The increasing need for a steady energy supply to enhance efficiency is progressively growing in both residential and manufacturing industries. This demand can be addressed by utilizing advanced technologies like a melting heat generator to produce significant amounts of heat and prevent overheating. Based on the above applications of melting heat, the consequences of melting heat transfer induction on ternary hybrid nanofluid (T-HNF) exposed to solar radiation mechanism in an erratic squeezing flow are considered. The nanoparticles Copper (Cu), Silicon dioxide (), Zirconium dioxide () are immersed in base fluid Engine oil (EO) resulting in T-HNF (Cu + + /EO). The model equation also takes into account the entropy generation minimization and Bejan number. Both the spectral collocation technique (SCT) and finite element scheme (FES) are applied to solve the ordinary differential equations (ODEs) through the Mathematica package. Our results reveal that the impact of three-component nanoparticles increases, while the solar radiation parameter raises the energy profile. Also, an increase in the magnetic field deteriorates the velocity distribution. The research has various potential applications, such as in ice and snow melting, solar thermal energy storage, and the food industry