A lattice Boltzmann method for two-phase nanofluid under variable non-uniform magnetic fields

In this study, a new lattice Boltzmann scheme is developed for the two-phase CuO-H2O nanomagnetic fluid (ferrofluid) under a non-uniform variable magnetic field. It introduces the second-order external force term including both MHD (magnetohydrodynamic) and FHD (ferrohydrodynamic) into the lattice Boltzmann equation. The square cavity and a heat source inside the circular cavity with natural convections of nanofluid are investigated, respectively. The effects of Rayleigh number (Ra), the volume fraction of nanoparticles (phi), Hartmann number (Ha) generated by MHD, and magnetic number (Mn-F) generated by FHD on the nanofluid flow and heat transfer properties, as well as the total entropy generation (S-tot) have been examined. The two-phase lattice Boltzmann model has demonstrated that it is more accurate in predicting the heat transfer of nanofluid than the single-phase model. Consequently, the results calculated by the single-phase and the two-phase methods show the opposite trends. It indicates that nanoparticles could enhance heat transfer with maximum values of 1.78% or deteriorate heat transfer with maximum values of 14.84%. The results of the circular cavity show that Ha could diminish the flow intensity, whereas Mn-F could enhance it. The average Nusselt number (Nu(ave)) on the heat source decreases with the augments of Ha and Mn-F but increases with Ra. An optimal volume fraction phi = 1% for heat transfer is obtained except for Ra = 10(4). S-tot achieves the maximum value at Ha = 40 when Ra = 10(5). It increases with a rise of Ra but reduces with an increment of phi. Published under an exclusive license by AIP Publishing.