Thermal Behavior of Carboxymethyl Cellulose Containing Alumina Nanoparticles at the Entrance Region of an Annulus

This paper investigates the thermal behavior of non-Newtonian nanofluids, specifically carboxymethyl cellulose (CMC) 0.5% and Al₂O₃ nanoparticles, in the fully developed region of a horizontal annulus. A three-dimensional axisymmetric, steady-state numerical solution is performed using the mixture multiphase model to compare with the results obtained from the single-phase model. The present study examines the effects of nanoparticle volume fraction ranging from 0.5% to 1.5% and particle diameters of 25 nm and 50 nm for various Reynolds numbers (Re) within the laminar flow regime. The results indicate that while the temperature profile distribution is slightly affected by changes in alumina concentration, significant variations are observed in the entrance region. Specifically, as Re is enhanced, the Nusselt number (Nu) is increased. For an outer wall heat flux of 1000 W/m² and a 1% concentration, Nu at the x/L = 0.25 section augments from 6.92 to approximately 13.14 as Re is enhanced from 5 to 500. Additionally, for the same conditions, Nu is about 0.78% higher for Al₂O₃ nanoparticles with a diameter of 25 nm than the ones with a diameter of 50 nm. In all cases, there is an acceptable agreement between the results obtained from the mixture and the single-phase models, with discrepancies of less than 1.13%.