In this paper, entropy generation due to the combined buoyancy-Marangoni convection of non Newtonian power-law nanofluids in a 3D heterogeneous porous cubic cavity is investigated in detail with the compact high order finite volume method. The fluid in the cavity is a CMC-based nanofluids containing CuO nanoparticles, and the numerical study is conducted for a wide range of heterogeneity level ranging from 0 to 1.5, Marangoni number from 0 to 1000, thermal Rayleigh number from 10(4) to 10(6), buoyancy ratio from -2.0 to -0.1, nanoparticle volume fraction from 0 to 0.1 and power-law index from 0.76 to 1.0 to identify the irreversibility characteristics. The results show that the total entropy generation is considerably affected by the heterogeneity in permeability; it increases when the level of heterogeneity increases. Marangoni number becomes a more effective parameter on total entropy generation for lower values of thermal Rayleigh numbers. For thermal dominated flow, the increase in the buoyancy ratio provokes various irreversibilities to enhance; on the other hand, for solutal dominated flow, the rise of the buoyancy ratio declines the entropy generation. Moreover, it is also shown that the enhancement of the nanoparticle volume fraction reduces the total entropy generation. Apart from that, our numerical tests show the flow field and entropy generation are influenced appreciably by the presence of the power-law index. (C) 2017 Elsevier Ltd. All rights reserved.