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ABSTRACT
In this study, convective heat transfer of Al2O3-water nanofluids (NFs) of various concentrations under laminar flow in a horizontal circular tube with and without considering particle aggregation was numerically investigated by a combined nanoparticle diameter distribution model (NDDM) with the Discrete Phase Model (DPM). Heat transfer coefficient (h), temperature distribution in axial and radial direction, and pressure drop (ΔP) were studied. It turns out that beside a slight pressure drop, heat transfer near the wall will significantly deteriorate when particle aggregation occurs. With an increase in Re numbers, the effects of particle aggregation on the heat transfer performance of the fluid will decrease.
Nomenclature
| Al2O3 | = | aluminum oxide (alumina) |
| Tb | = | base fluid temperature |
| c | = | heat capacity |
| Vi | = | nanoparticle volume fraction |
| Cc | = | Cunningham correction factor |
| vb | = | base fluid velocity |
| Df | = | fractal dimension |
| vp | = | particle velocity |
| Fd | = | drag force |
| vb | = | viscosity of the fluid |
| Fg | = | gravity force |
| vc,j | = | collision volume of the aggregate |
| Fb | = | Brownian force |
| FT | = | thermophoresis force |
| Fv | = | force due to lift motion |
| η | = | variety of correlations between the particle volume fraction and suspension viscosity |
| Fl | = | force due to virtual mass |
| η0 | = | viscosity of the basic fluid of dilute solution |
| Fp | = | force due to pressure gradient |
| Фtot | = | effective of total volume concentration of the aggregate |
| G | = | shear rate |
| βi,j | = | collision rate of particles |
| g | = | acceleration of gravity |
| σ | = | equivalent diameter |
| h | = | heat transfer coefficient (w/m2k) |
| λ | = | molecular mean free path of fluid |
| I | = | unit vector |
| ζi | = | unit-variance-independent Gaussian random number with zero-mean |
| k | = | thermal conductivity |
| λ0 | = | nanofluid thermal conductivity |
| Kn | = | Knudsen number |
| φ | = | nanofluids concentration |
| kB | = | Boltzmann constant |
| αb | = | stress tensor |
| Nu | = | Nusselt number |
| μb | = | shear viscosity of the fluid phase |
| Ni | = | number concentration of flocs |
| xi | = | number of primary particle in section i |
| p | = | pressure |
| Γi,j | = | fragment distribution function |
| ΔP | = | pressure drop |
| ρb | = | base fluid density |
| Pr | = | Prandtl number |
| ρp | = | particle density |
| Re | = | Reynold number |
| Subscripts | = | |
| Si | = | rate of particle breakage |
| b | = | base fluid |
| Sp | = | source term |
| p | = | particle |
| Si | = | rate of particle breakage |
| tot | = | total |
| t | = | time |
| Tp | = | particle temperature |
Nomenclature
| Al2O3 | = | aluminum oxide (alumina) |
| Tb | = | base fluid temperature |
| c | = | heat capacity |
| Vi | = | nanoparticle volume fraction |
| Cc | = | Cunningham correction factor |
| vb | = | base fluid velocity |
| Df | = | fractal dimension |
| vp | = | particle velocity |
| Fd | = | drag force |
| vb | = | viscosity of the fluid |
| Fg | = | gravity force |
| vc,j | = | collision volume of the aggregate |
| Fb | = | Brownian force |
| FT | = | thermophoresis force |
| Fv | = | force due to lift motion |
| η | = | variety of correlations between the particle volume fraction and suspension viscosity |
| Fl | = | force due to virtual mass |
| η0 | = | viscosity of the basic fluid of dilute solution |
| Fp | = | force due to pressure gradient |
| Фtot | = | effective of total volume concentration of the aggregate |
| G | = | shear rate |
| βi,j | = | collision rate of particles |
| g | = | acceleration of gravity |
| σ | = | equivalent diameter |
| h | = | heat transfer coefficient (w/m2k) |
| λ | = | molecular mean free path of fluid |
| I | = | unit vector |
| ζi | = | unit-variance-independent Gaussian random number with zero-mean |
| k | = | thermal conductivity |
| λ0 | = | nanofluid thermal conductivity |
| Kn | = | Knudsen number |
| φ | = | nanofluids concentration |
| kB | = | Boltzmann constant |
| αb | = | stress tensor |
| Nu | = | Nusselt number |
| μb | = | shear viscosity of the fluid phase |
| Ni | = | number concentration of flocs |
| xi | = | number of primary particle in section i |
| p | = | pressure |
| Γi,j | = | fragment distribution function |
| ΔP | = | pressure drop |
| ρb | = | base fluid density |
| Pr | = | Prandtl number |
| ρp | = | particle density |
| Re | = | Reynold number |
| Subscripts | = | |
| Si | = | rate of particle breakage |
| b | = | base fluid |
| Sp | = | source term |
| p | = | particle |
| Si | = | rate of particle breakage |
| tot | = | total |
| t | = | time |
| Tp | = | particle temperature |