# Film Boiling Analysis in Porous Media

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## Contents

### 10.3.4 Nucleate Site Density

The knowledge of distribution of nucleation sites is an important factor in determining the boiling characteristics of a surface under specific operating conditions. The number density of sites, or total number of active sites per unit area, is a function of contact angle, cavity half angle, and heat flux (or superheat) (Fig. 10.6), i.e.,

${N''_a} = f(\theta ,\phi ,\Delta T,{\rm{fluid properties}}) \qquad \qquad( )$

(10.78)

Equation (10.11) indicated that for a given local heat flux or superheat, a cavity will be active if Rmin is greater than Rb,

${R_{\min }} \ge \frac{{2\sigma {T_{sat}}}}{{{h_{\ell v}}{\rho _v}\Delta T}} \qquad \qquad( )$

(10.79)

Obviously each cavity on a real surface has a specific Rmin that is a function of geometry and the contact angle. Considering eqs. (10.78) and (10.79), one expects that as the wall superheat increases, Rmin decreases and the number of active sites having cavity radii greater than Rmin increases.

Lorenz et al. (1974) counted total active sites/cm2 on a #240 (sand paper) finished copper surface for different working fluids as a function of Rmin, which is shown in Fig. 10.14.

Figure 10.14 Number density of active sites for boiling on a copper surface (Lorenz et al., 1974).

Kocamustafaogullari and Ishii (1983) have correlated various existing experimental data of N''a for water on a variety of surfaces and pressure ranges from 1 to 198 atm by

${N''_a} = D_d^2{\left[ {{{\left( {\frac{{{D_c}}}{{{D_d}}}} \right)}^{ - 0.44}}F} \right]^{1/4.4}} \qquad \qquad( )$

(10.80) Where

$F = 2.157 \times {10^{ - 7}}{\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)^{ - 3.2}}{\left[ {1 + 0.0049\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)} \right]^{4.13}} \qquad \qquad( )$

(10.81)

${D_c} = 4\sigma \left[ {1 + ({\rho _\ell }/{\rho _v})} \right]/{p_\ell } \cdot \left\{ {\exp \left[ {{h_{\ell v}}({T_v} - {T_{sat}})/({R_g}{T_v}{T_{sat}})} \right] - 1} \right\} \qquad \qquad( )$

(10.82)

${D_d} = 0.0208\theta \sqrt {\frac{\sigma }{{g({\rho _\ell } - {\rho _v})}}} \cdot 0.0012{\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)^{0.9}} \qquad \qquad( )$

(10.83)

where Rg is the gas constant for the vapor. Wang and Dhir (1993a, 1993b) have studied number density for boiling of water at 1 atm on a mirror-finished copper surface, and they provided a mechanistic approach for relating the cavities that are present on the surface to the cavities that actually nucleate.