Numerical analysis of turbulent natural convection in the presence of wire-induced non-uniform magnetic field inside a porous medium

Turbulent natural convection of $F{e}_3{O}_4$-water ferrofluid with Reynolds Averaged Navier-Stokes (RANS) based turbulence model of $k-\omega$ in the presence of wire-induced non-uniform magnetic field inside a porous medium is simulated, numerically. To discretize and solve the related equations the FVM method and SIMPLE algorithm are implemented. For applying the non-uniform magnetic field, two wires carrying electric currents have been installed below and above the enclosure. Simulations are implemented for different Rayleigh numbers (${10}^6\le \mathrm{Ra}\le {10}^8$), porosity number of ($\eta =0.5\text{and}0.9$), volume fractions of nanoparticles $\left(0\le \varphi \le 4\%\right),$ magnetic field numbers $\left(0\le \mathrm{MFN}\le {10}^9\right)$. According to the results, in low Rayleigh number and high MFN, at the high-volume fraction of nanoparticles, applying a magnetic field optimally influenced transfer and Nusselt number. At high porosity numbers, low Ra numbers and $\varphi =4\%$, the heat transfer rate improved by up to 17 %. However, at high Ra numbers and $\text{high}\varphi$, applying the magnetic field reduces the Nusselt number by almost 12 %.