping by flux type

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Fig. 3

Energy fluxes at water vapor–liquid interface with grouping by species type

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Fig. 4

Schematic diagram of Ex1: cloud droplet with radiation; detail for individual droplet residing near top of cloud shown above cloud

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Fig. 5

Schematic diagram of Ex2: sweat cooling of radiatively and convectively heated flat plate with laminar boundary layer

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Fig. 6

Schematic diagram of Ex3: wet-bulb psychrometer with and without radiation

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Fig. 7

Schematic diagram of Ex4: effect of air leak on condenser performance

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Fig. 8

Schematic diagram of Ex4: detail of tube wall

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