The effect of an external magnetic field on the mixed convection Fe$_{3}$O$_{4}$/water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles 0 ≤ $\varphi$ ≤ 0.05, magnetic numbers 0 ≤ Mn ≤ 100, Reynolds numbers 100 ≤ Re ≤ 500, Darcy numbers 10$^{−3}$ ≤ Da ≤ 10$^{−1}$ and porosity parameters 0.7 ≤ $\epsilon$ ≤ 0.9 while fixing the Grashof number at 10$^{4}$. Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter.