The cooling of devices is a big challenge in the electronics industry, and most process units (graphical are central process units) experience defects under harsh temperature conditions, so dissipating generated heat under various working conditions should be studied seriously. This study investigates the magnetohydrodynamics of hybrid ferro-nanofluids in the presence of hydrophobic surfaces in a micro-heat sink. To scrutinize this study, a finite volume method (FVM) is applied. The ferro-nanofluid includes water as a base fluid and multiwall carbon nanotubes (MWCNTs) and Fe3O4 as nanoadditives, which are used in three concentrations (0, 1, and 3%). Other parameters such as the Reynolds number (5–120), Hartmann number (magnitude of the magnetic field from 0 to 6), and hydrophobicity of surfaces are scrutinized for their impacts on heat transfer and hydraulic variables as well as entropy generation variables. The outcomes indicate that increasing the level of hydrophobicity in surfaces leads simultaneously to improved heat exchange and reduced pressure drop. Likewise, it decreases the frictional and thermal types of entropy generation. Intensifying the magnitude of the magnetic field enhances the heat exchange as much as the pressure drop. It can also decrease the thermal term in entropy generation equations for the fluid, but increase the frictional entropy generation and adds a new term, magnetic entropy generation. Incrementing the Reynolds number improves the convection heat transfer parameters, although it intensifies the pressure drop in the length of the channel. Also, the thermal entropy generation and frictional entropy generation decrease and increase with an increasing flow rate (Reynolds number).
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