Modeling of Heat Transfer in Subglacial Effusive Eruptions
Abstract
We present a box-model for the cooling of an arbitrarily thick layer of lava erupted effusively under glaciers. The lava is treated as a large horizontal intrusion (sill or pillows) and we limit our study to the propagation of heat in the vertical direction. We assume that the melt water does not drain but accumulates at the eruption site, and subdivide the system into three boxes: the intruded body of magma, the water layer and the ice. The heat transfer problem also has three parts: conduction in the magma, magma-water heat transfer, water-ice heat transfer. The efficiency of heat transport between two layers generally depends on the temperature and properties of both substances, consequently the three problems need to be solved simultaneously to obtain a complete description of the system's response. The conduction of heat in the magma layer is treated as a Stefan problem featuring a gradual latent heat release (from liquidus to solidus temperatures) and an imposed heat flux boundary. The problem is solved numerically by the method of lines using the properties of an average Icelandic basalt. The heat flux boundary condition at the magma-water interface depends on the dynamics of pool boiling and natural convection.Cooling of a plane surface by convecting water is a common engineering problem and various theoretical and empirical correlation functions are available to predict the heat flux for a given range of heating surface temperatures and fluid properties. To predict the heat flux to the water as the magma surface temperature decreases a full boiling curve is constructed to cover the whole spectrum of boiling heat transfer modes (film boiling, transitional boiling, nucleate boiling, non-boiling convection). Finally, the melting of ice by convecting water is modelled using results derived from published laboratory and numerical experiments. The model predicts the energy distribution between the melt water and the ice as the magma cools. This allows us to set bounds on the melt rates that can be expected from effusive eruptions and on the volume and temperature of the melt water produced. The model predicts also the rate and extent of cooling of the magma unit and, thus, relates the degree of crystallization in the lava body to the subglacial setting. These are key parameters for the volcanological and glaciological analysis of subglacial eruptions as they can lead to pressure variations and morphological changes of the drainage system affecting both the eruptive style and the risk of catastrophic outburst floods.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2004
- Bibcode:
- 2004AGUSM.V21C..03F
- Keywords:
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- 1827 Glaciology (1863);
- 1878 Water/energy interactions;
- 8135 Hydrothermal systems (8424);
- 8400 VOLCANOLOGY