32 - Boiling

The Rosenhow correlation is a popular tool to predict nucleate boiling heat transfer: \[h = \mu_l \lambda \left[\frac{g(\rho_l-\rho_g)}{\sigma} \right]^{0.5}\left[\frac{C_{Pl}}{C_{sf}\lambda Pr_l} \right]^3(T_w-T_{\text{sat}})^2\] In this correlation \(\text{Pr}_l\) is the Prandtl number for the liquid and \(C_{sf}\) is an empirical coefficient which depends on the fluid/surface combination. For example, for water on polished stainless steel the recommended value for \(C_{sf}\) is 0.013. \(C_{sf}\) is meant to capture the effect of surface (micro-cavities) on nucleate boiling.

\(\sigma\) - surface tension of liquid vapor interface.

The subscripts \(l\)-refer to liquid; \(g\) refer to vapor.

The critical (and hence the maximum) heat flux is given by \[q_{\text{max}} = 0.18\rho_g\lambda\left[\frac{g\sigma(\rho_l-\rho_g)}{\rho_g^2} \right]^{1/4}\]

It is very desirable to be able to operate heat exchange equipment in upper end of nucleate boiling regime. Here the temperature difference is low while the heat flux is very high. Heat transfer coefficients in this range are enormous. However, it is very dangerous to run equipment near \(q_{\text{max}}\) in systems for which \(q\) is the independent variable (as in nuclear reactors).

If \(q\) is raised beyond the upper limit of the nucleate boiling regime, such a system will suffer a sudden and damaging increase of temperature. This transition is known by a variety of names: the burnout point (although a complete burning up or melting away does not always accompany it); the peak heat flux (a modest descriptive term); the boiling crisis (a Russian term); the DNB, or departure from nucleate boiling, and the CHF, or critical heat flux (terms more often used in flow boiling); and the first boiling transition (which term ignores previous transitions).