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

Abstract

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 ( φ), Hartmann number ( Ha) generated by MHD, and magnetic number ( MnF) generated by FHD on the nanofluid flow and heat transfer properties, as well as the total entropy generation ( Stot) 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 MnF could enhance it. The average Nusselt number ( Nuave) on the heat source decreases with the augments of Ha and MnF but increases with Ra. An optimal volume fraction φ  = 1% for heat transfer is obtained except for Ra = 104. Stot achieves the maximum value at Ha = 40 when Ra  = 105. It increases with a rise of Ra but reduces with an increment of φ.