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The current work examines the effects of a bottom trapezoidal solid body and a magnetic field on mixed convection in a lid-driven square cavity. The Al2O3-water nanofluid used is assumed to obey Buongiorno’s two-phase model. An isothermal heater is placed on the bottom base of the trapezoid solid body, while the cavity’s vertical walls are kept cold at temperature Tc. The top moving wall and the remaining portions of the cavity’s bottom wall are thermally insulated. The Galerkin weighted residual finite element method is employed to solve the dimensionless governing equations. The parameters of interest are the Richardson number (0.01 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 50), nanoparticle volume fraction (0 ≤ φ ≤ 0.04), and the length of the bottom base of the trapezoidal solid body. The obtained results show that increasing the Richardson number or decreasing the Hartmann number tends to increase the heat transfer rate. In addition, both the thermophoresis and Brownian motion greatly improve the convection heat transfer. It is believed that the current work is a good contribution to many engineering applications such as building design, thermal management of solar energy systems, electronics and heat exchange.

MHD Mixed Convection in a Lid-Driven Cavity with a Bottom Trapezoidal Body: Two-Phase Nanofluid Model