*5.3.1 The correlation of Goto et al.*

Apply equation from (81) to (91) to calculate pressure drop as below: Frictional pressure gradient:

$$\left(\frac{\text{dP}}{\text{dz}}\right)\_{\text{f}} = \Phi\_{\text{v}}^{2} \left(\frac{\text{dP}}{\text{dz}}\right)\_{\text{v}} = \Phi\_{\text{v}}^{2} 2 \text{f}\_{\text{e}, \text{v}, \text{Go}} (\text{Gr})^{2} / (\rho\_{\text{v}} \text{d}\_{\text{e}})$$

$$\begin{split} \mathbf{X}\_{\text{tt}} &= \left(\frac{1-\mathbf{x}}{\mathbf{x}}\right)^{0.9} \left(\frac{\rho\_{\text{v}}}{\rho\_{\text{l}}}\right)^{0.5} \left(\frac{\mu\_{\text{l}}}{\mu\_{\text{v}}}\right)^{0.1} = \left(\frac{1-0.5}{0.5}\right)^{0.9} \left(\frac{13.9}{1225.5}\right)^{0.5} \left(\frac{0.000253}{0.0000114}\right)^{0.1} \\ &= 0.1452 \end{split}$$

$$\Phi\_{\text{v}} = 1 + 1.64 \mathbf{X}\_{\text{tt}}^{0.79} = 1 + 1.64 \mathbf{0} \mathbf{x} 145 2^{0.79} = 1.3571$$

$$Re\_{\epsilon, v} = \frac{\mathbf{G} \times \mathbf{d}\_{\epsilon}}{\mu\_{v}} = \frac{222 \times 0.5 \mathbf{c} 0.00896}{0.0000114} = 87242.11$$

Compare Re e,v to get f e,v,Go

$$\text{Re}\_{\text{e,v}} \le 2000; = > \text{f}\_{\text{e,v,Go}} = 16/\text{Re}\_{\text{e,v}}$$

$$2000 \le \text{Re}\_{\text{e,v}} \le 2 \text{600}; = > \text{f}\_{\text{e,v,Go}} = 0.000147 \,\text{Re}\_{\text{e,v}}^{0.53}$$


#### **Table 2.**

*Heat transfer coefficient and pressure drop during the boiling process.*

*A Review on Convective Boiling Heat Transfer of Refrigerants in Horizontal Microfin-Tubes… DOI: http://dx.doi.org/10.5772/intechopen.100024*

$$2600 \le \text{Re}\_{\text{e,v}} \le 6500; \ = > \mathbf{f}\_{\text{e,v,Go}} = 0.046 \,\text{Re}\_{\text{e,v}}^{-0.2}$$

$$6500 \le \text{Re}\_{\text{e,v}} \le 12700; \ = > \mathbf{f}\_{\text{e,v,Go}} = 0.00123 \,\text{Re}\_{\text{e,v}}^{0.21}$$

$$12700 \le \text{Re}\_{\text{e,v}}; \ = > \mathbf{f}\_{\text{e,v,Go}} = 0.0092$$

With 12700≤ Re e,v ¼ 87242*:*11; ¼ >f e,v,Go ¼ 0*:*0092

$$\begin{split} \left(\frac{\text{dP}}{\text{dz}}\right)\_{\text{f}} &= \Phi\_{\text{v}}^{2} \left(\frac{\text{dP}}{\text{dz}}\right)\_{\text{v}} = \frac{\Phi\_{\text{v}}^{2} 2 \mathbf{f}\_{\text{e},\text{v},\text{Go}} (\text{Gx})^{2}}{(\rho\_{\text{v}} \text{d}\_{\text{e}})} = \frac{(1.3571)^{2} \text{x} 2 \mathbf{x} (0.0092) (222 \mathbf{x} \mathbf{0}.\mathbf{5})^{2}}{(13.9 \mathbf{x} \mathbf{0}.0089 \mathbf{6})} \\ &= 3352.52 \left(\frac{\text{Pa}}{\text{m}}\right) \end{split}$$

Apply the same procedure at each data point of quality x of refrigerant from 0.1 to 0.99 to determine heat transfer and pressure drop during the convective boiling. Data results are obtained in **Table 2**.
