In this study, the entropy treatment of a nanomaterial flow in the existence of Lorenz forces within a porous domain is carried out via the non-Darcy model. Fe3O4-water is the ferrofluid flowing through the porous enclosure under the magnetic force impact. Simulations for different Darcy, Rayleigh and Hartmann numbers have been reported by applying the novel numerical simulation approach of the control-volume FEM. The outputs of the simulations showed that increasing permeability makes Be to decline, boundary layer thickness enhances with a rise of Lorentz force. In the end, based on the obtained outcomes and employing curve-fitting on the plots, two precise formulas were suggested for the estimation of the Bejan number and average Nusselt number.
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