A dimensionless second-law-compliant integrated model for balanced humidification-dehumidification systems

This study presents a simplified, dimensionless, and second-law-compliant analytical model for balanced humidification–dehumidification desalination systems. By applying rigorous dimensionless analysis, the proposed model successfully reduces input parameters without compromising thermodynamic accuracy or predictive performance. The developed formulation eliminates nonphysical behavior, such as the emergence of multiple real roots that violate the second law of thermodynamics, through the introduction of explicit constraints and critical thresholds for enthalpy pinch and temperature. A key outcome of the analysis is the identification of a dimensionless dehumidifier slope that governs system behavior and inherently accounts for maximum temperature effects via normalized parameters. The model offers analytical insight into the relationship between air and water temperature profiles, enthalpy pinch, and thermal efficiency, thus simplifying the overall optimization process. The model is validated against the conventional numerical model for critical enthalpy pinch, gain output ratio, optimal mass flowrate ratio, and recovery ratio, achieving close agreement across a wide range of operating conditions. Case study results demonstrate the model’s practical utility, predicting a GOR of 2.27 at minimal thermal input with recovery ratio of 3.60 %. The proposed framework offers a scalable and thermodynamically consistent tool for humidification-dehumidification systems optimization and operational planning.