Laminar Mixed Convection of a Nanofluid in an Inclined Tube using Two-Phase Mixture Model

Low thermal conductivity of conventional heat transfer fluids such as water, oil, and ethylene glycol mixture is a serious limitation in improving the performance and compactness of heat exchanger devices. To overcome this disadvantage, there is a strong motivation to develop advanced heat transfer fluids with substantially higher thermal conductivity. An innovative way of improving the thermal conductivities of fluids is to suspend small solid particles in the fluid. Various types of powders such as metallic, non-metallic and polymeric particles can be added into fluids to form slurries. By improving the technology to make particles in nanometer dimensions, a new generation of solid–liquid mixture that is called nanofluid, was appeared [1]. The dispersion of a small amount of solid nanoparticles in conventional fluids changes their thermal conductivity remarkably. Some benefits of nanofluids that make them useful are: a tiny size, along with a large specific surface area, high effective thermal conductivity and high stability and less clogging and abrasion [2].Convective heat transfer with nanofluids can be modeled using the two-phase or single phase approach. The first provides the possibility of understanding the function of both the fluid phase and the solid particles in the heat transfer process. The second assumes that the fluid phase and particles are in thermal and hydrodynamic equilibrium. This approach is simpler and requires less computational time. Thus it has been used in several theoretical studies of convective heat transfer with nanofluids (see [3] for more references). However, due to the fact that the effective properties of nanofluids are not known precisely, the numerical predictions of this approach are, in general, not in good agreement with experimental results. Therefore, the concerns in single phase modeling consist in selecting the proper effective properties for nanofluids and taking into account the chaotic movement of ultra fine particles. To partially overcome this difficulty, some researches (for instance [4]) have used the dispersion model which takes into account the improvement of heat transfer due to the random movement of particles in the main flow. Due to several factors such as gravity, friction between the fluid and solid particles and Brownian forces, the phenomena of Brownian diffusion, sedimentation, and dispersion may coexist in the main flow of a nanofluid. This means that the slip velocity between the fluid and particles may not be zero [4]; therefore it seems that the two-phase approach could better model nanofluid behaviors. Recently Behzadmehr et al. [5] studied the turbulent forced convection of a nanofluid in a circular tube by using two-phase approach. Their comparison with the experimental results showed that the two-phase mixture model is more precise than the single phase model. Therefore, later Mirmasoumi and Behzadmehr [6] studied the laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model. This paper deals with mixed convection in an inclined tube. Thus the effect of tube inclinations on the nanoparticles distributions and on the hydrodynamics and thermal parameters are presented and discussed for different nanoparticles concentrations and different Gr numbers