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–H 2 O nanomagnetic fluid (ferrofluid) under non-uniform variable magnetic field. It introduces second-order external force term including both MHD (magnetohydrodynamic) and FHD (ferrohydrodynamic) into equation. The square cavity heat source inside circular with natural convections of nanofluid are investigated, respectively. effects Rayleigh number ( Ra), volume fraction nanoparticles φ), Hartmann Ha) generated by MHD, Mn F ) on flow transfer properties, as well total entropy generation S tot have been examined. model has demonstrated that it more accurate in predicting than single-phase model. Consequently, results calculated methods show opposite trends. indicates could enhance maximum values 1.78% or deteriorate 14.84%. Ha diminish intensity, whereas it. average Nusselt Nu ave decreases augments but increases Ra. An optimal φ = 1% obtained except Ra 10 4 . achieves value at 40 when 5 rise reduces an increment φ.