Heat transfer and planetary evolution

Abstract

The object of this account is to show how much one can interprete and predict about the present state of material forming planet size objects, despite the fact we do not and could never have the kind of exact or prior knowledge of initial conditions and in situ material behaviour that would make a formal mathematical analysis of the dynamical problems of planetary evolution an efficient or meaningful exercise. The interest and usefulness of results obtained within these limitations stem from the highly non linear nature of planetary scale heat transfer problems when posed in any physically plausible form. The non linearity arising from a strongly temperature dependent rheology assumed for in situ planetary material is particularly valuable in deriving results insensitive to such uncertainties. Qualitatively, the thermal evolution of a planet is quite unlike that given by heat conduction calculation below a very superficial layer, and much unnecessary argument and confusion results from a persistent failure to recognise that fact. At depths that are no greater on average than a few tens of kilometres in the case of Earth, the temperature distribution is determined by a convective flow regime inaccessible to the laboratory experimenter and to the numerical methods regularly employed to study convective movement. A central and guiding quantitative result is the creation in homogeneous planet size objects having surface temperatures less than about half the absolute melting temperature of their material, of internal states with horizontally averaged viscosity values ~ 1021 poise. This happens in times short compared with the present Solar System age. The significance of this result for an understanding of such processes and features as isostasy, continental drift, a minimum in seismic S wave velocity in Earth’s upper mantle, a uniformity of mantle viscosity values, the survival of liquid planetary cores and the differentiation of terrestrial planet material is examined. After a discussion and definition of uthospheric’ material, it is concluded that endogenous tectonic activity only continues on Earth’s surface on account of water enhancing the deformability of its rocks.