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Heat and mass transfer of countercurrent air-water flow in a vertical tube


The paper deals with the classification and the design features of direct contact heat exchangers used in various technological processes. It describes the existing two-phase flow regimes and the methods for heat and mass transfer prediction in heat exchangers with the direct contact of fluids in a vertical tube. The authors carried out the measurements of heat and mass transfer coefficients during the liquid film flow under the action of gravity towards the air flow in a vertical tube. The range of experimental variables is set to be the following: air mass flow rate is 1·10-3-4·10-3 kg/s, air inlet temperature is 26-28 °C, air inlet humidity is 38-50 %, water mass flow rate is 1.5·10-2 -4·10-2 kg/s, and water inlet temperature is 55-58 °C. It is shown that an increase in the fluid flow rate leads to the heat and mass transfer intensification due to an increase of waves on the film surface. The authors obtained new empirical correlations for calculating convective heat and mass transfer coefficients. These equations consider the influence of the water flow rate for the film Reynolds number. The described methods are recommended to be used in the range of air Reynolds numbers from 2300 to 6700 and film Reynolds numbers from 600 to 1300.

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\(c_{p,air}\) :

specific heat capacity of air, J/(kgK)

d air :

humidity ratio of air, kg water/kg dry air

D :

diffusion coefficient of water vapour into air, m2/s


inner diameter of flooding tube, m

F :

interphase surface area, m2

J :

diffusion flux, kg/(m2s)

h :

specific enthalpy, J/kg

h con :

convective heat transfer coefficient, W/(m2K)

h d :

mass transfer coefficient, m/s

\(h_{vl}\) :

latent heat of water, J/kg

m :

mass flow rate, kg/s

\(M_{{H_{2} O}}\) :

water molar mass (=18.02), g/mol

Nu :

Nusselt number (\(Nu = h_{con} \frac{d}{\lambda }\))

Pr :

Prandtl number

p par,air :

partial pressure of water vapour in moist air (\(p_{par,air} = 0.5\left[ {p_{par,in} + p_{par,out} } \right]\), Pa

p par,in :

partial pressure at the air inlet, Pa

p par,out :

partial pressure at the air outlet, Pa

Q :

heat transferred, W

R :

gas constant, (=8.314), J/(mol·K)

Re air :

Reynolds number of moist air (\({\text{Re}}_{air} = w_{air,in} d/v_{air}\))

Re film :

film Reynolds number (\({\text{Re}}_{film} = 4\Gamma /\mu_{air}\))

Sc air :

Schmidt number of moist air (\(Sc_{air} = v_{air} /D\))

Sh :

Sherwood number (\(Sh = h_{d} \frac{d}{D}\))

t :

temperature, °C

T db,aver :

average dry-bulb temperature of moist air (\(T_{db,aver}\)=\(0.5\left[ {T_{db,in} + T_{db,out} } \right]\)), K

w :

velocity, m/s

\(l\) :

height, m


mass flow rate per unit perimeter, (\(\Gamma = m_{w} /\left[ {\pi d} \right]\)), kg/(m s)

\(\Delta G\) :

consumption of moisture absorbed by air, kg/s

\(\Delta T\) :

mean logarithmic temperature difference, (\(\Delta T = \frac{{\left( {t_{w,in} - t_{db,our} } \right) - \left( {t_{w,out} - t_{db,in} } \right)}}{{\ln \frac{{\left( {t_{w,in} - t_{db,our} } \right)}}{{\left( {t_{w,out} - t_{db,in} } \right)}}}}\)), K

\(\eta_{DHE}\) :

heat balance factor

λ :

thermal conductivity, W/(mK)


dynamic viscosity, [Pa·s]

ν :

kinematic viscosity, m2/s

ψ :

relative humidity of air

atm :


air :

moist air

aver :


con :


db :


evap :


exp :


in :

tube inlet

out :

tube outlet

tot :


w :


wb :



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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations



Peter Barabash, Andrii Solomakha and Volodymyr Sereda contributed to the study conception and design. Material preparation, data collection and analysis were performed by Peter Strynada, Yang Liu, Andrii Solomakha, Volodymyr Sereda and Natalia Prytula. The first draft of the manuscript was written by Peter Barabash, Volodymyr Sereda, Natalia Prytula and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Volodymyr Sereda.

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Barabash, P., Solomakha, A., Sereda, V. et al. Heat and mass transfer of countercurrent air-water flow in a vertical tube. Heat Mass Transfer (2023).

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