Heat transfer of Fe3O4-water nanofluid in a permeable medium with thermal radiation in existence of constant heat flux

•Magnetic field effect on Fe3O4 -water nanofluid behavior is investigated.•CVFEM is applied to simulate this problem.•Nusselt number increases with rise of Darcy and Rayleigh numbers.•Nusselt number decreases with increase of Hartmann number.

Influence of non-uniform magnetic field on Fe3O4-water ferrofluid flow in a porous cavity is simulated. Shape factor effect on nanofluid properties is taken into consideration. Vorticity stream function formulation is reported. The solutions of final equations are obtained using CVFEM. Figures are depicted for different values of radiation parameter (Rd), Darcy number (Da), Fe3O4-water volume fraction (ϕ), Rayleigh (Ra) and Hartmann (Ha) numbers. Results show that augmenting in Hartmann number leads to decrease in velocity of nanofluid and heat transfer rate. Utilizing Platelet shaped nanoparticles results the highest Nusselt number.