Fractional modeling of a solar still incorporating nano-encapsulated phase change materials for enhanced thermal and exergy performance

This study presents a Caputo–Fabrizio fractional-order mathematical model to investigate the thermal behavior of a conventional solar still integrated with core–shell nano-encapsulated phase change materials (NEPCMs) for latent heat thermal energy storage. Two NEPCM configurations consisting of paraffin- and n -nonadecane-based cores encapsulated within silicon dioxide and polyurethane shells are considered to examine their influence on the thermo-exergetic performance of the system. The influence of the NEPCM volume fraction on thermal efficiency, exergy efficiency, freshwater productivity, and temperature variation is analyzed under summer and winter operating conditions. The model predictions are validated against experimental water-temperature data, At α = 1 , the numerical predictions are compared with the ODE45 solution to verify the accuracy of the proposed numerical scheme. Under winter conditions, the high-temperature paraffin/SiO 2 NEPCM mainly contributes through sensible heat storage, whereas the low-temperature n -nonadecane/polyurethane NEPCM undergoes phase change. The numerical results demonstrate that increasing the NEPCM volume fraction improves the overall performance of the solar still. For the paraffin/SiO 2 NEPCM under summer conditions, at ϕ = 0.02 , the average thermal efficiency, average exergy efficiency, and daily freshwater productivity reach 54.36%, 4.143%, and 5.889 kg m − 2 d a y − 1 , respectively, representing improvements of approximately 25.7%, 24.0%, and 26.9%, respectively, compared with the conventional case. The component-wise exergy analysis further identifies the absorber plate as the dominant source of irreversibility in the system. These findings demonstrate that the proposed fractional-order framework provides an effective computational approach for analyzing NEPCM-assisted solar stills and offers useful guidance for the selection of PCM melting temperature under different operating conditions.