Advancements in miniaturization demand efficient thermal management for compact, high-power-density electronic devices. Micro/minichannel heat sinks, known for their compactness and superior thermal performance, emerge as preferred solutions. This study employs a 3D numerical analysis to explore conjugate heat transfer in a rectangular minichannel with the Onsager-Wien effect induced active vortices. The analysis encompasses fully coupled governing equations for flow, heat transfer, electric potential, and charge transport solved using the finite volume framework of Open FOAM. The Onsager-Wien effect induces small vortices near electrodes, enhancing fluid mixing, depleting the thermal boundary layer, and intensifying heat transfer. This study investigates the effect of electric field strength and electrode configurations on different Reynolds number. Stable vortex structures are observed at low Reynolds numbers, but inertial forces dominate at higher Reynolds number, smearing off the vortices in the positive flow direction. Optimal performance is observed with smaller electrodes at higher Reynolds numbers, while larger electrodes excel at lower Reynolds numbers. Within the studied parameters, a 60.6% enhancement in heat transfer is achieved at an electric power consumption of just 30.1 mW. This numerical study establishes a benchmark for designing minichannel heat sinks, emphasizing enhanced heat transfer through thermal boundary layer depletion using weak to medium electric fields.