Editing Leidenfrost effect (section)

== Heat transfer correlations ==

The heat transfer coefficient may be approximated using Bromley's equation,<ref name="ReferenceA"/>

<math display="block">h=C{{\left[ \frac{k_{v}^{3}{{\rho }_{v}}g\left( {{\rho }_{L}}-{{\rho }_{v}} \right)\left( {{h}_{fg}}+0.4{{c}_{pv}}\left( {{T}_{s}}-{{T}_{sat}} \right) \right)}{{{D}_{o}}{{\mu }_{v}}\left( {{T}_{s}}-{{T}_{sat}} \right)} \right]}^{{}^{1}\!\!\diagup\!\!{}_{4}\;}}</math>

where <math>{{D}_{o}}</math> is the outside diameter of the tube. The correlation constant ''C'' is 0.62 for horizontal cylinders and vertical plates, and 0.67 for spheres. Vapor properties are evaluated at film temperature.

For stable film boiling on a horizontal surface, Berenson has modified Bromley's equation to yield,<ref name="ReferenceB">{{cite book |first1=James R. |last1=Welty |first2=Charles E. |last2=Wicks |first3=Robert E. |last3=Wilson |first4=Gregory L. |last4=Rorrer |title=Fundamentals of Momentum, Heat and Mass transfer |edition=5th |year=2008 |publisher=John Wiley and Sons |page=327 |isbn=978-0-470-12868-8 }}</ref>

<math display="block">h=0.425{{\left[ \frac{k_{vf}^{3}{{\rho }_{vf}}g\left( {{\rho }_{L}}-{{\rho }_{v}} \right)\left( {{h}_{fg}}+0.4{{c}_{pv}}\left( {{T}_{s}}-{{T}_{sat}} \right) \right)}{{{\mu }_{vf}}\left( {{T}_{s}}-{{T}_{sat}} \right)\sqrt{\sigma /g\left( {{\rho }_{L}}-{{\rho }_{v}} \right)}} \right]}^{{}^{1}\!\!\diagup\!\!{}_{4}\;}}</math>

For vertical tubes, Hsu and Westwater have correlated the following equation,<ref name="ReferenceB"/>

<math display="block">h{{\left[ \frac{\mu _{v}^{2}}{g{{\rho }_{v}}\left( {{\rho }_{L}}-{{\rho }_{v}} \right)k_{v}^{3}} \right]}^{{}^{1}\!\!\diagup\!\!{}_{3}\;}}=0.0020{{\left[ \frac{4m}{\pi {{D}_{v}}{{\mu }_{v}}} \right]}^{0.6}}</math>

where m is the mass flow rate in <math>l{{b}_{m}}/hr</math> at the upper end of the tube.

At excess temperatures above that at the minimum heat flux, the contribution of radiation becomes appreciable, and it becomes dominant at high excess temperatures. The total heat transfer coefficient is thus a combination of the two. Bromley has suggested the following equations for film boiling from the outer surface of horizontal tubes:

<math display="block">{{h}^{{}^{4}\!\!\diagup\!\!{}_{3}\;}}={{h}_{conv}}^{{}^{4}\!\!\diagup\!\!{}_{3}\;}+{{h}_{rad}}{{h}^{{}^{1}\!\!\diagup\!\!{}_{3}\;}}</math>

If <math>{{h}_{rad}}<{{h}_{conv}}</math>,

<math display="block">h={{h}_{conv}}+\frac{3}{4}{{h}_{rad}}</math>

The effective radiation coefficient, <math>{{h}_{rad}}</math> can be expressed as,

<math display="block">{{h}_{rad}}=\frac{\varepsilon \sigma \left( T_{s}^{4}-T_{sat}^{4} \right)}{\left( {{T}_{s}}-{{T}_{sat}} \right)}</math>

where <math>\varepsilon </math> is the emissivity of the solid and <math>\sigma </math> is the Stefan–Boltzmann constant.