# Effect of Nanofluids on Boiling Heat Transfer Performance
## 2 Nanofluid Application in Engineering
### Nanofluid Application in Heat Pipes  
Heat pipes operate under a number of physical constraints including the capillary, boiling, sonic and entrainment limits that fundamentally affect their performance [29]. Temperature gradients near the heated end may be high enough to generate significant Marangoni forces that oppose the return flow of liquid from the cold end in heat pipes. In the presence of significant Marangoni forces, dry out is not the initial mechanism limiting performance, but that the physical cause is exactly the opposite behavior: flooding of the hot end with liquid. The observed effect is a consequence of the competition between capillary and Marangoni-induced forces. Maximum heat transfer ability was estimated as the minimal value from the heat transfer abilities specified by the hydrodynamic, the sonic and the boiling crisis limitations in the HPs. These limitations were calculated as [30] follows. The hydrodynamic limit,  
\[\mathrm{Q_{max}^{hyd}}=2.19\frac{\mathrm{N}\cdot\mathrm{S}\cdot\mathrm{F_{W}}}{ \mathrm{L_{eff}}} \tag{1}\]  
The sonic limit,  
\[\mathrm{Q_{max}^{sn}}=\mathrm{F_{vc}}\cdot\mathrm{\rho_{v}}\cdot\mathrm{T} \cdot\sqrt{\frac{\gamma_{v}\mathrm{R_{\mu}^{v}}\mathrm{T_{s}}}{2\mu(\gamma_{v} +1)}} \tag{2}\]  
The boiling crisis limit,  
\[\mathrm{Q_{max}^{b}}=\mathrm{L_{ev}}\frac{2\pi\mathrm{\lambda_{eff}^{w}} \mathrm{T_{s}}}{\mathrm{r\rho_{v}}\ln(\frac{\mathrm{d}^{sh}}{\mathrm{d_{vc}}})} (\frac{2\beta}{\mathrm{r_{cr}^{b}}}-\mathrm{P_{c}}) \tag{3}\]  
Figure 2 depicts the choosing of the optimal wick parameters. It can be seen from Figure 2 that the heat transfer ability at saturation temperatures below \(-20\)\({}^{\circ}\)C is extremely low and in the temperature range of \(-60\)\({}^{\circ}\)C\(\sim\)\(0\)\({}^{\circ}\)C is specified by the sonic limit; at \(0\)\({}^{\circ}\)C\(\sim\)+40\({}^{\circ}\)C, the hydrodynamic limit; and at \(+40\)\({}^{\circ}\)C\(\sim\)+60\({}^{\circ}\)C, the boiling crisis limit. Heat pipe that is a compact and effective heat exchanger includes microchannel heat pipe, mesh wick heat pipe, sintered core heat pipe, oscillating heat pipe and thermosyphon heat pipe, and other heat pipe forms [31]. The researchers conducted experimental studies on different types of nanofluids such as Al\({}_{2}\)O\({}_{3}\)[32; 33], CuO [34; 35], SiO\({}_{2}\)[36; 37], Fe\({}_{2}\)O\({}_{3}\)[38; 39], and graphene nanosheets [40; 41; 42] in heat pipes. The results indicated that nanofluids can enhance heat transfer of the heat pipes. Figure 3 shows the working principle of the heat pipe. Figure 2: Choice of optimal wick parameters [30]. [PERSON] [18] et al. studied the heat transfer performance of heat pipes and mesh cores filled with water-based graphene oxide nanofluid (GON) with volume concentrations of 0.01% and 0.03%. The experimental results show that the nanofluid makes the wall temperature lower than the water. In addition, heat pipes containing graphene oxide exhibit lower evaporation heat resistance. The 0.01% GON exhibits better heat transfer due to the different nanoparticle layers deposited on the core structure. The nanoparticle deposition layer changes the capillary force, resulting in an increase in the maximum fluid velocity through the core structure. [PERSON] et al. [43] studied the heat transfer characteristics of graphene nanosheets (GNs) nanofluids in an oscillating heat pipe. The volume concentration of graphene was 1.2-16.7% and the filling rate was 45-90%. The results showed that compared with deionized water, GNs nanofluids improve the heat transfer characteristics of the oscillating heat pipe, and the optimum concentration is 2-13.8%, mainly because the addition of GNs reduces the drying phenomenon of the heated surface. In addition, [PERSON] [44], [PERSON] [45], [PERSON] [46], and others also studied the effect of nanofluids on the heat transfer of heat pipes, and found that the addition of nanofluids can enhance the heat transfer characteristics of heat pipes.