Transient thermo-optical and phase-change modeling of a parabolic trough solar collector integrated with Al ₂ O ₃ nano-enhanced PCM

Parabolic trough solar collectors (PTSCs) are a mature concentrating solar technology, but their performance is limited by solar intermittency. Integration with phase change materials (PCMs) can mitigate this limitation, yet conventional PCMs suffer from low thermal conductivity. Nano-enhanced PCMs (NePCMs) offer improved heat transfer, but most existing studies rely on simplified transient models and lack comprehensive annual performance assessment under realistic climatic conditions. To address this gap, this study develops a fully transient optical–thermal–phase-change model to investigate the annual performance of a PTSC integrated with NePCM. The coupled governing equations are discretized using a semi-implicit finite-difference scheme, while the melting and solidification processes are captured via a Stefan moving-boundary formulation and solved iteratively using a Gauss–Seidel algorithm. Hourly climatic data for Yazd (8760 h) are applied to resolve seasonal and diurnal variations. The results show that adding aluminum oxide (Al 2 O 3 ) nanoparticles significantly enhances system performance: at 1 wt% concentration, the annual thermal efficiency increases by 10% (to 52%) compared to pure paraffin, and the annual exergy efficiency reaches 31% (an improvement of 15% over the baseline). Monthly useful energy output rises to 440 kWh, and the levelized cost of heat is reduced to 0.085 $/kWh th , yielding the minimum payback period of about 5.2 years. Although the 3 wt% case achieves the highest instantaneous and monthly energy output (up to 470 kWh/month) and Carbon Dioxide (CO 2 ) avoidance (peaking at 120 kg/month), its economic performance deteriorates due to higher material costs. Overall, the results demonstrate that a 1 wt% nanoparticle loading offers the most favorable balance between thermodynamic performance, environmental benefit, and economic feasibility.