Since advective transport in a ferrofluid can be controlled by using an external magnetic field, magnetic nanofluid (ferrofluid) has various applications to heat transfer processes. Unlike free or forced convection, Ferrohydrodynamic convection is not yet well described. In the literature we see papers with constant magnetic fields; but the assumptions are not accurate, since the fields do not comply with the Maxwell’s equations of electromagnetism. In this study, forced convection heat transfer in a semi annulus lid under the influence of a variable magnetic field is studied. The enclosure is filled with ferrofluid (Fe3O4–water). Control Volume based Finite Element Method (CVFEM) is used to solve the governing equations considering both Ferrohydrodynamic (FHD) and Magnetohydrodynamic (MHD) effects. It is assumed that the magnetization of the fluid is varying linearly with temperature and magnetic field intensity. The effects Reynolds number, nanoparticle volume fraction parameter, magnetic number arising from FHD, and Hartmann number arising from MHD are analyzed. Obtained results indicate that the effects of Kelvin forces are more pronounced for high Reynolds number. Heat transfer enhancement has direct relationship with the Reynolds number and the magnetic number; while it has inverse relationship with the Hartmann number.
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