# Enhanced Heat Transfer Performance of the Tube Heat Exchangers Using Carbon-Based Nanofluids
## 4 Results and Discussion  
The Re of the test sample for THE at various experimental parameters is shown in Figure 4. The Re is in laminar flow under most of the experimental parameters (only two experimental parameters with water at 5.5 LPM had Re slightly higher than 2100). An increase in the \(\rho\) of the working fluid increases the Re, while an increase in the \(\mu\) of the working fluid decreases the Re at the same flow rate. The difference in \(\rho\) of water and CBNFs is very small (within 0.13%), so, the difference in Re that affects water and CBNFs is mainly due to the difference in \(\mu\) of water and CBNFs. CBNFs have a significantly higher \(\mu\) than that of water. Therefore, the Re of CBNFs is expected to be lower than that of water at the same flow rate and heating power. In terms of the average value of the overall flow range, the Re of 0.05 wt% CBNF and 0.2 wt% CBNF at a heating power of 80 W was 9.20% and 11.12% lower than that of water, respectively. Likewise, the Re of 0.05 wt% CBNF and 0.2 wt% CBNF at a heating power of 120 W was 9.73% and 11.74% lower than that of water, respectively. The \(P_{f}\) of test sample for THE at various experimental parameters is presented in Figure 5, according to which, the CBNFs flowing through THE have a greater \(P_{f}\) than water under the same flow rate and heating power. This phenomenon is mainly due to the higher \(\mu\) of CBNFs, which results in a higher pressure drop when flowing through THE. In addition, in the case of 5.5 LPM, the difference between the \(P_{f}\) of CBNFs and water increases significantly. This phenomenon occurs mainly because, at high flow rates, the two-phase flow characteristics of CBNFs are more obvious, which leads to an increase in pressure drop of the. In terms of the average value of the overall flow range, the \(P_{f}\) of 0.05 wt% CBNF and 0.2 wt% CBNF at a heating power of 80 W is 6.46% and 7.00% higher than that of water, respectively; likewise, the \(P_{f}\) of 0.05 wt% CBNF and 0.2 wt% CBNF at a heating power of 120 W is 6.70% and 6.75% higher than that of water, respectively. The pump power consumption (\(P_{pe}\)) of the test sample for THE system at various experimental parameters is presented in Figure 6. According to this figure, the use of CBNFs as a working fluid in THE system has little effect on \(P_{pe}\) compared with that of water under the same flow rate and heating power. Some 0.05 wt% CBNFs have a slightly lower \(P_{pe}\) than water when the heating power is 120 W. This phenomenon is mainly because CBNMs and GA in CBNFs provide a lubrication effect on the rotating machinery of the pump and reduce the effect of viscosity on the \(P_{pe}\). In addition, the flow resistance of the working fluid in the pipeline does not have a significant influence on the centrifugal pump. Therefore, we observed no fixed relationship between the \(P_{pe}\) in the system and the \(P_{f}\) of the working fluid in the for CBNFs and water. In terms of the average value of the overall flow range, the \(P_{pe}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 80 W was 0.64% and 2.86% higher than that of water, respectively; likewise, the \(P_{pe}\) of 0.05 wt% and 0.2 wt% CBNF at a heating power of 120 W had a difference of \(-\)0.65% and 1.48%, respectively, compared to that of water. Figure 4: The Re of test samples for THE at various experimental parameters. Figure 7 shows the \(T_{h}\) of test sample for THE at various experimental parameters. According to the figure, the use of CBNFs can reduce the \(T_{h}\) under the same flow rate and heating power, and in most cases, 0.2 wt% CBNF can reduce the \(T_{h}\) better than 0.05 wt% CBNF. A low heater temperature helps to extend the service life of the heater. Generally, a  
Figure 5: The \(P_{f}\) of test samples for THE at various experimental parameters. Figure 6: The \(P_{pe}\) of test samples for THE system at various experimental parameters. high-concentration NF has a higher \(k\) and can provide better heat conduction.