Magnetohydrodynamic mixed convective heat transfer augmentation in a rectangular lid-driven enclosure with a circular hollow cylinder utilizing nanofluids

• When the Richardson number ( Ri) rose from 0.1 to 10, the average heat transfer rate inside the cavity increased by 41.66 %. • The average heat transmission rate inside the cavity decreased by 37.50 %, when Hartmann number ( Ha) increases from 0 to 100. • Nanofluids are capable to modify both the thermal and flow fields. • The average heat transfer rate increased by 23.79 %, when cylinder diameter ( D) increases from 0.9 to 0.20 . The study of magnetohydrodynamic (MHD) effects in a rectangular lid-driven enclosure containing a circular hollow cylinder aims at the utilization of nanofluids markedly enhances heat transmission, leading to enhanced thermal performance and more efficient cooling approaches. The governing equations along with the boundary conditions of the problem have been transformed into a non-dimensional formulation. Finite element method based on Galarkin weighted residual has been employed to figure out the outcome of the non-dimensional and non-linear PDEs. The computational investigations of the flow and thermal field inside the enclosure have been performed by varying the governing and physical parameters, namely: Richardson number (0.1 ≤ Ri ≤ 10), Hartman number (0 ≤ Ha ≤ 100), cylinder diameter (0.09 ≤ D ≤ 0.20), solid volume fraction (0.001 ≤ δ ≤ 0.05)), inclination of magnetic field (0° ≤ ϕ ≤ 90°), and non-dimensional time (0.1 ≤ τ ≤ 1). The numerical investigation shows that the flow pattern, temperature distribution, average Nusselt number (Nu av ) at the heated surface, and average fluid temperature (θ av ) inside the enclosure are notably affected by the aforementioned parameters. In this study, six different water-based nanofluids containing different nanoparticles: Cu, Zn, ZnO, Al₂O₃, Fe₃O₄, and graphene have been considered. It was found that the graphene-water nanofluid demonstrated higher thermal efficiency than the other considered nanofluids. Computational results illustrate that the heat transfer rate increases by 41.66 % as the Richardson number increases from 0.1 to 10, indicating that the convective heat transfer mood is considerably improved. However, an increase in the Hartmann number from 0 to 100 leads to a 37.50 % reduction in average heat transfer within the cavity.