In the present chapter, based on (Russo, Numerical simulation of MagnetoHydroDynamics inside cardiovascular and respiratory systems, PhD Thesis. University of Rome Tor Vergata, A.A, 2014/2015), we present the study on the influence of the magnetic field in the fluid dynamics of airflow by coupling the Navier-Stokes and Maxwell equations. We investigate a section of the trachea by using the open-source software VMTK (Vascular Modelling Toolkit) to obtain the reconstructed geometries. We study both steady and unsteady states. In the steady state, we assume a parabolic velocity profile at the inlet, whereas in the unsteady state, we employ a Womersley-periodic velocity profile. As far as the outlet boundary conditions are concerned, in the steady state, we set-up a constant flow rate, whereas in the unsteady state, we impose the value of air velocity. As far as the magnetic field is concerned, we study the magnetic field generated by a rectangular coil.