This work explores the effect of heat transfer by boiling on the cooling rates of pyroclasts produced during hydromagmatic eruptions. A numerical heat transfer model has been developed for spherical particles that combines intraparticle conduction with heat transfer from the particle surface by boiling water. This model is used to explore heat loss with time for a range of particle diameters. The results are combined with estimates of time available for cooling in order to calculate the heat removed during the eruption.
The results of this model are applied to a sample with the same particle size distribution as material recovered from the Icelandic Gjálp eruption which took place under the Vatnajökull ice cap in October 1996. The model calculation of heat removed during the eruption is relative to the local ambient temperature of meltwater in the ice cavity. It may be adjusted to the ice melting temperature datum, to allow comparison with the values estimated for the Gjálp eruption that are reported in Gudmundsson et al. . The heat transfer model indicates that, relative to 0 °C, the sample transfers around 70% of its heat during the eruption. This can be compared with 63-77% determined by heat balance calculations (Gudmundsson et al. 2004) based on volumes of ice melted.
Although there are significant areas of uncertainty in the calculations, this model gives insight into the processes involved. In particular, both incomplete heat transfer and elevated local cavity fluid temperature appear to limit heat removed during the eruption. Further work will focus on the effect of (1) nonspherical particles, (2) uncertainty in the boiling heat transfer equations and (3) a drained but moist (steamfilled) cavity compared with a flooded cavity.
 Gudmundsson, M.T., Sigmundsson, F., Bjornsson, H. & Hognadottir, T. (2004). The 1996 eruption at Gjálp, Vatnajökull ice cap, Iceland: efficiency of heat transfer, ice deformation and subglacial water pressure. Bulletin of Volcanology 66, 46-65.