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Abstract
This study presents a comprehensive three-dimensional coupled numerical model for a solar-driven desalination device incorporating a capillary-structured porous membrane (CPM). The governing equations-encompassing conjugate heat transfer, capillary-driven mass transport, Darcy-Brinkman momentum, and interfacial evaporation via the Hertz-Knudsen formulation-are solved simultaneously using an adaptive finite-volume method (FVM) on a mesh of 6.4 × 106 control volumes, achieving a second-order L² error of 0.28%. Parametric optimisation over porosity (φ = 0.20-0.90) and capillary diameter (d=10-200 μm) identifies the global optimum at φ=0.65 and d=35 μm, yielding a peak thermal efficiency of η=83.7 ± 2.2% and a daily freshwater productivity of 14.8 ± 0.8 kg/m2d under 1000 W/m2 irradiance a 97.9% improvement over conventional flat-plate absorbers.
A solar desalination system based on a capillary-structured porous membrane (CPM) was investigated using a three-dimensional mathematical model based on the Darcy–Brinkman–Forchheimer framework. Heat transfer, mass transport, and capillary-driven momentum equations were solved in a fully coupled manner. The adaptive finite volume method (FVM) was implemented with second-order accuracy on a computational mesh consisting of 6.4×106 control volumes. Parametric optimization was performed over a porosity range of φ=0.20-0.90 and capillary diameter range of d=10-200μm. The model results were validated against laboratory experiments. Evaporation kinetics were described using the Hertz–Knudsen equation, while salt transport was modeled using a reactive advection–diffusion equation.
At the optimal configuration of φ=0.65 and d=35μm, the thermal efficiency reached η=83.7±2.2%, while the daily water yield achieved 14.8±0.8 . These values are higher than those of a conventional flat-plate absorber by 97.9% and 185%, respectively. The numerical model showed excellent agreement with experimental data, with a mean absolute error (MAE) of 1.9% and a coefficient of determination R2=0.9974. Capillary-driven lateral flow reduced concentration polarization by 44.3% and decreased the effluent total dissolved solids (TDS) to 62±12 , which is eight times lower than the WHO standard limit. The optimal porosity peak (φ ≈0.645) remained stable regardless of variations in solar irradiance. Compared to the conventional absorber, the capillary-based system reduced salt concentration from 480 to 62 , significantly improving water purity.
References
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