Impact of nanoparticle mean diameter and the buoyancy force on laminar mixed convection nanofluid flow in an elliptic duct employing two phase mixture model

Laminar mixed convection Al2O3–water nanofluid flow in an elliptic tube has been simulated. Effects of the nanoparticles mean diameter and buoyancy force on the nanofluid flow behaviors in the elliptic tube have been investigated. The two phase mixture model has been employed to consider the solid nanoparticle behaviors in the base fluid (water). Three-dimensional Navier–Stokes, energy and volume fraction equations have been discretized using the Finite Volume Method (FVM). A uniform heat flux has been applied at the wall boundary conditions. The Brownian motions of nanoparticles have been considered to determine the thermal conductivity and dynamics viscosity of Al2O3–water nanofluid, which depend on the temperature. Variation of the nanoparticles distribution, velocity profiles, friction coefficient and Nusselt number with the nanoparticle mean diameter and Richardson number have been presented and discussed. The generated secondary flows have a major role on the thermal and hydraulic behaviors of nanofluid flow and the nanoparticle distribution. The secondary flows are affected by both the nanoparticle diameter and buoyancy force. At a given Reynolds and Richardson number, an increase in size of nanoparticles reduces the Nusselt number while it does not have a significant effect on the friction factor. Increasing the Richardson number augments the Nusselt number as well as the friction coefficient. There are non-linear relations between the size of the nanoparticle and the nanofluid flow behaviors.