Entropy generation analysis for thermomagnetic convection of paramagnetic fluid inside a porous enclosure in the presence of magnetic quadrupole field

The entropy generation characteristics for thermomagnetic convection in a porous cavity filled with paramagnetic air in the presence of a magnetic quadrupole field are investigated numerically using a finite volume method. The vertical walls of the porous cavity are maintained at different temperatures, whereas the horizontal walls are insulated. The Darcy–Brinkman–Forchheimer model is used for mathematical formulation of the fluid flow in porous media. Thermal, frictional and total entropy generation and Bejan number for a selected range of magnetic force number ( γ = 1–100), Darcy number ( Da = 5 × 10 −4 –5 × 10 −2 ) and Rayleigh number ( Ra = 10 4 –10 6 ) are examined for both cases: (1) with gravity and (2) without gravity. The results indicate that the magnetic field had little or no effect on the total entropy generation for the lower values of Darcy number and the process is dominated by the heat transfer irreversibility. In contrast, the magnetic force provokes various irreversibilities to rise as a result of improved convection at higher Darcy numbers, and the irreversibility is dominated by the viscous effects. This work may give an insight into the design-related concept of entropy generation for various thermal systems and clarifying energy loss.