$A$	membrane area (m2)
$a_w$	water activity in NaCl solution
$Cp,c$	heat capacity of cold fluid (J kg−1K−1)
$Cp,h$	heat capacity of hot fluid (J kg−1K−1)
$c_a$	mass transfer coefficient of air gap region (kg m−2 Pa−1 s−1)
$c_m$	mass transfer coefficient of membrane (kg m−2 Pa−1 s−1)
$c_T$	overall mass transfer coefficient of membrane (kg m−2 Pa−1 s−1)
$d$	thickness of empty channel (m)
$D$	equivalent hydraulic diameter of empty channel (m)
$D_{h,h}$	equivalent hydraulic diameter of hot side (m)
$D_{h,c}$	equivalent hydraulic diameter of cold side (m)
E	deviation of experimental results from the theoretical predictions
$f_F$	Fanning friction factor
$h_c$	convection coefficient of cold stream (W m−2 K−1)
$h_h$	convection coefficient of saline stream (W m−2 K−1)
$H_i$	hydraulic dissipate energy (J kg−1),$i=promoter,empty$
$H_m$	thermal convection coefficient of membrane (W m−2 K−1)
$I_E$	increased percentage of permeate flux
$I_P$	raised percentage of hydraulic loss
$L$	axial distance (m)
$k_a$	thermal conductivity of the air gap (W m−1 K−1)
$k_m$	thermal conductivity of the membrane (W m−1 K−1)
$k_f$	thermal conductivity coefficient of aqueous solution (W m−1 K−1)
$k_g$	thermal conductivity coefficient of the vapor in the membrane pore (W m−1 K−1)
$k_s$	thermal conductivity coefficient of the solid membrane material (W m−1 K−1)
$k_m$	thermal conductivity of the membrane (W m−1 K−1)
$k_p$	thermal conductivity of cooling plate (W m−1 K−1)
$\ell w_f$	friction loss of conduits (J kg−1)
$M_W$	molecular weight of water (kg mol−1)
$\dot{m}$	mass flow rate (kg s−1)
$N^{″}$	permeate flux (kg m−2 s−1)
$Nu$	Nusselt number
$N{u}^E$	enhanced Nusselt number with inserting turbulence promoter
$N{u}_{lam}$	Nusselt number for laminar flow
$P$	pressure (Pa)
$P_1^{sat}$	saturation vapor pressure in the saline feed stream (Pa)
$P_3^{sat}$	saturation vapor pressure in the hot feed flow side (Pa)
$P_w{}^{sat}$	saturated vapor pressure of pure water (Pa)
$Pr$	Prandtl number
$q$	heat transfer flux (W)
$q_{}^{″}$	heat transfer rate (W/m2)
$Q$	volumetric flow rate (m3 s−1)
$R$	gas constant (8.314 J mol−1 K−1)
$Re$	Reynolds number
$r$	radius of membrane pore (m)
$T$	temperature (°C)
$T_m$	mean temperature in membrane (°C)
$T_{PC}$	temperature polarization coefficients
$\overline{v}$	average velocity (m s−1)
$We$	$\mathsf{\Lambda }$-ribs carbon-fiber width
${\left|Y_m\right|}_{\ell n}$	natural log mean mole fraction of air
$x_{NaCl}$	liquid mole fraction of NaCl
$x_w$	liquid mole fraction of water
$z$	axial coordinate along the flow direction (m)
Greek letters
${\alpha }^E$	heat-transfer enhancement factor
$\beta$	aspect ratio of the channel
$\Delta P$	vapor pressure difference of membrane (Pa)
${\delta }_m$	thickness of membrane (µm)
$\epsilon$	membrane porosity
${\epsilon }_e$	channel voidage
$\lambda$	latent heat of water (J/kg)
$\mu$	fluid viscosity (kg s−1 m−1)
$\rho$	density (kg m−3)
$T_{PC}$	temperature polarization coefficients
Subscripts
1	on membrane surface in cold feed side
2	on membrane surface in hot feed side
a	in the air gap
c	in the cold feed flow channel
f	in the condensate film
h	in the hot feed flow channel
m	in the membrane
p	in the cooling plate
carbon fiber	inserting $\mathsf{\Lambda }$-ribs carbon-fiber open slots
empty	module with inserting nylon fiber as supporters
exp	experimental results
in	at the inlet
lam	module with empty channel
out	at the outlet
theo	theoretical predictions
Superscripts
E	the channel with inserting $\mathsf{\Lambda }$-ribs carbon-fiber open slots