Terms	Definition
${\delta }_m$	Membrane thickness $\left(\mathrm{m}\right)$
$ϵ$	Membrane porosity
${\eta }_{II}$	Exergy efficiency
$\kappa$	Membrane permeability $\left({\mathrm{m}}^2\right)$
$\mu$	Dynamic viscosity of fluid $\left(\mathrm{Pa}\mathrm{s}\right)$
${\mu }_f$	Dynamic viscosity of the feed stream $\left(\mathrm{Pa}\mathrm{s}\right)$
${\xi }_0$	Specific Gibbs free energy of the dead state $\left({\mathrm{J}\mathrm{kg}}^{-1}\right)$
$\rho$	Density of feed stream $\left({\mathrm{kg}\mathrm{m}}^3\right)$
$\tau$	Membrane tortuosity
${\omega }_i$	Mass fraction of component $\text{“}i\text{”}$
${\omega }_{s,in}$	Mass fraction of salt at the inlet
$a$	Fiber spacing parameter
$a_w$	Activity coefficient of water
$A^t$	Total non-flow exergy $\left(J\right)$
$b_i^t$	Specific flow exergy of stream $\text{“}i\text{”}$ $\left({\mathrm{J}\mathrm{kg}}^{-1}\right)$
$C_1$	Knudsen diffusion coefficient $\left({\mathrm{s}\mathrm{mol}\mathrm{kg}}^{-1}{\mathrm{m}}^{-1}\right)$
$C_2$	Poiseuille diffusion coefficient $\left({\mathrm{s}\mathrm{mol}\mathrm{kg}}^{-1}{\mathrm{m}}^{-1}\right)$
$C_p$	Heat capacity of fluid $\left({\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}\right)$
$C_t$	Total diffusion coefficient $\left({\mathrm{s}\mathrm{mol}\mathrm{kg}}^{-1}{\mathrm{m}}^{-1}\right)$
$d_p$	Mean pore diameter $\left(\mathrm{m}\right)$
$D_i^m$	Mixture average diffusion coefficient of component “i” $\left({\mathrm{m}}^2{\mathrm{s}}^{-1}\right)$
$D_{sw}$	Diffusion coefficient for salt in water $\left({\mathrm{m}}^2{\mathrm{s}}^{-1}\right)$
$E_k$	Kinetic energy $\left(\mathrm{J}\right)$
$E_p$	Potential energy $\left(\mathrm{J}\right)$
$E{x}_{irr}$	Total exergy loss due to system irreversibility $\left(\mathrm{W}\right)$
$E{x}_{solar}$	Solar exergy flux $\left(\mathrm{W}\right)$
$E{x}_t$	Total Thermal Exergy Flux $\left(\mathrm{W}\right)$
$h_0$	Specific enthalpy of dead state $\left({\mathrm{J}\mathrm{kg}}^{-1}\right)$
$h_i$	Specific enthalpy of stream “i” $\left({\mathrm{J}\mathrm{kg}}^{-1}\right)$
$\widehat{h_m}$	Convective heat transfer coefficient $\left({\mathrm{Wm}}^{-2}{\mathrm{K}}^{-1}\right)$
$H_{vap}$	Heat of vaporization of water $\left({\mathrm{kJ}\mathrm{mol}}^{-1}\right)$
$\stackrel{\rightharpoonup }{\stackrel{\rightharpoonup }{I}}$	Identity tensor
${\stackrel{\rightharpoonup }{j}}_{ci}$	Mixture diffusion correction term $\left({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\right)$
${\stackrel{\rightharpoonup }{j}}_i$	Diffusive flux of component $\text{“}i\text{”}$ in the feed stream $\left({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\right)$
$k_f$	Thermal conductivity of feed stream $\left({\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}\right)$
$L_m$	Length of membrane module $\left(\mathrm{m}\right)$
${\dot{m}}_i$	Mass flowrate of stream $“i”$ $\left({\mathrm{kg}\mathrm{s}}^{-1}\right)$
$M_i$	Molar mass of component $“i”$ in membrane feed $\left({\mathrm{kg}\mathrm{mol}}^{-1}\right)$
$M_n$	Mean molar mass of the feed stream $\left({\mathrm{kg}\mathrm{mol}}^{-1}\right)$
$n$	Number of fibers in a module
$\stackrel{\rightharpoonup }{n}$	Normal vector
$N$	Mass flux of water vapor across membrane $\left({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\right)$
$\widehat{N}$	Total Number of Streams entering and leaving
${\stackrel{\rightharpoonup }{N}}_i$	Total mass flux of component “i” within the membrane feed stream $\left({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\right)$
${\stackrel{\rightharpoonup }{N}}_w$	Total mass flux of water within the membrane feed stream $\left({\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}\right)$
$p_0$	Dead state pressure $\left(\mathrm{Pa}\right)$
$P_f$	Pressure of the feed stream $\left(\mathrm{Pa}\right)$
$\mathsf{\Delta }P$	Transmembrane change in pressure $\left(\mathrm{Pa}\right)$
$P_m$	Average pressure within the membrane $\left(\mathrm{Pa}\right)$
$P_{sat}$	Saturation pressure of water $\left(\mathrm{Pa}\right)$
$P_{vac}$	Vacuum pressure $\left(\mathrm{Pa}\right)$
$q$	Volumetric flowrate $\left({\mathrm{m}}^3{\mathrm{s}}^{-1}\right)$
${\stackrel{\rightharpoonup }{q}}_f$	Conductive heat flux in the membrane feed stream $\left({\mathrm{W}\mathrm{m}}^{-2}\right)$
$q_m$	Transmembrane heat flux $\left({\mathrm{W}\mathrm{m}}^{-2}\right)$
$Q_{solar}$	Solar energy $\left(\mathrm{W}\right)$
$r$	Radial spatial variable $\left(\mathrm{m}\right)$
$R$	Ideal gas constant $\left({\mathrm{J}\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}\right)$
$R_i$	Inner radius of the membrane $\left(\mathrm{m}\right)$
$\widehat{R_k}$	Specific Gas constant for component “k” $\left({\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}\right)$
$R_o$	Outer radius of membrane $\left(\mathrm{m}\right)$
$s_i$	Specific entropy of stream “i” $\left({\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}\right)$
$s_0$	Dead state-specific entropy $\left({\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}\right)$
$S$	Entropy $\left({\mathrm{J}\mathrm{K}}^{-1}\right)$
$T_0$	Dead State temperature $\left(\mathrm{K}\right)$
$T_f$	Feed stream temperature $\left(\mathrm{K}\right)$
$T_{f,in}$	Feed temperature at inlet $\left(\mathrm{K}\right)$
$T_m$	Feed stream temperature at membrane interface $\left(\mathrm{K}\right)$
$T_{sun}$	Temperature of the Sun $\left(\mathrm{K}\right)$
${\stackrel{\rightharpoonup }{u}}_f$	Feed velocity $\left({\mathrm{m}\mathrm{s}}^{-1}\right)$
${\stackrel{\rightharpoonup }{u}}_{f,in}$	Feed velocity at inlet $\left({\mathrm{m}\mathrm{s}}^{-1}\right)$
$U$	Internal Energy $\left(\mathrm{J}\right)$
$V$	Volume $\left({\mathrm{m}}^3\right)$
$W_t$	Mechanical Power $\left(\mathrm{W}\right)$
$x_k$	Mole fraction of component k
$x_k^0$	Dead state mole fraction of component k
$x_s$	Mole fraction of salt in feed stream
$z$	Axial spatial variable $\left(\mathrm{m}\right)$