Exploration of melting heat transfer and entropy generation in a magnetized hybrid nanoliquid over an extending sheet of varying thickness

The analysis of melting heat transfer over an expansive sheet of variable thickness is of the utmost importance in various industrial and engineering sectors, such as injection molding of polymers and composites, cooling of nuclear reactors, hot rolling, etc. Thus, the current work examines the flow dynamics, melting heat transport, and entropy generation of a magneto-hybrid nanofluid over a stretching device with variable thickness in porous media. A water-based hybridized nanofluid is formed using copper $\left(\mathrm{Cu}\right)$ and aluminium oxide $\left({\mathrm{Al}}_2{O}_3\right)$ nanoparticles in the presence of thermal radiation, viscous dissipation, and Joulean heating. The transport partial derivatives were transmuted to ordinary derivatives using appropriate similarity quantities. These equations were numerically solved through shooting techniques combined with the Runge–Kutta–Fehlberg (RKF) method. Diverse figures and tables are sketched to illustrate the outcomes of the various parameters involved in the study. The investigation reveals an enlargement in the heat-bounding surface with an escalation in the magnitude of volume fraction, melting heat transfer, and magnetic field terms. In contrast, the momentum-bounding surface depletes with these parameters. Furthermore, as thermal radiation and Eckert numbers rise, the thermal gradient increases. The entropy generation increases with higher Brikman number and porosity term, but the melting heat parameter causes a decline in the entropy profiles.