Electroosmotic effect on the flow of hybrid nanofluid containing para and ferri-magnetic nanoparticles through the micro-channel implementing Darcy law

This study investigates the flow of an incompressible electroosmotic hybrid nanofluid through a micro-channel. The hybrid nanofluid consists of paramagnetic (Ta) and ferrimagnetic (Fe₃O₄) nanoparticles suspended in ethylene glycol. The Darcy model is applied to the porous media in the momentum equation, and its effects are also considered in the temperature equation, accounting for frictional and Joule heating effects. The micro-channel is influenced by both pressure and magnetic flux. The study derives an exact solution for the proposed model and evaluates key engineering parameters, such as the heat transfer rate. The findings show that a higher particle volume fraction reduces the velocity distribution, while an increased Darcy parameter decreases the rate of heat transfer. Additionally, the heat transfer rate diminishes with increasing Darcy parameter and electric flux. Notably, the ferrimagnetic nanofluid exhibits better thermal conductivity than the paramagnetic nanofluid.