Heat diffusion and size reduction of a spherical magma chamber

An analytical solution is derived for the size reduction of a spherical magma chamber cooling by conduction. The use of moving boundary conditions and the constraint of a spherical symmetry allow one to ignore the details of the heat redistribution processes which take place within the magma chamber. The dependence of the solution on the initial conditions is investigated. A simple solution is found for short time, which is shown to be valid for times long enough to make it useful in the volcanological context. Moreover, the general solution confirms that the hydrothermal contribution to heat transfer in Phlegraean Fields cannot be extremely important.