Magnetohydrodynamic and ferrohydrodynamic

Magnetohydrodynamic and ferrohydrodynamic are investigated in this chapter. The existence of a magnetic field has a noticeable effect on heat transfer reduction under natural convection and mixed convection, but in many engineering applications such as magnetic sensors, magnetic storage media, and cooling systems of electronic devices, increasing heat transfer from solid surfaces is a goal. Therefore, the effect of the magnetic field on nanofluid flow and heat transfer has been considered via several examples. There are two models for simulating nanofluid flow and heat transfer: single phase and two phase. In the single-phase model, nanoparticles are in thermal equilibrium, and there are not any slip velocities between the nanoparticles and fluid molecules; thus, they have a uniform mixture of nanoparticles. In the two-phase model, the nanoparticles cannot accompany the fluid molecules because of some slip mechanisms such as Brownian motion and thermophoresis, so the volume fraction of the nanofluid may not be uniform anymore, and there would be a variable concentration of nanoparticles in a mixture. Finally, the governing equations for natural convection and mixed convection of nanofluids are presented considering a magnetic field.