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Mesoscopic theory is applied to show the nanoparticles migration through a porous 3D cavity. Various amounts of Lorentz forces, buoyancy and Darcy number on working fluid behavior are considered and depicted. Al_(2)O_(3)-H_(2)O is selected including Brownian motion effect. Outputs are illustrated in views of streamlines, isokinetic and isotherms contours. Outputs display that the enhancing magnetic forces lead to rise in conduction mode. Nu_ave augments with the decrease in Lorentz forces while it improves for stronger Lorentz forces.

Lattice Boltzmann method modeling of magnetic water-based nanofluid through a permeable 3D enclosure