## 4 Results and Discussion
### Effects of Air Speed on Heat Transfer  
By referring to ASHRAE Handbook [20], the heat transfer rate of the heat exchanger Q is calculated via Equation (1):  
\[\text{Q}=\dot{m}\times C_{p}\times\Delta T=\frac{V\times A}{v}\times C_{p} \times(T_{out}-T_{in}) \tag{1}\]  
The results are shown in Figure 7. In general, the heat transfer rates increase as the airspeed increases due to faster forced convective heat removal rate by faster-moving air, irrespective of surface coating conditions. On the other hand, the fin pitch effect varies and depends on the surface conditions. For the hydrophilic coating cases, a smaller pitch results in a larger heat transfer as expected due to a larger FPI. But for the uncoated cases, the pitch  
Figure 6: Pressure drop for heat exchanger with different fin densities.  
of 2.0 mm gives the smallest heat transfer rate; whereas, for the hydrophobic cases, the pitch of 2.5 mm gives the largest results. Furthermore, at the pitch of 1.5 mm, the heat transfer rates of the three types of surfaces are comparable. At the pitch of 2.0 mm, the heat transfer rates of both coated surfaces are still comparable and larger than that of the uncoated surface. However, at the pitch of 2.5 mm, in contrast to the largest heat transfer rate of the hydrophobic coated surface, the hydrophilic coated surface results in the smallest heat transfer rate. That is, at this pitch, hydrophobic coating is better than that without coating in heat transfer, consistent with that of [PERSON] et al. [21]. At this larger pitch, water droplets condensed on the surface can be readily blown away from the hydrophobic surface, but not from the hydrophilic surface due to film formation; thus, resulting in the difference. However, even though the hydrophobic surface gives the largest heat transfer rate, the water droplet being carried away by the air could cause undesirable reliability issues of electronic components and systems and should be avoided. Moreover, the hydrophobic coating also results in larger pressure drops as depicted in Figure 6 which lead to larger energy consumption.  
In other words, both surface coating and morphology could affect the heat transfer rates and could lead to unexpected results of the fin pitch effect as in the cases of both uncoated and hydrophobic coated surfaces. These unexpected situations deserve further investigation for its clarification and practical applications.  
Figure 7: Air heat exchange rates for heat exchanger with different fin densities.  
To further examine the behavior of heat exchanger performance, the pressure drops and heat transfer rates described above are non-dimensionalized in terms of Euler number (\(E_{u}\)) [22], Reynolds number (\(R_{e}\)), and Nusselt number (\(N_{u}\)) through Equations (2)-(4):  
\[E_{u}=\frac{\Delta P}{\frac{1}{2}\rho u_{c}^{2}N} \tag{2}\]  
\[R_{e}=\frac{\rho\times V\times D}{\mu} \tag{3}\]  
\[N_{u}=\frac{h\times D}{k} \tag{4}\]  
In the equations, \(\Delta P\), \(\rho\), \(u_{c}\), \(N\), \(V\), \(D\), and \(\mu\), \(h\), and \(k\) represent the pressure drop, air density, velocity in the constriction area, number of tube rows, velocity, characteristic length, air dynamic viscosity, film coefficient, and thermal conductivity, respectively. Physically, the \(E_{u}\) number is the percentage of the flow kinetic energy being lost per fin due to flow resistance (exhibited by the pressure drop); a larger \(E_{u}\) number indicates a larger energy loss. The \(R_{e}\) number denotes the relative contribution between the inertial and viscous forces; a larger \(R_{e}\) number implies a larger inertial force due to fluid motion. The \(N_{u}\) number represents the relative heat transfer contribution due to fluid motion versus due to fluid conduction; a larger \(N_{u}\) number represents a higher heat transfer rate by the fluid motion. Hence, in practical applications, a smaller \(E_{u}\) number