Natural convection in the ferrofluid enclosed in a porous and permeable cavity

The thermal transfer in the water-based ferrofluid enclosed porous cavity attached with a novel permeable (suction/injection) chamber is investigated within this research. The mathematical analysis of the problem is fulfilled with the modified Rosensweig-model (mRm) accounting for the Darcy porous medium in cooperation with the energy equation. The relevant governing equations are numerically treated via the successive-over-relaxation method (SOR) based on a special finite difference scheme. The pertinent effects of physical parameters on the convection and heat transfer of the ferrofluid inside the cavity are examined in detail. It is determined that the Nusselt number enhances at the left wall but it is reduced at the right wall if one increases either (i) the concentration of the ferroparticles or (ii) the Lorentz force. But the effect of Kelvin force is different from the effect of the Lorentz force on the Nusselt number in the sense that; the Nusselt number decays at the left wall but it intensifies at the right wall if we increase the Lorentz force or its representative the Hartmann number. In addition, the Nusselt number at the left wall of the cavity rises about 1.4 times if the Hartmann number increases from 0 to 50. The problem setup in the current work may be useful in the applications regarding bio-medical, pharmaceutical and engineering industries. The generated results from the present work quantitatively as well as qualitatively match with the existing literature.