Cylindrical cell model for direct contact membrane distillation (DCMD) of densely packed hollow fibers

• Heat, mass, and momentum transfer phenomena are simultaneously solved.
• Temperature profiles vary linearly in the longitudinal direction of all regions.
• Vapor and heat flux are proportional to the fiber thickness to the power of −2/3.
• The hot-out/cold-in mode provides higher performance than hot-in/cold-out mode.
• Theoretical maximum length of the hollow fiber membrane is analytically derived.

Temperature profiles in hollow fiber (HF)–direct contact membrane distillation (DCMD) are modeled analytically using the standard perturbation theory and the method of separation of variables. The theoretical results explain experimental observations reported in the literature. For HF–MD, new basic quantities Fw and Sw are proposed instead of conventional mass and heat flux definitions, respectively. Temperature varies linearly in the longitudinal direction, and Fw and Sq are proportional to the membrane thickness to the power of −2/3. The stream speed of the hot feed primarily controls mass transfer, and the lumen flow rate significantly influences the heat transfer. An analytical expression of the theoretical maximum membrane length is derived, which decreases with transmembrane temperature difference and increases with feed and permeate streams. The best performance of HF–DCMD operation in terms of mass and heat transfer can be reached by using a short HF membrane with fast stream speeds. For membranes of similar pore size and thickness, MD membranes of high porosity will give better performance by providing sparser pore structures and consequently lower spatial fraction for heat transfer.

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