| Summary: | An attempt is made to model the thermal history of a self-gravitating Moon. Since the Rayleigh number at the end of the accretionary stage is supercritical, thermal convection in the Moon is likely to have occurred as early as 4.6 billion years ago. A combination of the Stokes equation of viscous flow and the heat transfer equation is solved, using the finite element method. The numerical code used is a modification of Gartling's NACHOS, a general purpose code for transient, two-dimensional incompressible fluid flow problems. The effects of melting, viscous dissipation and adiabatic gradient are included. A uniform distribution of radioactive nucleides is assumed, and their decay with time is taken into account. The code also allows for the simulated growth of a core of 300 km radius, and the energy that such a process releases into the convecting mantle. Viscosity is assumed to be Newtonian, appropriate for a mantle of dry olivine composition. An accretionary initial temperature profile is chosen that remains everywhere below the basalt solidus. Thus unlike in previous lunar models, no initial "basalt sea" is assumed. The algorithms developed in this study have been made general enough to model the thermal histories of any of the terrestrial planets, so that these results may then be compared with those of "convection-simulated" and parametrized convection models.
The results show that the convection pattern is dominated by a L-2 mode, and that viscosity is the predominant factor in controlling the nature of the thermal evolution. Partial melting is observed very early in the Moon's history, which could be related to the formation of the lunar basalt maria. The present day lithospheric thickness of the model is about 600 km and core-mantle temperatures are close to 1600(DEGREES)K. Surface heat flux is 15.3 mW/m('2), higher than the "steady state" value by about 12%.
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