Entropy generation and natural convection of nanoparticle-water mixture (nanofluid) near water density inversion in an enclosure with various patterns of vertical wavy walls

Entropy generation due to laminar natural convection of Cu–water nanofluid near the density maximum of water in a two-dimensional enclosure with various patterns of vertical wavy walls is investigated numerically. In order to study the nature of irreversibility in terms of entropy generation in the presence of nanoparticle near water density inversion, the second law of thermodynamics is applied. The governing equations are formulated using both the Boussinesq and non-Boussinesq homogenous models and solved on a non-uniform mesh using a pressure-based finite volume method. The calculations are performed for Ra number of 105, 106 and a range of nanoparticle volume fraction from 0 and 0.05. The results are presented and discussed in terms of streamlines, isotherms patterns, contours of local entropy generation, average Nusselt number and average entropy generation. It was found that both the density inversion and the presence of nanoparticles play a significant role in the flow field structure, heat transfer characteristics and entropy generation. It was concluded that the Boussinesq approximation gave rise to the higher average heat transfer rate and entropy generation as compared to non-Boussinesq approximation. In addition, the average Nusselt number and entropy generation were found to decrease as the volume fraction of nanoparticle increased. Finally, the formation of bi-cellular flow structure substantiates the effective role of density inversion of water in the free convection characteristics.