# Numerical Study of Heat Transfer Enhancement for Laminar Nanofluids Flow
## 3 Results & Discussion
### Case 1: Water-Based Nanofluid in Straight Tube with Constant Heat Flux Using SPH
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Case** & **Base Fluid** & **Nanoparticles** & **Boundary Condition** & **Model** & **vol\%** & **Geometry** \\ \hline
1 & Water & Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO & Constant Heat Flux & SPH & 0–10 & S. Tube \\
2 & EG & Al\({}_{3}\)O\({}_{3}\), TiO\({}_{3}\), CuO, SiO\({}_{2}\), ZnO & Constant Heat Flux & SPH & 0–10 & S. Tube \\
3 & Turbine Oil & Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO & Constant Heat Flux & SPH & 0–10 & S. Tube \\
4 & Water & Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO & Constant Temperature & SPH & 0–10 & S. Tube \\
5 & Water & Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO & Constant Heat Flux & SPH & 0–10 & Microtube \\
6 & Water & Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO & Constant Heat Flux & SPD & 0–10 & S. Tube \\ \hline \end{tabular}
\end{table} 
Table 6: Cases considered to determine the heat transfer coefficient (HTC) enhancement of laminar nanofluids. SPH: single-phase model; SPD: the single-phase dispersion model. Figure 2: Effect of nanoparticle concentration in tube flow: (**a**) fluid temperature profiles at tube exit; (**b**) axial development of wall temperature. of the wall shear stress. Although, the use of nanofluids has heat transfer enhancement capabilities due to their increase viscosity, they will also increase friction/pressure losses. For example, [PERSON] et al. [21] found that there is a 2.5-fold increase in the wall shear stress with a \(\phi_{b}\) = 5% for an Al\({}_{2}\)O\({}_{3}\)-water nanofluid. Because of the friction/pressure losses, the benefits of the higher transfer rates versus the corresponding and drastic increases in viscosity must be considered. In this study, two different nanoparticle concentrations (\(\phi_{b}\) = 1% and \(\phi_{b}\) = 4%) of the water-based Al\({}_{2}\)O\({}_{3}\) nanofluid were used to determine the effect of the nanoparticle concentration. Figure 4 shows that the Nu increases with an increase in nanoparticle concentration for any given value of Re. This is mainly because the nanoparticles increase the thermal conductivity of the base fluid and, hence, augments the convective heat transfer. At low Re (below 100) the Nu is 2.2 times higher for \(\phi_{b}\) = 4% as compared to \(\phi_{b}\) = 1%. For high Re (above 1000) Nu increases less than 10%. Considering this reduction of Nu and the increases of the wall shear stresses using more than \(\phi_{b}\) = 5%, a higher nanoparticle concentration would have to be determined by the specific application. Figure 5 shows a comparison of Nu for the different nanoparticles considered. Among the nanoparticles studied Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\), CuO, SiO\({}_{2}\), ZnO there is evidence that the Al\({}_{2}\)O\({}_{3}\) nanofluid has a marginally higher value (by 4%) of Nu for the Al\({}_{2}\)O\({}_{3}\)-water based nanofluid as compared to the ZnO-water nanofluid. This enhancement in the Nu is relatively lower as the Pr of all the selected  
Figure 4: Comparison of Nu for an Al\({}_{2}\)O\({}_{3}\)-water nanofluid at \(\phi_{b}\) = 0%, 1% and 4%. Figure 3: Effect of nanoparticle concentration in tube flow: (**a**) axial development of T\({}_{m}\); (**b**) axial development of wall temperatures. nanofluids are in the range of 6.7 to 7.3 at \(\phi_{b}\) = 4%. The Nu of SiO\({}_{2}\)-water nanofluid was the second highest since SiO\({}_{2}\) nanofluid has the highest average velocity among the fluids because of the lowest value of density (\(\rho\) = 1046 kg/m\({}^{3}\)). The result indicate that the fluid velocity plays a role on the heat transfer.