In this chapter, based on (Russo, Numerical simulation of magneto-hydro-dynamics inside cardiovascular and respiratory systems. University of Rome Tor Vergata, A.A, 2014/2015.), we present the basis of the numerical approach to Magneto-Hydro-Dynamics (MHD). This branch of fluid dynamics studies the interaction between the flow of electrically conducting fluids and the electromagnetic fields. We show the fundamental conservation equations, i.e. mass, momentum and energy, and their applications to fluid dynamics. A similar discussion for electromagnetic equations is then undertaken; Maxwell equations are derived, and, as the last step, the Navier-Stokes and Maxwell equations are coupled to get the MHD equations. The behaviour of magnetic nanoparticles under the influence of an external magnetic field is investigated. The particles are laden in both air and blood, circulating inside the airways and the hepatic artery. To achieve this goal, the mhdFOAM solver of the OpenFOAM package is modified.