Innovative multiphysics heat transfer modeling of a non-uniform mini-channel with Fe3O4 nanofluid under a dipole magnetic field

• Magnetic fields on Nanofluid in non-uniform mini-channel is simulated. • Magnetic fields induce vortices, enhancing convective heat transfer in mini-channels. • A 5.37 % rise in average Nusselt number is achieved at 0.65 A·m magnetic strength. • Kelvin body force modifies flow and improves thermal mixing in ferrofluid mini-channels. • Findings support compact heat exchanger design for microelectronics and energy systems. Despite advancements in heat transfer enhancement using nanofluids and mini-channels, the study of non-uniform converging-diverging mini-channels containing ferrofluids under the influence of a magnetic field remains underexplored. It is highlighted that the simultaneous combination of four main features, namely mini-channel dimensions, non-uniform geometry, nanofluid flow, and the presence of a magnetic field, creates a complex and unique problem that is addressed in this research. This configuration offers strong potential for high-performance thermal management in electronics, microreactors, and biomedical devices. To address this aim, a carefully validated numerical study is conducted using the Finite Element Method (FEM) in COMSOL Multiphysics, incorporating User-Defined Functions (UDFs), to simulate the water-based ferrofluid containing 0.4 % Fe₃O₄ nanoparticles through a converging–diverging mini-channel under dipole magnetic fields with strengths varying from 0 to 0.65 A·m. Key variables analyzed include temperature distribution, velocity profiles, and local Nusselt numbers. The results show that increasing the magnetic field strength induces vortex formation, enhancing convective heat transfer. At a magnetic field strength of 0.65 A·m, the average Nu increases by 5.37 %, and the midline outlet temperature decreases by 1.74 % (from 321.45 K to 315.85 K) compared to the no-field case. The velocity profiles shift, with the maximum velocity increasing and localized flow disturbances near the bottom wall enhancing mixing. This study demonstrates that magnetic field-induced flow modulation significantly enhances heat transfer in non-uniform mini-channels, offering a promising approach for improving thermal management and enabling the development of efficient, compact heat exchangers for advanced energy and cooling applications.