Numerical study and optimization of a ferrofluid-filled cavity with thick vertical walls and an elliptical obstacle at the center

This paper investigates the ferrofluid flow within a square cavity considering the effects of viscosity. An elliptical obstacle with a high temperature is placed in the center of the cavity, and the vertical walls are cooled and covered with a conductive layer of varying thickness. Electrical current-carrying wires alongside the cooled walls generate the Kelvin force in the ferrofluid. Variables studied include the Ra and Ha, varying magnetic fields (MF), the thickness and thermal conductivity of the conductive wall, and the aspect ratio (AR). The equations are solved using the finite element method, and entropy (EnY) data and Nu are studied using the response surface method. Statistical analysis revealed that the AR significantly impacts the variations in the Ha and MNF. Results indicated that increasing the Ha decreases the generated EnY and the \({Nu}_{\text{m}}\) ${\mathit{Nu}}_{\text{m}}$ in the cavity, whereas increasing the strength of the varying MF increases both the generated EnY and the \({Nu}_{\text{m}}\) ${\mathit{Nu}}_{\text{m}}$ . An increase in the AR also leads to increased EnY production and \({Nu}_{\text{m}}\) ${\mathit{Nu}}_{\text{m}}$ . The maximum and minimum Nu were observed at conductive wall thicknesses of 0.05 and 0.1, respectively, with a difference of 88.6%. Increasing the wall thickness reduces thermal EnY by up to 91%, fluid EnY by 82.3%, and total EnY by 90.7% compared to their maximum values. Increasing the Ra from 1000 to 1,000,000 results in a 296, 2355, and 65.8% increase in the \({Nu}_{\text{m}}\) ${\mathit{Nu}}_{\text{m}}$ , fluid EnY, and total EnY, respectively, while reducing thermal EnY by 19.6% and Be by 88.8%.