Numerical simulation of thermomagnetic convection of air in a porous square enclosure under a magnetic quadrupole field using LTNE models

In this paper, thermomagnetic convection of air in a two-dimensional porous square enclosure under a magnetic quadrupole field has been numerically investigated. 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 and the energy for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. The results are presented in the form of streamlines and isotherms and local and average Nusselt numbers. Numerical results are obtained for a range of the magnetic force parameter from 0 to 100, the Darcy number from 10−5 to 10−1 and dimensionless solid-to-fluid heat transfer coefficient from 1 to 1000. The results show that the magnetic force number, Darcy number, Rayleigh number and dimensionless solid-to-fluid heat transfer coefficient have significant effect on the flow field and heat transfer in a porous square enclosure. The flow characteristics presents two cellular structures with horizontal symmetry about the middle plane of the enclosure and the Nusselt numbers are increased as the magnetic force number increases under the non-gravitational condition. The average Nusselt number respects the trend of decrease at first and then increases when the magnetic force number increases under gravitational condition. The non-equilibrium effect on fluid phase temperature and solid phase temperature gradually reduces with the increase of value of H.