# Enhanced Heat Transfer Performance of the Tube Heat Exchangers Using Carbon-Based Nanofluids
## 4 Results and Discussion
However, most of the total heat transfer capacity of the working fluid in the HE with forced circulation comes from convective heat transfer. The primary factors affecting the convective heat transfer performance are the flow rate of the working fluid and the contact state between the working fluid and the tube wall. The variation in the \(k\) of the working fluid has little effect on the total heat transfer capacity so that two CBNFs with a four-fold difference in concentration have no significant difference in reducing the \(T_{h}\). Therefore, the factor that CBNFs can reduce is mainly that the \(T_{h}\) should be a better combination between the tube wall and the working fluid. Furthermore, CBNFs can achieve a higher mass flow rate because of their higher \(\rho\) under the same volumetric flow rate and heating power. Therefore, a higher mass flow rate of the working fluid can also provide a larger convective heat transfer capacity and thus reduce the \(T_{h}\). In terms of the average value of the overall flow range, the \(T_{h}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 80 W was found to be 0.09 \({}^{\circ}\)C and 0.39 \({}^{\circ}\)C lower than that of water, respectively, while the \(T_{h}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 120 W was 0.28 \({}^{\circ}\)C and 0.23 \({}^{\circ}\)C lower than that of water, respectively. The \(\Delta T_{h-w}\) (temperature difference between heater and working fluid) of test sample for THE at various experimental parameters is presented in Figure 8, according to which, the \(\Delta T_{h-w}\) of CBNFs is smaller than that of water under the same flow rate and heating power, indicating that using CBNF as the working fluid in THE can obtain a higher \(HTC\) (refer to Equation (1)). In terms of the average value of the overall flow range, the \(\Delta T_{h-w}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 80 W is 1.97% and 3.70% lower than that of water, respectively, while the\(\Delta T_{h-w}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 120 W is 2.77% and 2.34% lower than that of water, respectively. Figure 7: The \(T_{h}\) of test samples for THE at various experimental parameters. The \(HTC\) of the test sample for THE at various experimental parameters is shown in Figure 9. The figure shows that the \(HTC\) of CBNFs in most cases (except 0.05 wt% CBNF at 4.5 LPM and 80 W) was higher than that of water under the same flow rate and heating power, indicating that using CBNF as the working fluid in THE can lead to a higher convective heat transfer performance. In terms of the average value of the overall flow range, the \(HTC\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 80 W was 2.40% and 4.52% higher than that of water, respectively, while the \(HTC\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 120 W was 3.33% and 2.96% higher than that of water, respectively. While CBNFs as the working fluid can lead to a high convective heat transfer performance, its use in the system also leads to higher \(P_{pe}\). To further compare the efficiency of the THE system using different working fluids, this study defined the performance index (\(PI_{e}\)) as the ratio of the \(HTC\) to the \(P_{pe}\) as shown in Equation (10). \[PI_{e}=\frac{HTC}{P_{pe}} \tag{10}\]  
The \(PI_{e}\) of the test sample for the THE system at various experimental parameters is shown in Figure 10. In terms of the overall average value, the \(PI_{e}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 80 W was 1.72% and 1.54% higher than that of water, respectively, while the \(PI_{e}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 120 W was 4.04% and 1.42% higher than that of water, respectively. These \(PI_{e}\) values show that the system efficiency of 0.05 wt% CBNF was better than that of 0.2 wt% CBNF and is more suitable for the THE system. Figure 8: The \(\Delta T_{h\text{-}w}\) of test samples for THE at various experimental parameters.