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Unformatted text preview: 4 is the Stefan–Boltzman constant. Note that the temperature in
this case must be expressed in K, not °C, and that surface tension and the
Stefan–Boltzman constant share the same symbol.
You may be tempted to simply add the convection and radiation heat transfers to determine the total heat transfer during film boiling. However, these
two mechanisms of heat transfer adversely affect each other, causing the total
heat transfer to be less than their sum. For example, the radiation heat transfer
from the surface to the liquid enhances the rate of evaporation, and thus
the thickness of the vapor film, which impedes convection heat transfer. For
qrad qfilm, Bromley determined that the relation
q total ·
q film 3·
4 rad Natural
Ts – Tsat Other properties are as listed before in connection with Eq. 10–2. We used a
modified latent heat of vaporization in Eq. 10–5 to account for the heat transfer associated with the superheating of the vapor.
The vapor properties are to be evaluated at the film temperature, given as
Tf (Ts Tsat)/2, which is the average temperature of the vapor film. The
liquid properties and hfg are to be evaluated at the saturation temperature at the
specified pressure. Again, this relation will give the film boiling heat flux in
W/m2 if the properties are used in the units specified earlier in their descriptions following Eq. 10–2.
At high surface temperatures (typically above 300°C), heat transfer across
the vapor film by radiation becomes significant and needs to be considered
(Fig. 10–12). Treating the vapor film as a transparent medium sandwiched between two large parallel plates and approximating the liquid as a blackbody,
radiation heat transfer can be determined from
q rad Nucleate
relations 1/4 where kv is the thermal conductivity of the vapor in W/m · °C and
relations Critical heat
flux relation (10-7) correlates experimental data well.
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