Effects of a magnetic quadrupole field on thermomagnetic convection of air in a porous square enclosure

• The air thermomagnetic convection under a magnetic field is numerically investigated.
• The scalar magnetic potential method is used to calculate the magnetic field.
• The Brinkman–Forchheimer extended Darcy model is used to solve the momentum equations.
• The flow pattern of the air changes with the increase of the magnetic force.
• The magnetic field intensity has important impact on the flow field and heat transfer.

The thermomagnetic convection of air in a two-dimensional porous square enclosure under a magnetic quadrupole field is investigated numerically. The scalar magnetic potential method is used to calculate the magnetic field. A generalized model, which includes a Brinkman term, a Forcheimmer term and a nonlinear convective term, is used to solve the momentum equations. The flow and temperature fields for the air thermomagnetic convection are presented and the local and average Nusselt numbers on the walls are calculated and compared. The results show that the magnetic field intensity, Darcy number and Rayleigh number have a significant effect on the flow field and heat transfer in a porous square enclosure.