In the present study, the magnetohydrodynamics (MHD) mixed convection of different nanofluids in two cylinders with an inner rotating cylinder is numerically investigated. Three nanoparticles, including Cu, Al2O3, and TiO2, were used as the working fluid. The geometry includes two cylinders, one fixed while another one rotates. Three configurations have been considered, including (1) eccentric cylinders with an eccentricity of + e, (2) concentric cylinders, and (3) eccentric cylinders with an eccentricity of −e. The governing equations were solved using the finite element method (FEM). The nanoparticles’ volume fraction (0 ≤ Φ≤ 0.2), Darcy number (0.001 ≤ Da ≤ 0.1), Richardson number (0.1 ≤ Ri ≤ 10), Hartman number (0 ≤ Ha ≤ 60), the inclination angle of the magnetic field (0◦ ≤ γ ≤ 135◦) and porosity coefficient (0.05 ≤ ε ≤ 1) on Nusselt number and heat transfer have been studied. Also, the influence of the inner cylinder rotation on the heat transfer and flow pattern was investigated. It was found that the average Nusselt number rises by rising porosity, the volume fraction of nanoparticles, and Richardson, while it decreases by increasing the Hartmann number; for example, the Nusselt number decreased by about 54% as the Hartmann number increased from 0 to 100. Besides, it was observed that a sinusoidal trend is observed in the average Nusselt number by increasing the inclination angle of the magnetic field from between 0° and 135°. The results revealed that for the magnetic field’s angle of γ = 90◦, the maximum heat transfer is obtained. The most optimal case, in terms of heat transfer rate, is achieved when the inner cylinder rotates, γ = 90◦, and Cu-water nanofluid is used as a working fluid
