Lattice Boltzmann method for thermomagnetic convection and entropy generation of paramagnetic fluid in porous enclosure under magnetic quadrupole field

In this study, thermomagnetic convection in a porous cavity filled with paramagnetic fluid under a magnetic quadrupole field is studied using lattice Boltzmann method (LBM), and the corresponding entropy generation is analyzed. The horizontal walls of the porous enclosure are adiabatic, and the temperatures of the vertical walls are different. The effects of Darcy number (Da), porosity (ε), and magnetic force number (γ) on the heat transfer, fluid flow, and entropy generation characteristics are investigated. The results show that, as the magnetic force number increases, the flow is strengthened. The local Nusselt numbers (Nu_loc) increase and the average Bejan number (Be_ave) decreases under the non-gravitational condition. Nu_loc change a little along the hot wall due to the lower value of Darcy number and higher values of Darcy number lead to higher buoyancy forces, Nu_loc change significantly under the gravitational or non-gravitational condition. Moreover, the average Nusselt number (Nu_ave) and total entropy generation (S_total) slightly decrease at first and thereafter increase when the magnetic force dominates the entire domain under the gravitational condition. It is also observed that, when ε₀ = ε₁ = 0.5, γ > 10, the average Nusselt number (Nu_ave) is significantly higher than in the other cases. Furthermore, the average Nusselt number (Nu_ave) reaches its minimum value when ε₀ = ε₁ = 0.5, γ = 4.