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Heat transfer with change of phase
DOI 10.1615/hedhme.a.000214
2.10 DIRECT CONTACT HEAT TRANSFER
2.10.3 Heat Transfer with Phase Change
H.R. Jacobs
A. Evaporation and Boiling
Evaporation of drops moving through a gas-vapor mixture occurs in gas quenching systems and in combustion systems, to name a few applications. Extensive stuthes have been reported in the literature. Prakash and Sirignano (1980), Sirignano (1983) and Law (1984) have made careful reviews of the literature and described numerical models for both single drops and sprays. While much of what lias been reported has been directed at the combustion problem, it is generally applicable to a broader array of problems. Almost all models of the evaporation problem have been directed toward the high void fraction, low holdup regimes. Thus, models based on single drops are widely used. Models dealing with close proximity of drops undergoing evaporation have only been solved for two or three drops traveling along the same path or along parallel paths in tandem. Extension of the work of Wilson and Jacobs (1993), or Evans (1994) is needed to account for mass transfer; although, an approximate model dealing with low blowing rates was analyzed by Thompson and Jacobs (1985).
The basic models for the evaporation process are similar to those for laminar film boiling in that it is necessary to model the internal-to-drop flow as well as the external-to-drop flow. Most combustion models assume relatively strong internal circulation. For example, Rangel and Sirignano (1987) assumed that the drops in their system offered negligible internal resistance and assumed essentially a lumped mass model. This places the drop at its saturation temperature throughout, and requires only the external flow over a sphere to be resolved. This solution, of course, is subject to the concentration of noncondensables in the continuum. For evaporation of drops into a superheated stream of its own vapor the problem is of course easier. For large drops, Carey and Hawks (1995) report
\[\label{eq1}\mbox{Nu} = 2\frac{\ln(Ja_{v} + 1)}{Ja_{v}} \mbox{where}\; \mbox{the}\; Ja_{v} = \frac{c_{pv} (T_{\infty} - T_{R})}{h_{lg}}\tag{1}\]
and for microdroplets
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