Roman symbols
C	Molar concentration of water in air, molm−3
cp	Heat capacity at constant pressure, Jkg−1 K−1
D	Diffusion coefficient of water in air, m2 s−1
E	Evaporation flux of the water contained in the ASL, m s−1
f	Correlation to express the Sherwood number as a function of Re and β, -
g	Correlation to express the Nusselt number as a function of Re and β, -
h	Ratio of the radii of airways in two successive generations, -
k	Mass transfer coefficient between the mucosa and the airway, m s−1
L	Length of the airway, m
${\mathcal{L}}_m$	Molar latent heat of vaporization, J mol−1
M	Mass of the body, kg
$\mathcal{M}$	Molar mass of water, kg mol−1
n	Number of generations in the bronchial region of the lungs, -
Nu	Nusselt number of the heat transfer between the mucosa and the lumen, -
P	Power extracted from a tissue, J s−1
Pr	Prandtl number of the air, -
Q	Volumetric flow rate of air, m3 s−1
R	Radius of the airway, m
Re	Reynolds number of the flow in the airway, -
RH	Relative humidity of the air, -
Sc	Schmidt number of the air, -
Sh	Sherwood number of the mass transfer between the mucosa and the lumen, -
t	Time, s
T	Temperature, K
u	Heat transfer coefficient between the mucosa and the airway, W m−2 K−1
v	Velocity of the air, m s−1
W	Rate of water removal from the ASL, m3 s−1
Greek symbols
α	Thermal diffusivity, m2 s−1
β	Aspect ratio of the airway, -
δ	Thickness, m
η	Efficiency of the water extraction from the mucosa, -
$\overline{\eta }$	Efficiency of the heat extraction from the bronchial wall, -
γ	Ratio of the expiration duration to the inspiration duration, -
λ	Thermal conductivity, W m−1 K−1
Λ	Dimensionless number, see Equation (8)
Λ′	Dimensionless number, see Equation (23)
ν	Kinematic viscosity, m2 s−1
ϕ	Factor accounting for the increase of the cardiac flow rate during an effort, -
Φ	Dimensionless number, see Equation (9)
Ψ	Dimensionless number, see Equation (3)
$\overline{\text{Ψ}}$	Dimensionless number, see Equation (6)
ρ	Density, kg m−3
Θ	Dimensionless constant, -
ψ	Factor accounting for the increase of the ventilation rate during an effort, -
Abbreviations, subscripts, and superscripts
-	No subscript in a physicochemical property refers to the air
ỹ	Dimensionless version of y
0	At the top of the trachea during inspiration
ASL	Airway Surface Liquid
av	Averaged on a flow cross-section
b	Body
exp	Related to the expiration
l	Liquid phase
i	In generation i
in	At the inlet of the airway
insp	Related to the inspiration
max	Maximal
sat	Saturated with water
SM	Supplementary Material
tot	Total respiratory cycle
out	At the outlet of the airway
w	Tissues composing the wall of the airway
μ	At the ASL–lumen interface
Other symbols
[]	Velocity average on the entire lumen of the airway