Comparative analytical assessment of stagnant-water and liquid motion in bubble-column humidifiers for HDH desalination

This study presents a unified analytical framework that enables, for the first time, a direct mechanistic comparison between coil-heated stagnant-water and liquid-motion enhancement in bubble-column humidifiers under identical geometric, thermal, and operating conditions. Rather than introducing new transport correlations, the framework integrates established hydrodynamic, heat-transfer, and mass-transfer relations into a common analytical structure that isolates the relative influence of stagnant-water and liquid circulation on humidifier performance. This capability cannot be achieved through previously published stagnant-water or moving-water models, which were developed independently under different assumptions and boundary conditions. The stagnant-water model introduces a coil-heated configuration intended to promote thermal distribution within the column and sustain stable interfacial conditions for heat and mass transfer, thereby enhancing thermal stability and vapor absorption compared with the conventional moving-water design. The model predictions showed excellent agreement with benchmark experimental data, with mean absolute percentage errors below 2% and maximum relative deviations below 3.33% across all validated cases. Results indicate that increasing the air superficial velocity from 0.03 to 0.15 m/s increases the total heat transfer rate by more than 80% and the mass transfer coefficient by approximately 20%, while reducing humidifier effectiveness from 73% to 63% because of reduced bubble residence time. Coil geometry significantly affected thermal performance, with increasing coil length and outer diameter reducing the heating-coil outlet water temperature by approximately 4.4% and 3.4%, respectively. The comparative analysis further demonstrates that stagnant-water configuration exerts a stronger influence on humidifier performance than liquid motion under the investigated conditions. Overall, the stagnant-water configuration achieved up to 38% higher effectiveness, 18% higher outlet air temperature, and 40% higher outlet humidity ratio than the moving-water model. These findings provide new design-level insight into the relative roles of thermal distribution and liquid circulation in HDH bubble-column humidifiers and identify coil-heated stagnant-water configurations as a promising strategy for improving humidification performance. Accordingly, this work supports SDG 6 (Clean Water and Sanitation) and SDG 7 (Affordable and Clean Energy) by advancing energy-efficient HDH desalination technology for sustainable freshwater production.