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Numerical simulation of magnetohydrodynamic natural convection heat transfer in a rhombic enclosure of inclination angle 45 ∘ containing copper-water nanofluid has been presented in this paper. The top and bottom walls of the enclosure are subjected to non-uniform heating while left wall being subjected to lower temperature and right wall being maintained adiabatic. The finite element strategy (COMSOL Multiphysics) is used to solve the governing equations. The numerical simulations are done for the parametric values: 10 4 ≤ Rayleigh number ≤ 10 6 ; 0 ≤ Hartmann number ≤ 100; 0 ≤ volume fraction of nanofluid ≤ 0.05. The phase deviation angle (top wall) is varied in the range from 0 to π with amplitude of non linear heating being maintained constant. The motivation of this research goes with the fact that the associated transport phenomenon conveys the implication of designing an optimal thermal system analogous to the theme of non-uniform heating, with the phase angle being a crucial design parameter. The numerical results depict to the fact, that the rate of heat transfer follows non-monotonic trends and is considerably influenced by interplay of the phase shift angle, Rayleigh number and Hartmann number. The results showed that at Rayleigh number ≥ 10 5 , the heat transfer rate gets inhibited by enhancing the magnetic field intensity. The impact of different types of nano particles is illustrated by comparing the results with the results of three different nanofluids, silver– water, titanium dioxide–water and diamond–water nanofluids. [ABSTRACT FROM AUTHOR]