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In this work, the finite element method is employed to simulate heat transfer and irreversibilities in a mixed convection two-phase flow through a wavy enclosure filled with water–alumina nanoliquid and contains a rotating solid cylinder in the presence of a uniform magnetic field. Impact of the variations of undulations number (0 ≤ N ≤ 5), Ra (10 3  ≤ Ra ≤ 10 6 ), Ha (0 ≤ Ha ≤ 100), and angular rotational velocity (− 500 ≤ Ω ≤ 500) were presented. Isotherms distribution, streamlines and isentropic lines are displayed. The governing equations are verified by using the Galerkin Finite Element Method (GFEM). The Nusselt numbers are calculated and displayed graphically for several parametric studies. The computational calculations were carried out using Buongiorno's non-homogeneous model. To illustrate the studied problem, a thorough discussion of the findings was conducted. The results show the enhacement of the maximum value of the flow function and the heat transfer process by increasing the value of Rayleigh number. Furthermore the irreversibility is primarily governed by the heat transfer component and the increment of the waviness of the active surfaces or the cylinder rotational velocity or hartmann number will suppress the fluid motion and hinders the heat transfer process.

Galerkin finite element analysis of magneto two-phase nanofluid flowing in double wavy enclosure comprehending an adiabatic rotating cylinder