# 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  
In the first case, water-based nanofluids with the constant wall heat flux (\(q_{w}^{\prime\prime}\) = 10,000 W/m\({}^{2}\)) were considered. Figure 2 shows the results for the fluid temperature in the radial direction and the wall temperature at the constant values of Re = 500 and T\({}_{0}\) = 293.15 K. It may be noted from Figure 2a,  
Figure 1: Comparison of Nu for Al\({}_{2}\)O\({}_{3}\)-water nanofluid. (**a**) Constant heat flux condition at \(\phi_{b}\) = 1%. (**b**) Constant wall temperature condition at \(\phi_{b}\) = 4%. that the fluid temperature decreases with an increase of the nanoparticle concentration from 0 to 10%, especially near the tube wall, suggesting a higher heat transfer rate (above 10%) with nanoparticles. Figure 2b demonstrates the diminution of the wall temperature at different nanoparticle concentrations. The wall temperature decreases by 40 K for the Al\({}_{2}\)O\({}_{3}\)-water nanofluid with nanoparticle concentrations from 0 to 10%. The diminution in temperature reflects a better heat transfer rate at the tube wall. These effects may be explained by the fact that with the presence of the nanoparticles, the thermal properties of the resulting mixture have become more important as the product of \(\rho C_{p}\) and the thermal conductivity have increase with respect to pure water. Figure 3 shows the effect of nanoparticle concentration on the fluid mean temperature and wall temperature in axial direction. It may be noted from Figure 3a that the fluid mean temperature decreases with an increase in the value of \(\phi_{b}\). The decrease in the fluid mean temperature is caused mainly due to the higher thermal conductivity (up to 32%) of the Al\({}_{2}\)O\({}_{3}\)-water nanofluid. The radial, wall and fluid mean temperatures demonstrate that Al\({}_{2}\)O\({}_{3}\)-water nanofluid offers a higher thermal capacity as compared to the water. It may also be observed that at the higher thermal conductivity, the wall-to-fluid heat transfer is more important as it augments the heat transfer rate. Three nanoparticles (Al\({}_{2}\)O\({}_{3}\), TiO\({}_{2}\) and CuO) with two different concentrations (\(\phi_{b}=1\%\) and \(\phi_{b}=10\%\)) were considered to investigate the thermal efficiency of the nanofluids with increase in the particle concentrations as shown in Figure 3b. For the higher nanoparticle concentration (\(\phi_{b}=10\%\)), the wall temperature for Al\({}_{2}\)O\({}_{3}\)-water nanofluid is lower than the TiO\({}_{2}\)-water and CuO-water nanofluids. This lower temperature can be explained with the higher values of thermal conductivity which is 4% higher as compared to TiO\({}_{2}\)-water and 1% higher as compared to CuO-water. The results revealed that Al\({}_{2}\)O\({}_{3}\)-water nanofluids will have a higher transfer coefficient (at least 1%) than the other two nanofluids considered. The nanoparticles concentration has effect on heat transfer performance. A larger number of nanoparticles in the base-fluid increases the thermal conductivity of the nanofluid but it is accompanied with higher values