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Purpose The purpose of this paper is to investigate the convective heat transfer of magnetic nanofluid (MNF) inside a square enclosure under uniform magnetic fields considering nonlinearity of magnetic field-dependent thermal conductivity. Design/methodology/approach The properties of the MNF (Fe3O4+kerosene) were described by polynomial functions of magnetic field-dependent thermal conductivity. The effect of the transverse magnetic field (0 < H < 105), Hartmann Number (0 < Ha < 60), Rayleigh number (10 <Ra <105) and the solid volume fraction (0 < φ < 4.7%) on the heat transfer performance inside the enclosed space was examined. Continuity, momentum and energy equations were solved using the finite element method. Findings The results show that the Nusselt number increases when the Rayleigh number increases. In contrast, the convective heat transfer rate decreases when the Hartmann number increases due to the strong magnetic field which suppresses the buoyancy force. Also, a significant improvement in the heat transfer rate is observed when the magnetic field is applied and φ = 4.7% (I = 11.90%, I = 16.73%, I = 10.07% and I = 12.70%). Research limitations/implications The present numerical study was carried out for a steady, laminar and two-dimensional flow inside the square enclosure. Also, properties of the MNF are assumed to be constant (except thermal conductivity) under magnetic field. Practical implications The results can be used in thermal storage and cooling of electronic devices such as lithium-ion batteries during charging and discharging processes. Originality/value The accuracy of results and heat transfer enhancement having magnetic field-field-dependent thermal conductivity are noticeable. The results can be used for different applications to improve the heat transfer rate and enhance the efficiency of a system.

-In this paper, the natural convection heat transfer process is investigated inside an annular enclosure filled with a magnetic nanofluid (Fe 3 O 4 magnetic nanoparticles dispersed in Kerosene). A uniform magnetic field (H) is applied along the axial direction of the enclosure. Thermal conductivity (k) is considered as a function of magnetic field. A nonlinear relationship between magnetic field and thermal conductivity in the magnetic nanofluid (MNF) is assumed and interpolated. Finite element method is utilized to solve the governing equations and calculate the Nusselt number and it is presented as a function of volume fraction and magnetic field strength. The results show the significant effect of applied magnetic field on heat transfer rate, more specifically on Nu, in the enclosure when higher volume fractions of nanoparticles are used. Thermal conductivity enhancement as a result of using magnetic field can be used for various applications such as thermal energy storage in which the heat transfer needs to be accurately controlled.