Thermal evolution of cooling magma chambers
We calculate the variations of temperature fields in magma chambers and the surrounding material. In a suggested two-dimensional model, a viscous hot melt occupies a horizontal layer (a magma chamber) within a thicker solid layer. The geometry of this system and a temperature gradient in its solid part are initial conditions. Thermal convection starts in the melt and the magma chamber begins to cool, owing to heat loss through conduction in the surrounding solid medium. Melting occurs at liquid/solid interfaces, followed by solidification of the melt. We solve equations of thermal convection and heat conduction in liquid and solid regions, respectively. Numerical solutions are obtained by the single-region method where equations are applied to the whole region and the moving phase boundary results from calculations. The problem so formulated reduces to generalized equations of thermal convection with the effective heat capacity which includes heat generation in the Stefan problem. An additional function enters the right-hand side of the Stokes equation. This function is such that generalized equations reduce to the usual equations of thermal convection within the melt and to the heat conduction equation in the solid part of the system. We calculate thermal regimes of magmatic chambers for various geometries. We also obtain time dependence of heat flows at liquid/solid interfaces and at the Earth's surface.