Irreversibility analysis of cross-flow in Eyring–Powell nanofluid over a permeable deformable sheet with Lorentz forces

The objective of this research is to explore the potential of utilizing renewable energy ships (RES) as a sustainable alternative and reducing the need for marine diesel oil (MDO) within the shipping industry. The current work concentrates on increasing the thermal performance in RES via the utilization of nanofluids (NFs) that contain a mixture of the base water fluid and single titania or titanium dioxide (TiO₂) nanoparticles (NPs). Furthermore, the implementation of the entropy generation (EG) minimization and Eyring–Powell fluid model in parabolic trough solar collectors with Lorentz forces is employed for RES. Moreover, the results indicate that the skin friction coefficient (SFC) and local Nusselt number (LNN) supplements resulted in an increase of approximately 1.02% and 0.04% for the stable solutions (SBES), which can be attributed to the greater concentration of the titania NPs. Meanwhile, for the case of unstable solutions (USBES), the enhancement was observed up to 1.38% and 0.31%, respectively. Also, the solar radiation parameter played an important role in enhancing the LNN, resulting in an increase of approximately 5.8% and 4.35% for SBES and USBES, respectively. This article provides vital contributions to the sector of sustainable transportation by giving valuable information on the construction and improvement of thermal solar energy technologies.