An analytical study of the periodic laminar forced convection of non-Newtonian nanofluid flow inside an elliptical duct

In this study, an analytical solution was obtained for a laminar forced convection of non-Newtonian nanofluid flowing inside an elliptical duct, with inlet temperature varying periodically with the time. The solution was obtained using the Generalized Integral Transform Technique (GITT). The thermal behavior of Cu-water non-Newtonian nanofluid, described by the power-law model was investigated. Also, an accurate correlation was established to estimate the thermal length required to achieve 99% of the amplitude attenuation. The results show a significant effect of aspect ratio β/α and fluid behavior index on the temperature amplitude reduction. For instance, an elliptical duct with β/α = 0.25 reduces the thermal length Lth more than 50% compared with circular duct. Adding nanoparticles until 5% increases the heat transfer coefficient up to 27% for the cylindrical tube. Besides, the heat transfer coefficient is improved over 42% relatively to the cylindrical configuration by reducing the aspect ratio to 0.25. Therefore, adding 5% of nanoparticles both using an elliptical duct with β/α = 0.25, improves the mean heat transfer coefficient around 83% compared to the flow of water base fluid inside a cylindrical duct.