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

Abstract

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.

Keywords:

• Darcy law
• electroosmotic effect
• hybrid nanofluid
• micro parallel channel
• paramagnetic and ferrimagnetic nanoparticles

Authors contributions

Muhammad Ramzan: supervision, conceptualization. Javaria Akram: writing–review and editing, software. Nazia Shahmir: writing–original draft, methodology. C. Ahamed Saleel: formal analysis, investigation. Ahmed S. Sowayan: software, methodology, investigation. Seifedine Kadry: visualization, validation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/173/45.