A highly mixed convection due to the movements of two perpendicular walls of odd-shaped enclosures is examined. The upper and right boundaries are partially heated, and several heating situations based on the positions of the active parts are considered. Also, several directions of the lid-walls movements are examined. The inner medium is a heat generating and the considered Lorentz force is inclined with angle Φ. The mathematical formulations are based on the Brinkman-extended non-Darcy model. The containers are filled with ternary composition nanofluids. The components of the ternary nanofluids are spherical Al2O3 nanoparticles, MWCNT cylindrical nanoparticles and platelet graphene nanoparticles and suitable correlations for the thermophysical properties are introduced. The numerical simulations are carried out using the finite element method (FEM) based on the characteristics–based split (CBS) algorithm. The major outcomes revealed that the ternary composition nanofluids cause an enhancement in the heat transfer rate by 17.65% comparing to the mononanofluids. Also, to get the best mixed convection situation, it is recommended to locate the heat sources in the middle of the outer perpendicular walls, set Re ≥ 100 and make the lower perpendicular walls move in anticlockwise direction to get the best mixed convection situation.