Question 9.10: The pool boiling of Example 9.1 takes place with a tube-wall...
The pool boiling of Example 9.1 takes place with a tube-wall temperature of 537.5 K, at which film boiling occurs. Estimate the heat-transfer coefficient for this situation. In addition to the data given in Example 9.1, the heat capacity and thermal conductivity of the vapor are C_{P, V} = 2360 J/kg · K and k_{V} = 0.011 W/m · K.
For pool film boiling on a horizontal tube, the Bromley equation is applicable. The following data are obtained from Example 9.1:
\rho_{L}=567 kg / m ^{3}\quad \quad\mu_{V}=7.11 \times 10^{-6} kg / m \cdot s
\rho_{V}=18.09 kg / m ^{3}\quad \quad D_{o}=1 \text { in. }=0.0254 m
\lambda=272,000 J / kg \quad \quad T_{\text {Sat }}=437.5 K
The temperature difference is:
\Delta T_{e}=T_{w}-T_{s a t}=537.5-437.5=100 K
The heat-transfer coefficient for film boiling is obtained by substituting into Equation (9.101).
\frac{h_{fb} D_{o}}{k_{V}}=0.62\left[\frac{g \rho_{V}\left(\rho_{L} – \rho_{V}\right) D_{o}^{3}\left(\lambda + 0.76 C_{P, V} \Delta T_{e}\right)}{k_{V} \mu_{V} \Delta T_{e}}\right]^{0.25}
=0.62\left[\frac{9.81 \times 18.09(567 – 18.09)(0.0254)^{3}(272,000 + 0.76 \times 2360 \times 100)}{0.011 \times 7.11 \times 10^{-6} \times 100}\right]^{0.25}
\frac{h_{f b} D_{o}}{k_{V}}=341.57
h_{f b}=341.57 \times k_{V} / D_{o}=341.57 \times 0.011 / 0.0254
h_{f b}=148 W / m ^{2} \cdot K
The radiative heat-transfer coefficient is estimated using Equation (9.103). Assuming an emissivity of 0.8 for the tube wall, we have
h_{ r }=\frac{\epsilon \sigma_{S B}\left(T_{w}^{4} – T_{s a t}^{4}\right)}{T_{w} – T_{s a t}}=\frac{0.8 \times 5.67 \times 10^{-8}\left[(537.5)^{4}-(437.5)^{4}\right]}{537.5 – 437.5}
h_{ r }=21 W / m ^{2} \cdot K
Since h_{ r } < h_{f b}, Equation (9.104) is used to obtain the effective heat-transfer coefficient:
h_{ t }=h_{f b}+0.75 h_{ r }=148+0.75 \times 21 \cong 164 W / m ^{2} \cdot K
This value is one to two orders of magnitude lower than the heat-transfer coefficient for nucleate boiling calculated in Example 9.1.