*Heat Transfer - Design, Experimentation and Applications*

Although small in magnitude, it is observed, with the increase of the liquid superheat, *Ustb* decreases for a same-sized bubble. This is due to the same reason: with the increase of added mass at a higher rate for higher liquid superheat (see Eq. (9)), the bubble deformed at a faster rate causing more drag force and reduced velocity. Sideman and Taitel's [24] also overserved similar phenomena of reduced bubble velocity with the increase of temperature.

shape and velocity were compared against the past works and found to be in good

Likewise, bubble growth due to the convective action in the previous section, vapour bubble size reduction (i.e. condensation) was simulated using the same convective heat transfer mechanism due to the temperature gradient between vapour and water phase. Eq. (1)–(8) are also applicable here. *Smass*, however, needs

*n*

Where: *Smass*\_*cell n*ð Þ is the 3D spatial interfacial cell-by-cell mass transfer rate from the condensing bubble; *abcell n*ð Þ is the local bubble surface area at the interface cell and

! *hif* <sup>¼</sup> *kl*

*Db*

� *Nucond* (19)

*<sup>l</sup>* For Steam-Water flow at near

*<sup>b</sup> Pr*�0*:*<sup>4564</sup> *<sup>l</sup> Ja*�0*:*<sup>2043</sup> *<sup>l</sup> Reb* = 1000–6000

*<sup>l</sup> Ja*�0*:*<sup>31</sup> *<sup>l</sup> Re <sup>b</sup>*≈1000 � 3400

� � For Narrow channel

� � 20 < *Reb <* 700

atmospheric pressure and for void fraction up to 30 percent.

> 18 < *Ja <* 36 1.87 < *Pr <* 2.03 0.8 mm < *D <* 6 mm

> > *Ja*≈10 � 30

*Reb* = 335–1770 *Pr* ≈ 1.7 *Ja = 20–60*

1.8 < *Pr <* 2.9 12 < *Ja <* 100

subcooling. Interfacial (convective) heat transfer coefficient (*hif*) can be calculated

Eq. (12)–(14) can also be used here to determine Reynolds number, Bubble Velocity and Bubble Diameter. Next using this *Reb*, Condensate Nusselt number (*Nucond*) can be calculated from the correlations. **Table 5** shows some of the notable relations found in the literature. A preference was given to the relations having Jacob number (*Ja*) – a dimensionless number which is usually used for boiling, evaporation and condensation applications. To check the model's sensitiveness, Condensing bubble volume reduction with time for various correlations was investigated [31]. The correlations exhibit a wide discrepancy in volume reduction rates,

*hif* � *abcell n*ð Þ � Δ*Tsub hfg*

(18)

to be treated in the opposite way for mass loss from the vapour bubble.

*Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an…*

*Smasscell n*ð Þ <sup>¼</sup> <sup>X</sup>

can be obtained from the ISM simulation (see **Figure 4**). Δ*Tsub* is the liquid

*kl*

**Reference Correlation Proposed Valid For**

*Nucond* <sup>¼</sup> <sup>1</sup>*:*<sup>46</sup> *Re* <sup>0</sup>*:*<sup>61</sup>

*<sup>b</sup> α*<sup>0</sup>*:*<sup>328</sup>*Ja*�0*:*<sup>308</sup>

*<sup>b</sup> Pr*<sup>0</sup>*:*<sup>33</sup>

*<sup>l</sup>* <sup>1</sup> � *Ja*<sup>0</sup>*:*<sup>1</sup>

*<sup>l</sup>* <sup>1</sup> � <sup>1</sup>*:*2*Ja*<sup>9</sup>*=*<sup>10</sup>

*<sup>l</sup> Fob*<sup>0</sup>

*<sup>l</sup> Fo*<sup>2</sup>*=*<sup>3</sup> *b*0

*<sup>b</sup> Pr*<sup>1</sup>*=*<sup>3</sup>

*<sup>b</sup> Pr*<sup>1</sup>*=*<sup>3</sup>

*Nucond* <sup>¼</sup> *hifDb*

*Smass* <sup>¼</sup> <sup>X</sup> *n*

by the following condensation correlation:

Zeitoun et al. [25] *Nucond* <sup>¼</sup> <sup>2</sup>*:*<sup>04</sup> *Re* <sup>0</sup>*:*<sup>61</sup>

Kim & Park [27] *Nucond* <sup>¼</sup> <sup>0</sup>*:*<sup>2575</sup> *Re* <sup>0</sup>*:*<sup>7</sup>

Yuan et al. [29] *Nucond* <sup>¼</sup> <sup>0</sup>*:*<sup>6</sup> *Re* <sup>1</sup>*=*<sup>2</sup>

Warrier et al. [30] *Nucond* <sup>¼</sup> <sup>0</sup>*:*<sup>6</sup> *Re* <sup>1</sup>*=*<sup>2</sup>

*Condensate Nusselt number correlations.*

Lucic & Mayinger

[28]

**Table 5.**

**133**

agreement.

Thus,

*3.2.1 Numerical features*

*DOI: http://dx.doi.org/10.5772/intechopen.96303*
