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

Abstract

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.

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Abbreviations

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

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

ρ:

Density kg/m3

μ:

Dynamic viscosity NS/m2

\( \bar{\rho } \) :

Mean mixture density of air

φ:

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

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Correspondence to Amin Jodat.

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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

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Keywords

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