MHD mixed convection of a Cu–water nanofluid flow through a channel with an open trapezoidal cavity and an elliptical obstacle

In the current work, numerical simulations are achieved to study the properties and the characteristics of fluid flow and heat transfer of (Cu–water) nanofluid under the magnetohydrodynamic effects in a horizontal rectangular canal with an open trapezoidal enclosure and an elliptical obstacle. The cavity lower wall is grooved and represents the heat source while the obstacle represents a stationary cold wall. On the other hand, the rest of the walls are considered adiabatic. The governing equations for this investigation are formulated, nondimensionalized, and then solved by Galerkin finite element approach. The numerical findings were examined across a wide range of Richardson number (0.1 ≤ Ri ≤ 10), Reynolds number (1 ≤ Re ≤ 125), Hartmann number (0 ≤ Ha ≤ 100), and volume fraction of nanofluid (0 ≤ φ ≤ 0.05). The current study's findings demonstrate that the flow strength increases inversely as the Reynolds number rises, which pushes the isotherms down to the lower part of the trapezoidal cavity. The Nu_avg rises as the Ri rise, the maximum Nu_avg = 10.345 at Ri = 10, Re = 50, ? = 0.05, and Ha = 0; however, it reduces with increasing Hartmann number. Also, it increase by increasing ?, at Ri = 10, the Nu_avg increased by 8.44% when the volume fraction of nanofluid increased from (? = 0–0.05).