Thermal investigation of humidification process using the Poppe method, a semi-analytical method

• The Poppe approach is used to evaluate humidifier properties. • Akbari-Ganji's method (AGM) is utilized to solve sets of differential equations. • The dimensionless parameters extracted from the Poppe method including θ , C 1 , C 2 , C 3 , M R , and ω 0 , evaluate humidifier outlet dimensionless parameters such as Ω, H, and M e . • The mass transfer coefficient is evaluated versus θ and Γ for optimal dimensionless parameters. This study evaluates the humidification process in a humidifier using the Poppe method’s nonlinear ordinary differential equations (ODEs), which captures heat and mass transfer mechanisms with higher accuracy than conventional models. The nonlinear ODEs are extracted, non-dimensionalized, and solved numerically using the semi-analytical method. The dimensionless formulation enables a detailed analysis of outlet air relative humidity and the increase in the air mass flow rate by absorbing moisture. By use of a semi-analytical method, the influence of extracted dimensionless parameters on the performance of the humidification cycle is shown, and the mass transfer coefficient is estimated. The semi-analytical method is a fast and grid-independent tool for analyzing complex and nonlinear problems. The effect of dimensionless parameters on the humidification performance are investigated. The results show that at higher saline water temperatures, heat and mass transfer between water and air grows, leading to higher humidification potential. Either increasing dimensionless number related to the air enthalpy and mass flow rate ratio or decreasing dimensionless number related to Lewis factor result in a higher humidification ability. In addition, reducing dimensionless number related to water vaporization decreases the energy required for water evaporation, thereby increasing the humidification potential. An increase in water mass flow per unit area means a higher ability of humidification, causing mass transfer coefficient to grow. Among all tested parameters, mass flow rate ratio and increasing dimensionless number related to the air enthalpy exhibit the highest mass transfer coefficient, which peaks at 9.38×10 -4 kg/m 2 s when optimal conditions are met.