Novel time-fractional modeling for parabolic trough collectors using mono/hybrid nanofluids and nanocoating

Abstract

This paper proposes a novel time-fractional model to simulate the behaviour of double U-tube parabolic trough collectors (PTCs). The model's parameters, including the fractional order, were optimized to achieve the closest agreement with experimental measurements obtained in Kafrelsheikh, Egypt. Subsequently, the optimal model was used to study the variations in the thermal performance's results for summer and winter conditions, and to investigate the potential for enhancing the PTC thermal performance by incorporating different nanomaterial types at different concentrations individually and in mixture into the PTC's heat transfer fluid (HTF) and absorber tube coating. The optimum solution obtained was for the case of $\alpha =0.64$ at which the calculated average water outlet temperature was $56.15°C$ compared with an average value of $56.22°C$ obtained from experimental results. For the case of nanofluids, several types were introduced at different concentrations individually and in the mixture, including Titanium dioxide (TiO₂), Copper oxide (CuO) and Aluminum oxide (Al₂O₃). Thermophysical properties of the introduced hybrid nanofluids were calculated and plotted for various internal concentrations as well. For the case of using nanocoating, the addition of nanomaterials was carried out in two scenarios; the first one represents adding carbon nanotubes (CNTs) with specific mass concentration, while the second one represents adding an equal mixture of CNTs and CuO nanoparticles (1:1) with the same total specific mass concentration.