Experimental comparison of the ability of Dalton based and similarity theory correlations to predict water evaporation rate in different convection regimes


This paper investigates the ability of two widely used evaporation models: Dalton based correlations and similarity theory results by comparing with experimental measurements. A series of experimental investigations are carried out over a wide range of water temperatures and air velocities for 0.01 ≤ Gr/Re 2 ≤ 100 in a rectangular heated pool. The results show that for forced convection regime satisfactory results can be achieved by using the modified Dalton correlations, while, due to ripples appear on the water free surface, similarity theory under predicts the evaporation rate. In the free convection regime, Dalton based correlations even with modification are not able to predict acceptable results. For mixed convection regime, although both the similarity theory and Dalton based correlations without modification are not able to predict the mild non-linearity behavior between water evaporation rate and vapor pressure difference, but they obtain relatively satisfactory results. A dimensionless correlation using the experimental data of all convection regimes is proposed to cover different water surface geometries and air flow conditions.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


\( D_{{H_{2} o,Air}} \) :

Binary mass diffusion coefficient m2/s

D h :

Hydraulic diameter of rectangular duct (m)

g :

Gravitational acceleration m/s2

\( g_{{m,H_{2} o}} \) :

Mass transfer coefficient

Gr :

Mass transfer Grashof number

H :

Height of rectangular duct (m)

h fg :

Enthalpy of vaporization (J/kg)

k :

Thermal conductivity w/mk

L :

Length of water pan (m)

\( \dot{m}_{e} \) :

Evaporation rate of water kg/m2h

\( m_{{f\,H_{2} o}} \) :

The mass fractions of water

Nu :

Nusselt number

P :

Pressure (Pa)

Pr :

Prandtl number

P v,s :

Saturated vapor pressure at the water surface

P v, :

Saturated vapor pressure at the ambient air

R 2 :

Correlation coefficient

Re :

Reynolds number

Sc :

Schmidt number

Sh :

Sherwood number

T :

Temperature (K)

T s :

Free surface temperature (K)

t :

Time (h)

V :

Velocity of air

W :

Width of the test chamber

\( X_{{H_{2} o}} \) :

Vapor mole fraction


Density kg/m3


Dynamic viscosity NS/m2

\( \bar{\rho } \) :

Mean mixture density of air


Relative humidity

g :

Moist air property including dry air and water vapor

s :

Properties at the surface of the water

free :

Free convection flow regime

forced :

Forced convection flow regime

mixed :

Mixed convection flow regime


Average properties at the ambient air

total :

Sum of free and forced convection component


  1. 1.

    Steeman J, Joen C, Belleghem MV, Janssens A, Paepe MD (2009) Evaluation of the different definitions of the convective mass transfer coefficient for water evaporation into air. Int J Heat Mass Transf 52:3757–3766

    Article  Google Scholar 

  2. 2.

    Paukan MT (1999) An experimental investigation of combined turbulent free and forced evaporation. Exp Thermal Fluid Sci 18:334–340

    Article  Google Scholar 

  3. 3.

    Sartori EA (2000) Critical review on equations employed for the calculation of the evaporation rate from free water surfaces. Sol Energy 68:77–89

    Article  Google Scholar 

  4. 4.

    Asdrubali F (2008) A scale model to evaluate water evaporation from indoor swimming pools. Energy Build 41:311–319. doi:10.1016/j.enbuild.2008.10.001

    Google Scholar 

  5. 5.

    Tang R, Etzion Y (2004) Comparative studies on the water evaporation rate from a free water surface and that from a free surface. Build Environ 39:77–86

    Article  Google Scholar 

  6. 6.

    Moghiman M, Jodat A (2007) Effect of air velocity on water evaporation rate in indoor swimming pools. ISME 8:19–30

    Google Scholar 

  7. 7.

    Dalton J (1802) Experimental essays on the constitution mixed gases; on the force of steam or vapor from water and other liquids in different temperatures, both in a Torricellian vacuum and in air; on evaporation and on the expansion of gases by heat. Mem Manch Lit Philos Soc 5–11:535–602

    Google Scholar 

  8. 8.

    Lienhard JH, Lienhard VJH (2005) A heat transfer text book. Phlogiston Press, New York

    Google Scholar 

  9. 9.

    Ashrae (1999) Ashrae handbook HVAC application. American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc., Atlanta

  10. 10.

    Rowher C (1931) Evaporation from free water surface. US Department of Agriculture in cooperation with Colorado Agricultural Experiment Station. Tech Bull 271:96–101

  11. 11.

    Carrier WH (1918) The temperature of evaporation. ASHVE Trans 24:25–50

    Google Scholar 

  12. 12.

    Boetler LMK, Gordon HS, Griffin JR (1946) Free evaporation into air of water from a free horizontal quiet surface. Ind Eng Chem 38(6):596–600

    Article  Google Scholar 

  13. 13.

    Marek R, Straub J (2001) Analysis of the evaporation coefficient and the condensation coefficient of water. Int J Heat Mass Transf 44:39–53

    MATH  Article  Google Scholar 

  14. 14.

    Moghiman M, Jodat A, Javadi M (2007) Experimental investigation of water evaporation in indoor swimming pools. Int J Heat Mass Tech 25(2):43–47

    Google Scholar 

  15. 15.

    Al-Shamimiri M (2002) Evaporation rate as a function of water salinity. Desalination 150:189–203

    Article  Google Scholar 

  16. 16.

    Hinchley JW, Himus GW (1924) Evaporation in currents of air. J Soc Chem Ind 7:57–63

    Google Scholar 

  17. 17.

    Incropera FP, Dewitt DP (2002) Fundamentals of heat and mass transfer. Wiley, New York

    Google Scholar 

  18. 18.

    Boukadida N, Nasrallah SB (2001) Mass and heat transfer during water evaporation in laminar flow inside a rectangular channel—validity of heat and mass transfer analogy. Int J Therm 40:67–81

    Google Scholar 

  19. 19.

    Iskra CR, Simonson CJ (2007) Convective mass transfer coefficient for a hydro dynamically developed airflow in a short rectangular duct. Int J Heat Mass Transf 50(11–12):2376–2393

    Article  Google Scholar 

  20. 20.

    Pauken MT, Tang TD, Jeter SM, Abdel-Khalik SI (1993) A novel method for measuring water evaporation into still air. ASHRAE Trans 99(1):297–300

    Google Scholar 

  21. 21.

    Shah MM (2002) Rate of evaporation from undisturbed water pools to quiet air: evaluation of available correlations. Int J HVAC&R 8:125–131

    Article  Google Scholar 

  22. 22.

    Sharply BF, Boetler LMK (1938) Evaporation of water into quiet air from a one foot diameter surface. Ind Eng Chem 30(10):1125–1131

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Amin Jodat.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jodat, A., Moghiman, M. & Anbarsooz, M. Experimental comparison of the ability of Dalton based and similarity theory correlations to predict water evaporation rate in different convection regimes. Heat Mass Transfer 48, 1397–1406 (2012). https://doi.org/10.1007/s00231-012-0984-z

Download citation


  • Evaporation Rate
  • Similarity Theory
  • Sherwood Number
  • Convection Regime
  • Vapor Pressure Difference