Critical investigation of thermally developing nanofluid flow within slippery tubes and channels: An extended Graetz-Nusselt problem with longitudinal conduction and power-law nanofluid

The Graetz-Nusselt problem is addressed with non-Newtonian power-law nanofluid with slip boundary conditions. In the said fluid model, the power-law coefficient m and flow index n depend on the nanoparticles concentration φ. The Al_2 O_3-water nanofluid is considered and results are obtained for typical values of nanoparticle concentration i.e., φ=1%,2%,3%,4% and 5%. First of all, we calculate the analytical solution of fully developed velocity field for power-law nanofluid via Navier linear slip law. Next, the temperature profile is obtained by utilizing the condition of specified surface temperature. The longitudinal conduction (realizable for small Peclet number) is also considered. The graphical results of mean temperature and local Nusselt number are presented for various values of slip length, nanoparticle concentration, power-law index and Peclet number. As expected, the concentration of nanoparticles boosts the heat transfer rate while the slippery boundaries always provide larger flow rates of nanofluid. The analysis reveals that local Nusselt number and mean temperature are enhanced in the presence of nanoparticles concentration. Furthermore, the thermal entry length is considerably enhanced upon raising the nanoparticle concentration and slip length. Moreover, the impact of slip length on local Nusselt number is opposite to the effect of Péclet number.