**2.1 The flow pattern map of Rollmann and Spindler**

Rollmann and Spindler [1] modified the procedure from Wojtan et al. [2] and introduced their method to build the flow pattern map for boiling in microfin tube as given in below (**Figure 2**):

Void fraction ε: Rouhani-Axelsson correlation

$$\mathbf{e} = \frac{\mathbf{x}}{\rho\_{\rm V}} \left( [\mathbf{1} + \mathbf{0}.\mathbf{1}2(\mathbf{1} - \mathbf{x})] \left[ \left( \frac{\mathbf{x}}{\rho\_{\rm V}} \right) + \left( \frac{\mathbf{1} - \mathbf{x}}{\rho\_{\rm L}} \right) \right] + \frac{\mathbf{1}.\mathbf{1}8(\mathbf{1} - \mathbf{x}) [\mathbf{g}\sigma(\rho\_{\rm L} - \rho\_{\rm V})]^{0.25}}{\mathbf{G}\rho\_{\rm L}^{0.5}} \right)^{-1} \tag{1}$$

Stratified angle θstrat: Biberg correlation [19]

$$\begin{split} \boldsymbol{\Theta}\_{\text{strat}} &= 2\pi - 2 \left\{ \pi (\mathbf{1} - \boldsymbol{\varepsilon}) + \left( \frac{3\pi}{2} \right)^{1/3} \left[ \mathbf{1} - 2(\mathbf{1} - \boldsymbol{\varepsilon}) + (\mathbf{1} - \boldsymbol{\varepsilon})^{\ddagger} - \boldsymbol{\varepsilon}^{\ddagger} \right] \\ &- \frac{1}{200} (\mathbf{1} - \boldsymbol{\varepsilon}) \boldsymbol{\varepsilon} [\mathbf{1} - 2(\mathbf{1} - \boldsymbol{\varepsilon})] \left[ \mathbf{1} + 4 \left( (\mathbf{1} - \boldsymbol{\varepsilon})^2 + \boldsymbol{\varepsilon}^2 \right) \right] \right\} \end{split} \tag{2}$$

Geometrical parameters for two phase flow in a circular tube are showed in **Figure 3**.

$$\mathbf{A}\_{\rm LD} = \frac{\mathbf{A}\_{\rm L}}{\mathbf{D}^2} = \frac{\mathbf{A}(\mathbf{1} - \boldsymbol{\varepsilon})}{\mathbf{D}^2} \tag{3}$$

$$\mathbf{A}\_{\rm VD} = \frac{\mathbf{A}\_{\rm V}}{\mathbf{D}^2} = \frac{\mathbf{A}\varepsilon}{\mathbf{D}^2} \tag{4}$$

**Figure 2.** *Flow pattern map of Rollmann and Spindle [1].*

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

#### **Figure 3.**

*Geometrical parameters of stratified flow in circular tube.*

$$\mathbf{h}\_{\rm LD} = \mathbf{0}.5 \left( \mathbf{1} - \cos \left( \frac{2\pi - \theta\_{\rm strat}}{2} \right) \right) \tag{5}$$

$$\mathbf{P\_{iD}} = \sin\left(\frac{2\pi - \theta\_{\text{start}}}{2}\right) \tag{6}$$

Transition between stratified flow and stratified wavy flow:

$$\mathbf{G\_{stat}} = \left\{ \frac{4\mu\_{\rm L}\mathbf{g}(\rho\_{\rm L} - \rho\_{\rm V})\rho\_{\rm V}\mathbf{e}(\mathbf{1} - \mathbf{e})}{\mathbf{S\_2x}^2(\mathbf{1} - \mathbf{x})} \right\}^{1/3} + \mathbf{C\_5}; \mathbf{S\_2} = 0.02844; \mathbf{C\_5} = 22.9 \text{ kg/s} \text{m}^2. \tag{7}$$

Transition between slug flow and stratified wavy flow:

$$\mathbf{G\_{slug}} = \left\{ \frac{16 \widehat{\mathbf{A\_V^2}} \mathbf{gD} \rho\_\perp \rho\_\mathbf{V}}{\mathbf{x^2} \pi^2 \sqrt{1 - \left(2 \widehat{\mathbf{H\_L}} - \mathbf{1}\right)^2}} \mathbf{C\_6}^2 \left[ \frac{4 \pi^2}{\mathbf{S\_1^2} \widehat{\mathbf{H\_L}}^2} \left( \frac{\mathbf{F} \mathbf{r}}{\mathbf{W} \mathbf{e}} \right)\_\mathbf{L} + 1 \right] \right\}^{0.5} + \mathbf{C\_7}; \left( \frac{\mathbf{F} \mathbf{r}}{\mathbf{W} \mathbf{e}} \right)\_\mathbf{L} = \frac{\sigma}{\mathbf{gD^2 \rho\_\perp}}; \mathbf{S\_1} $$
 
$$= 5.889; \mathbf{C\_6} = 1.015; \mathbf{C\_7} = -53.35 \mathbf{k} \mathbf{g/s^2}^2, \tag{8}$$

where HL is liquid height, H f<sup>L</sup> ¼ HL*=*D and AV is gas phase area, A f<sup>V</sup> ¼ AV*=*D. Transition between stratified wavy flow and helix flow:

$$\mathbf{G}\_{\text{SW}} = \left\{ \frac{\mathbf{16} \widehat{\mathbf{A}}\_{\text{Vg}}^{\mathbf{\widehat{3}}} \mathbf{D} \rho\_{\text{L}} \rho\_{\text{V}}}{\mathbf{x}^{2} \pi^{2} \sqrt{1 - \left( 2 \widehat{\mathbf{H}}\_{\text{L}} - \mathbf{1} \right)^{2}}} \mathbf{C}\_{6}^{2} \right\}^{0.5} + \mathbf{C}\_{7} \text{, for } \mathbf{x} \ge \mathbf{0}.3; \mathbf{C}\_{6} = \mathbf{0}.8441; \mathbf{C}\_{7} $$
  $= \mathbf{0} \text{ kg/s} \text{m}^{2} $ .

For x ≥ 0.3 the transition curve in Eq. (3) was applied. With x < 0.3 the linear equation With the lope of transition curve from x ≥ 0.3.

Transition between slug/helix flow and helix flow:

$$\mathbf{G}\_{\text{Slug-helix}} = \left\{ \frac{\mathbf{1} \mathbf{\widetilde{G}\_{\text{V}}^{\text{S}} \mathbf{g} \mathbf{D} \rho\_{\text{L}} \rho\_{\text{V}}}{\mathbf{x}^{2} \pi^{2} \sqrt{1 - \left(2 \mathbf{\widetilde{H}\_{\text{L}}} - 1\right)^{2}}} \mathbf{C}\_{6}^{2} \right\}^{0.5} + \mathbf{C}\_{7}; \mathbf{C}\_{6} = \mathbf{1}.754; \mathbf{C}\_{7} $$
 
$$= -84.79 \text{ kg/s} \text{m}^{2}. \tag{10}$$

Transition between helix flow and annular flow:

$$\mathbf{G\_{slug}} = \left\{ \frac{\mathbf{16\widehat{A\_{g}^{\*}}} \mathbf{g\_{D}} \mathbf{D} \rho\_{\mathrm{L}} \rho\_{\mathrm{V}}}{\mathbf{x^{2}} \omega^{2} \sqrt{\mathbf{1} - \left( 2 \mathbf{\widehat{H\_{L}}} - \mathbf{1} \right)^{2}}} \mathbf{C\_{6}} ^{2} \left[ \frac{4 \pi^{2}}{\mathbf{S\_{1}}^{2} \widehat{\mathbf{H\_{L}}}^{-2}} \left( \frac{\mathbf{F} \mathbf{r}}{\mathbf{W} \mathbf{e}} \right)\_{\mathrm{L}} + 1 \right] \right\}^{0.5} + \mathbf{C\_{7}}; \mathbf{S\_{1}} = 57.71; \mathbf{C\_{6}} $$
  $= 1.772; \mathbf{C\_{7}} = -25.39 \text{ kg/s} ^{2}$ .

The classification of the regimes on the map:

