Latin Letters		SI Units
$A_{IN}$	Inner surface Area	[m2]
${\tilde{C}}_p,{\widehat{C}}_p$	Molar, mass, heat capacity at constant pressure	[J mol−1 K−1], [J kg−1 K−1]
$d_{IN}$	Inner diameter of a fiber	[m]
$d_{OUT}$	Outer diameter of a fiber	[m]
$d_{lm,m}$	Logarithmic mean diameter of the membrane $d_{lm,m}=\frac{d_{OUT}-d_{IN}}{\ln \frac{d_{OUT}}{d_{IN}}}$	[m]
$d_{lm,j}$	Logarithmic mean diameter of the membrane layer j	[m]
$d_S$	Shell diameter	[m]
$d_{p,j}$	Pore diameter of the membrane layer j	[m]
$d_{pm}$	Mean pore diameter of the membrane	[m]
$D_{W,Kn}$	Knudsen diffusion coefficient of water	[m2 s−1]
$D_{WG}$	Molecular diffusion coefficient of water in gas	[m2 s−1]
$D_{Weq}$	Equivalent diffusion coefficient of water	[m2 s−1]
D	Molecular diffusion coefficient	[m2 s−1]
f	Fanning factor	[dimensionless]
$G_{in}$	Inlet stream of gas
$G_{out}$	Outlet stream of gas
$G{z}_H,G{z}_M$	Graetz number for heat, mass transfer	[dimensionless]
h	Convective heat transfer coefficient	[W m−2 K−1]
$J_w$	Mass flux of water across the membrane (defined in Equation (2))	[kg m−2 s−1)
$k_w$	Mass transfer coefficient of water	[m s−1]
$k_{S,L}$	Mass transfer coefficient of salt in liquid	[m s−1]
$k^{\mathit{cond}.}$	Thermal conductivity coefficient	[W m−1 K−1]
$k_m^{cond.}$	Pseudo-thermal conductivity of the membrane (defined in Equation (9a))	[W m−2 K−1]
$L_{\mathit{eff}}$	Effective length of membrane module (Figure 1c)	[m]
$L_{\mathit{tot}}$	Total length of membrane module	[m]
$L_{\mathit{in}}$	Inlet stream of liquid
$L_{\mathit{out}}$	Outlet stream of liquid
$m_{w,\mathit{liquid} \mathit{phase}}$	Mass of water in the liquid side	[kg]
$m_{\mathit{tot},\mathit{liquid} \mathit{phase}}$	Total mass of solution in the liquid side	[kg]
M	Molar mass	[kg mol−1]
$\stackrel{·}{n}$	Molar flow rate	[mol s−1]
$N_w^{\prime }$	Transmembrane Molar flow rate of water per unit length per fiber	[mol m−1 s−1]
$N_f$	Number of fibers	[dimensionless]
Nu	Nusselt number	[dimensionless]
P	Pressure	[Pa]
Pr	Prandtl number	[dimensionless]
$P_w^{*}$	Vapor pressure of water	[Pa]
$Q_L^{\prime }$	Heat flow rate per unit length per fiber in the liquid thermal boundary layer	[W m−1]
$Q_{\mathit{net}}^{\prime }$	Net transmembrane heat flow rate per unit length per fiber	[W m−1]
Re	Reynolds number	[dimensionless]
$R_g$	Universal gas constant	[J mol−1 K−1]
$S_{\mathit{Nacl}}$	Salinity of NaCl solution	[g NaCl kg−1 Solution]
Sc	Schmidt number	[dimensionless]
Sh	Sherwood number	[dimensionless]
T	Temperature	[K]
$v_{\mathit{L}}$	Liquid velocity in lumen-side (defined in Equation (15))	[m s−1]
$V_{0,\mathit{G}}$	Gas interstitial velocity in shell-side (defined in Equation (21))	[m s−1]
x	Mole fraction in liquid phase	[dimensionless]
y	Mole fraction in gas phase	[dimensionless]
z	Axial coordinate in membrane module	[m]
Greek Letters		SI Units
${\gamma }_{w,Lm}$	Activity coefficient of water at liquid/membrane interface	[dimensionless]
$\delta$	Thickness	[m]
${\left(\epsilon /\tau \right)}_j$	Porosity-tortuosity ratio of the membrane layer j	[dimensionless]
${\left(\epsilon /\tau \right)}_m$	Mean porosity-tortuosity ratio of the membrane	[dimensionless]
${\epsilon }_p$	Packing factor of the membrane module	[dimensionless]
$\eta$	Dynamic viscosity	[Pa s]
$\lambda$	Molar latent heat of vaporization	[J mol−1]
$\rho$	Density	[kg m−3]
Superscripts and Subscripts
a	Air
G	Gas side
Gb	At gas bulk
Gm	At gas/membrane interface
IN	Inlet section
j	Layer j (j = S for support, j = 1 for layer1, j = 2 for layer 2, j = 3 for layer 3)
L	Liquid side
Lb	At liquid bulk
Lm	At liquid/membrane interface
s	Salt
solid	Solid portion of the membrane
w	Water