*Heat Transfer - Design, Experimentation and Applications*

superheated liquid which exists close to the heated surface and is metastable in nature [7]. Although the bubble growth rate in this region is not that significant with compared to the initial pre-departure growth, the bubble will grow for the convective action (convective boiling) with the presence of superheated liquid. Vapour bubble size, shape, and rise velocity for this superheated liquid region can significantly affect the heat and mass transfer mechanism involve. It is thus critical to understand and predict the behaviour and properties of rising and simultaneously growing vapour bubbles. In this section, the growth of a rising vapour bubble is numerically investigated in quiescent superheated water under the influence of buoyancy and surface tension forces with special emphasis given to heat and

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

Both the water and the vapour phases can be assumed to experience the same '*mixture velocity*' at any local point within the computational domain, and the twofluid system can be approximated as a one-fluid mixture. The mixture density and viscosity of each control volume can be calculated based on the volume fraction (*α*),

> liquid phase interface gas phase

*ρ* ¼ ð Þ 1 � *α ρ<sup>g</sup>* þ *αρ<sup>l</sup>* (2) *μ* ¼ ð Þ 1 � *α μ<sup>g</sup>* þ *αμ<sup>l</sup>* (3)

� �*Smass* (4)

*Smass* (5)

(1)

1 0<*α* <1 0

The variable density and viscosity are then estimated using the *α* value:

Where: Subscripts *l* and *g* indicate liquid (water) and gas (vapour) phases. When the mass transfer is considered, a source term needs to be added to the *α*-

<sup>þ</sup> <sup>∇</sup>*:*ð Þ¼ *<sup>α</sup><sup>V</sup>* <sup>1</sup>

*ρg* � 1 *ρl*

!

*ρ*

<sup>þ</sup> <sup>∇</sup>ð Þ¼� *<sup>ρ</sup>V:<sup>V</sup>* <sup>∇</sup>*<sup>p</sup>* <sup>þ</sup> *<sup>ρ</sup><sup>g</sup>* <sup>þ</sup> <sup>∇</sup>*:<sup>μ</sup>* <sup>∇</sup>*<sup>V</sup>* <sup>þ</sup> <sup>∇</sup>*V<sup>T</sup>* � � <sup>þ</sup> *<sup>F</sup><sup>σ</sup>* (6)

ð Þþ *ρ*E ∇ð Þ¼ *V*ð Þ *ρ*E þ *p* ∇ð Þþ *k*∇*T Sheat* (7)

mass transfers due to the convective action.

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

*α* ¼

*∂α ∂t*

Where: *Smass* is the interfacial mass transfer source term.

<sup>∇</sup>*:<sup>V</sup>* <sup>¼</sup> <sup>1</sup>

Where: *p*, *g* and *F<sup>σ</sup>* are the pressure, gravity and surface tension force

Similarly, the continuity equation becomes:

The Momentum equation is:

*∂ρV ∂t*

The Energy equation is:

*∂ ∂t* 8 ><

>:

*3.1.1 Numerical features*

transport equation:

respectively.

**125**

which has the following values:

summing the volumes of individual triangular columns – refer to **Figure 5**. For the surface translation and the remeshing process, see Ho et al. [4].
