The present work analyses magnetohydrodynamic natural convection heat transfer and entropy generation in rhombic enclosures filled with Cu-water nanofluids. Numerical simulations were executed for varying Rayleigh number (Ra) in the range 10(3)-10(6), Hartmann number (Ha) in the range 0-100 and inclination angles of the enclosure (30, 45 and 60) considering three different volume fractions of the nano fluid (1%, 3% and 5%). The results indicate that at low Ra, the heat transfer rate remains invariant with the variation in Ha. At high Ra (>10(5)), the presence of the magnetic field is more perceptible implying that the reduction in heat transfer rate with the increase in magnetic field intensity is far more significant. The heat transfer rate enhances with the increase in inclination angle for all Ha for Ra =10(3) and 10(4). However, at high Ra (=10(5) and 10(6)) the trend becomes contrasting due to the interplay of buoyancy and Lorentz forces. There exists an operating range of Ha in the convection regime wherein the efficacy of the nanofluid in augmenting the heat transfer rate is negated when compared to the corresponding performance of the base fluid. The concomitant thermal identity resulting due to the combined interactions of Hartmann number and volume fraction of the nanofluid have been presented. The entropy generation rate decreases with the increase in Ha for all values of Ra and inclination angles of the enclosure. (C) 2019 Elsevier Ltd. All rights reserved.