Development of artificial intelligence computing techniques and \({\varvec{\alpha}}\)-cut fuzzy-based mathematical model to study heat transfer through a cylindrical surface with nanoparticle aggregation: an application to parabolic trough solar collector

The aggregation effect of nanoparticles influences the properties of nanoparticles in the working fluid, subsequently influencing the effective characteristics of the resulting fluid. The present investigation examines the heat transfer of a TiO₂/ethylene glycol nanofluid flowing through a receiver tube within a parabolic trough solar collector with the nanoparticles aggregation effect. Solar collectors transform incident sunlight to thermal energy through absorption, which is used for different purposes. The flow within the receiver tube is modeled using a cylindrical surface representation. Furthermore, the analysis considers the impact of natural convection and thermal radiation. To consider the influence of aggregation, revised forms of the Krieger–Dougherty model and the Maxwell and Bruggeman models are applied to estimate the effective viscosity and thermal conductivity of TiO₂/ethylene glycol nanofluid, respectively. Nanoparticle aggregates are not exactly spherical, but the aggregate represents an approximation to spherical shape. This information implies that certain uncertainty or fuzziness is involved with the effective volume fraction of NPs aggregates. Therefore, the authors have developed a mathematical model in a fuzzy setting. The fuzzy differential equations are modeled using the triangular fuzzy numbers developed by \(\alpha\)-cut, where \(\alpha \in \left[ {0,\,1} \right]\). In addition, two different artificial intelligence computing techniques using artificial neural network and fuzzy particle swarm optimization are also designed to predict the Nusselt number of the nanofluid flowing inside the tube.