Numerical simulation on magnetohydrodynamics convection in annulus inclined elliptical enclosure

The present work numerically demonstrates the uniform magnetohydrodynamics Newtonian, laminar natural convection in elliptical cold enclosure with inner hot circular body considering the influence of its vertical movement on the fluid flow and heat transfer. The gap area between the elliptical enclosure and the inner body had been filled by the Al2O3-water nanofluid in the upper layer, whereas lower layer has been filled by the porous medium that has been saturated by an identical nanofluid. The local thermal equilibrium model had been implemented to model the nanofluid and porous media. Additionally, Darcy-Brinkman model considered in the representation of the porous media. The three governing equations of heat and fluid flow like energy and momentum of fluid, in addition to the continuity equation, had been solved numerically utilising finite element formulation. The parameters under investigation are the Rayleigh number value $\left({{{10}<^>3} \le Ra \le {{10}<^>6}} \right)$103 <= Ra <= 106, Darcy number $\left({{{10}<^>{ - 5}} \le Da \le {{10}<^>{ - 1}}} \right)$10-5 <= Da <= 10-1, and Hartmann number $\left({0 \le Ha \le 60} \right)$0 <= Ha <= 60. Additionally, two geometrical parameters had been selected, which are the three different locations of inner cylinder (top, middle, bottom), as well as the four different values of the enclosure's orientation angle $\left({\gamma = 0<^>\circ ,\gamma = 90<^>\circ ,\gamma = 180<^>\circ ,\gamma = 270<^>\circ } \right)$gamma=0 degrees,gamma=90 degrees,gamma=180 degrees,gamma=270 degrees. The results have been presented to reflect the influence of the abovementioned parameters on isotherms and streamlines, besides Nusselt's number. It has been proved that to improve the heat transfer rate, it is better to locate inner body in bottom region. The Nusselt number increases by 17.44% when it is moved from the top to the bottom. Additionally, the Nusselt number along the elliptical enclosure attached to the nanofluid layer when rotating the elliptical body from $\left({\gamma = 0<^>\circ } \right)$gamma=0 degrees into $\left({\gamma = 180<^>\circ } \right)$gamma=180 degrees leads to lower the Nusselt number by 32.3372%. This result is exactly inverse considering Nusselt number along nanofluid-porous layer which proved that increasing the orientation angle from $\left({\gamma = 0<^>\circ } \right)$gamma=0 degrees to $\left({\gamma = 180<^>\circ } \right)$gamma=180 degrees contributed to enhancing Nusselt number by 24.7009%.