The variations of heat transfer and slip velocity of FMWNT-water nano-fluid along the micro-channel in the lack and presence of a magnetic field

• The effects of Ha, Re, slip coefficient and nano-particles volume fraction were investigated.
• The stronger magnetic field leaded to less maximum of U at horizontal centerline and greater fluid velocity near the walls.
• Magnetic field affected severely the slip velocity along the walls of micro-channel.

Simulation of forced convection of FMWNT-water (functionalized multi-walled carbon nano-tubes) nano-fluid in a micro-channel under a magnetic field in slip flow regime is performed. The micro-channel wall is divided into two portions. The micro-channel entrance is insulated while the rest of length of the micro-channel has constant temperature (TC). Moreover, the micro-channel domain is exposed to a magnetic field with constant strength of B0. High temperature nano-fluid (TH) enters the micro-channel and exposed to its cold walls. Slip velocity boundary condition along the walls of the micro-channel is considered. Governing equations are numerically solved using FORTRAN computer code based on the SIMPLE algorithm. Results are presented as the velocity, temperature, and Nusselt number profiles. Greater Reynolds number, Hartmann number, and volume fraction related to more heat transfer rate; however, the effects of Ha and ϕ are more noteworthy at higher Re.