Heat transfer and entropy generation of water-Fe3O4 nanofluid under magnetic field by Euler-Lagrange method

The Euler-Lagrange method is considered to simulate the water-Fe3O4 nanofluid inside a circular tube. The non-uniform magnetic field is employed to a part of the tube. The effects of Reynolds number, concentration and magnetic field are investigated. The obtained results show that by increasing the magnetic field strength, global frictional entropy generation rate enhances. Meanwhile, with the application of the magnetic field, the frictional entropy generation rate in the central region of the tube and the vicinity of the wall decreases and increases, respectively. Additionally, the Bejan number is approximately 1 near the outlet. Also, there is a non-uniform distribution for nanoparticles, and the concentration of nanoparticles in the tube center is higher than the wall adjacency. Moreover, the wall temperature of the tube decreases in the part where the magnetic field is applied. The use of nanoparticle leads to an increase in the convective heat transfer coefficient. The velocity of the nanofluid in the central part of the tube decreases with the application of the magnetic field. But, the flow velocity near the wall increases with increasing magnetic field strength.