Modeling of the air gap membrane distillation (AGMD) process for whey treatment: A CFD approach with RSM

• Integrating CFD with Response Surface Methodology (RSM) to model and optimize AGMD, followed by experimental validation. • Implemented a detailed mass transfer mechanism in the membrane, incorporating Knudsen, viscous, and molecular diffusions. • Conducted a detailed parametric analysis on permeate flux, thermal efficiency, temperature polarization coefficient (TPC), and overall heat transfer coefficient. • Achieved optimal conditions delivering 6.94 LMH permeate flux, 92 % thermal efficiency, and 6.8 % whey concentration at the outlet. • Provided practical design and operational recommendations for energy-efficient AGMD application in dairy wastewater valorization. The dairy industry is a key source of industrial wastewater. Given the global water shortage and a majority of seawater is unsuitable for drinking or most daily human needs, many industries rely on wastewater treatment to reclaim and reuse their water. This study presents a computational fluid dynamics (CFD) simulation of an Air Gap Membrane Distillation (AGMD) system. The governing equations for momentum, heat, and mass conservation in channels were solved using the finite element method in COMSOL Multiphysics. This work presents the first CFD-based RSM optimization of AGMD for whey treatment, providing a high-fidelity model that integrates Knudsen-molecular-viscous diffusion mechanisms to identify globally optimal operating conditions. The model matches experiments with 14 % average error, confirming its reliability. A comprehensive parametric analysis was performed to evaluate permeate flux, thermal efficiency, temperature polarization, and overall heat transfer coefficient. Optimization using Response Surface Methodology (RSM) identified the best operating conditions. The workflow yields an operating envelope that elevates permeate flux and thermal efficiency, while quantifying Temperature Polarization Constant (TPC) and overall heat transfer coefficient trade-offs, informing module design. These findings provide valuable insights into the design and operation of AGMD systems for energy-efficient wastewater valorization in the dairy sector.