Determination of Heat and Mass Transport Correlations for Hollow Membrane Distillation Modules

Development and optimization of the membrane distillation (MD) process are strongly associated with better understanding of heat and mass transport across the membrane. The current state-of-the-art on heat and mass transport in MD greatly relies upon the use of various empirical correlations for the Nusselt number ( Nu ), tortuosity factor ( τ ), and thermal conductivity ( κ m ) of the membrane. However, the current literature lacks investigations about finding the most representative combination of these three parameters for modeling transport phenomena in MD. In this study, we investigated 189 combinations of Nu , κ m , and τ to assess their capability to predict the experimental flux and outlet temperatures of feed and permeate streams for hollow fiber MD modules. It was concluded that 31 out of 189 tested combinations could predict the experimental flux with reasonable accuracy (R 2 > 0.95). Most of the combinations capable of predicting the flux reasonably well could predict the feed outlet temperature well; however, the capability of the tested combinations to predict the permeate outlet temperatures was poor, and only 13 combinations reasonably predicted the experimental temperature. As a generally observed tendency, it was noted that in the best-performing models, most of the correlations used for the determination of κ m were parallel models. The study also identified the best-performing combinations to simultaneously predict flux, feed, and permeate outlet temperatures. Thus, it was noted that the best model to simultaneously predict flux, feed, and permeate outlet temperatures consisted of the following correlations for τ , Nu , and κ m : = ε 1 − 1 − ε 1 / 3 , N u = 0.13 R e 0.64 P r 0.38 , κ m = 1 − ε κ p o l + ε κ a i r where ε , Re , Pr , κ p o l , and κ a i r represent membrane porosity, Reynolds number, Prandtl number, thermal conductivities of polymer and air, respectively.