This study is conducted to explore the impact of thermal dispersion and melting on the natural convective nanofluid (nickel zinc ferrite + SAE 20W-40 motor oil) flow over a stretching sheet in a Darcy porous medium. An irreversibility analysis has also been performed using the second law of thermodynamics. The fundamental nonlinear partial differential equations (PDEs) are converted into a system of dimensionless nonlinear ordinary differential equations (ODEs) through Lie group similarity transformations and then solved by employing the spectral local linearization method implemented in MATLAB software. It is noteworthy to highlight that the validation results indicate a strong concurrence with existing findings in previously published literature. After simulation, it is specified that the thermal dispersion disrupts the entropy (by 63.7%) and enhances the surface friction. Likewise, the heat transfer rate improves by 1.5% with the melting effect and 58.7% with the Darcy number. The results indicate that the brick-shaped particles exhibit a higher rate of heat transfer and lower entropy production. Further, this work has many uses such as, core, microwave, and biomedical applications like tumor treatments, bone plate surgeries, EMI (electromagnetic interfaces), electronics cooling, and aerodynamic extrusion processes, in the design of passive ventilation systems.