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ABSTRACT
This study compares the prediction of two types of Computational Fluid Dynamics (CFD) models to investigate the turbulent forced convection of the Cu-water nanofluid in a tube with a constant heat flux on the tube wall. One of the CFD models is based on a single-phase (or homogeneous) model and the other is the Eulerian–Eulerian (two-fluid) two-phase model. The Reynolds number is between 10,000 and 25,000, whereas the volume fraction of the Cu particles is in the range of 0–1.5%. The results from the CFD models are compared with the results from experimental investigations in the literature. Both the single-phase and two-phase models overpredict the Nusselt number in most of the cases investigated. Unexpectedly, the two-phase model was found to be relatively less accurate than the single-phase model. The present study suggests a correction of the two-phase model in terms of selecting an appropriate effective conductivity of the solidus phase and this has resulted in a significant improvement in the predictions of the accuracy of the model. A correlation describing the effective conductivity of the solidus phase of Cu-water nanofluid as a function of the Reynolds number and particle concentrations is developed for use in the Eulerian–Eulerian two-phase model. To the best of our knowledge, such an improvement to a two-phase model has been presented for the first time.
Nomenclature
| CD | = | drag coefficient |
| cp | = | specific heat capacity at constant pressure (J/kg · K) |
| dp | = | nanoparticle diameter (m) |
| Fd | = | drag force (N) |
| h | = | heat transfer coefficient based on mean temperature (w/m2 k) |
| hv | = | volumetric heat transfer coefficient (W/m3 k) |
| hp | = | liquid-particle heat transfer coefficient (W/m2 k) |
| I | = | turbulent intensity |
| I0 | = | initial turbulent intensity |
| k | = | thermal conductivity (W/m K) |
| k | = | turbulence kinetic energy (m2/s2) |
| Nu | = | Nusselt number (h.D/λ) |
| Nup | = | particle Nusselt number |
| p | = | static pressure (N/m2) |
| Pr | = | liquid Prandtl number |
| q″ | = | heat flux (w/m2) |
| Re | = | Reynolds number |
| Rep | = | Reynolds number |
| r,z | = | 2D axisymmetric coordinates (m) |
| T | = | temperature (K) |
| t′ | = | fluctuating part of temperature (K) |
| V | = | velocity (m/s) |
| u′ | = | fluctuating part of velocity (m/s) |
| Greek Letters | = | |
| ϵ | = | dissipation rate of turbulence kinetic energy (m2/s3) |
| μ | = | dynamic viscosity (kg/m s) |
| μt | = | turbulent viscosity (kg/m s) |
| ρ | = | density (kg/m3) |
| β | = | friction coefficient (kg m−3 s−1) |
| Γ | = | defined in Eq. (34) |
| ν | = | kinematic viscosity |
| ϕ | = | particle volume fraction |
| Subscripts | = | |
| eff | = | effective |
| f | = | fluid |
| p | = | particle phase |
| r | = | radial direction |
| s | = | solid |
| w | = | wall |
| z | = | axial direction |
| - | = | mean |
| 0 | = | initial |
Nomenclature
| CD | = | drag coefficient |
| cp | = | specific heat capacity at constant pressure (J/kg · K) |
| dp | = | nanoparticle diameter (m) |
| Fd | = | drag force (N) |
| h | = | heat transfer coefficient based on mean temperature (w/m2 k) |
| hv | = | volumetric heat transfer coefficient (W/m3 k) |
| hp | = | liquid-particle heat transfer coefficient (W/m2 k) |
| I | = | turbulent intensity |
| I0 | = | initial turbulent intensity |
| k | = | thermal conductivity (W/m K) |
| k | = | turbulence kinetic energy (m2/s2) |
| Nu | = | Nusselt number (h.D/λ) |
| Nup | = | particle Nusselt number |
| p | = | static pressure (N/m2) |
| Pr | = | liquid Prandtl number |
| q″ | = | heat flux (w/m2) |
| Re | = | Reynolds number |
| Rep | = | Reynolds number |
| r,z | = | 2D axisymmetric coordinates (m) |
| T | = | temperature (K) |
| t′ | = | fluctuating part of temperature (K) |
| V | = | velocity (m/s) |
| u′ | = | fluctuating part of velocity (m/s) |
| Greek Letters | = | |
| ϵ | = | dissipation rate of turbulence kinetic energy (m2/s3) |
| μ | = | dynamic viscosity (kg/m s) |
| μt | = | turbulent viscosity (kg/m s) |
| ρ | = | density (kg/m3) |
| β | = | friction coefficient (kg m−3 s−1) |
| Γ | = | defined in Eq. (34) |
| ν | = | kinematic viscosity |
| ϕ | = | particle volume fraction |
| Subscripts | = | |
| eff | = | effective |
| f | = | fluid |
| p | = | particle phase |
| r | = | radial direction |
| s | = | solid |
| w | = | wall |
| z | = | axial direction |
| - | = | mean |
| 0 | = | initial |