On the heat and mass transfer from an ascending magma

The maximum heat transfer possible from a sphere of magma ascending through a viscous lithosphere is estimated using a Nusselt number formulation. An upper bound is found for the Nusselt number by using the characteristics of a potential flow which, it is argued, is similar in the limit to a non-isothermal Stokes-flow in which the fluid (wall rock) viscosity is sensitive to temperature. A set of cooling curves are calculated for a magma ascending at a constant velocity beneath an island arc. If the magma is to arrive at the surface without solidifying its ascent velocity must be greater than about 5.8 × 10^?3 cm s^?1, for a magma radius of 1 km, and greater than about 2.7 × 10^?5 cm s^?1, for a magma radius of 6 km. If the magma begins its ascent crystal free it will generally become superheated over most of its ascent. Using essentially the same formulation as for heat transfer the mass transfer to or from a spherical body of magma ascending at these velocities is given approximately by ΔC ? ΔW/10, where ΔC is the change in weight percent of a component in the magma during ascent and ΔW is the compositional contrast of that component between the magma and its wall rock.