ISPH simulations for a variable magneto-convective flow of a ferrofluid in a closed space includes open circular pipes

The time-dependent ferrofluid flow in a square enclosure that includes an open circular pipe has been studied. A variable magnetic field resulting from a magnetic source that is located at a specific point outside the enclosure is taken into account and different thermal conditions are assumed for the inner circular pipe. The mixture consists of water as a based ferrofluid and Fe3O4 as nanoparticles. In addition, basics of the magnetohydrodynamics (MHD) and the ferrohydrodynamics (FHD) are considered during the mathematical formulations of the current physical model. The novel Incompressible Smoothed Particles Hydrodynamics (ISPH) method is applied to solve the dimensionless governing equations. The controlling parameters for this situation are the Hartmann number, magnetic number, solid volume fraction and different locations of the heated part on the inner circular pipe. It is found that maximum values of the stream function are reduced by 74.3% when the Hartmann number Ha is increased from 0 to 30. In addition, insertion the heated part at the bottom right part of the inner pipe gives a best rate of the heat transfer compared to other thermal conditions.