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• Study MHD mixed convection from two rotating cylinders in a porous trapezoid. • Study on Cu-water nanofluid in a porous medium with different Darcy numbers. • Higher effect of vertical magnetic on decreasing the stream function. • High effect of magnetic field angle on temperature and irreversibilities. The numerical simulation of MHD mixed convection due to a rotating circular solid cylinder in a trapezoidal enclosure filled with a Cu-water nanofluid saturated with a porous media was presented in the current paper. The midpoint of the top wall of the enclosure is considered as a center of a cylinder which has a different radius. The remaining of this wall is considered adiabatic. The bottom wall is heated with the temperature of T h and moving to the right hand, while sidewalls are kept isolated and stationary. The Hartmann number, thermal conductivity ratio, angular rotational velocity, Richardson number, inclination angle, cylinder radius, Darcy number, nanofluid concentration vary in the ranges of 0 to 100, 1 to 10, -5 to 5, 0.01 to 100, 0° to 90°, 0.2 to 0.4, 10 −5 to 10 −1 and 0 to 0.1, respectively. While the convection heat transfer coefficient is considered constant at (h = 5). It was found that, the vertical magnetic field decreases the stream function values more than the inclined and the horizontal fields. Also, the inclination angle of the magnetic field has a profound influence on the thermal performance inside the enclosure. The average Nusselt number rises by raising the Hartmann number, thermal conductivity ratio, cylinder radius and Darcy number, while it decreases by increasing the Richardson number. It was found also that, when the cylinder rotates in a counter clockwise direction (i.e., Ω = 5) and (K r = 10), the Nu ave decreases by about (90 %) when the (Ri) increases from 0.01 to 100. While, it increase by about (35 %) when the (Ha) increases from 0 to 100. Image, graphical abstract [ABSTRACT FROM AUTHOR]