Natural convection heat transfer in corrugated annuli with H₂O-Al₂O₃ nanofluid

The present work includes a numerical study of natural convection heat transfer in symmetrical and unsymmetrical corrugated annuli filled with H₂O-Al₂O₃ nanofluid. In this study, higher and lower temperatures were kept constant at inner and outer cylinders of the annulus; respectively. Eight mathematical models with an aspect ratio of 1.5 were developed to find the best model giving the highest heat transfer rates. The stream-vorticity formulation in curvilinear coordinates was used to solve the governing equations of heat transfer and fluid motion. The influences of Rayleigh number. $$ Ra $$ and volume fraction of nanoparticles. ( $$ on isotherms, streamlines, local and average Nusselt numbers on the inner and outer cylinder were investigated. The results show that the heat transfer rate is significantly increased with an increase in nanoparticles volume fraction and Rayleigh number. The activity of the heated surface is increased with an increase in the undulation number, but the flow motion tends to be most difficult in the spaces between active undulation walls. Moreover, the heat transfer rates in unsymmetrical annuli are relatively higher than the rates in the symmetrical annuli. There are no evident changes in isotherms with an increase in the nanofluid volume fraction. Correlations for the mean Nusselt number on the inner and outer walls of annulus were deduced as a function of Rayleigh number and nanoparticles volume fraction for eight models with an accuracy range of 8-15 %.