How is heat transferred from the core through the mantle to the crust? So, there are three main methods of transferring heat: radiation, convection/mass transfer, and conduction. Presumably radiation is not a major method of heat transport between the core and the crust, because it requires transparent materials (or a vacuum), and I don't think there is much of either in the mantle. Presumably conduction is the only significant method of transport in the crust, apart from volcanos.

So, in the mantle, between the core, where heat is generated, and the crust, where it is eventually dissapated, what proportion of heat is transported via convection and conduction?
It is still a little known fact that radiation play an important role in the Earth's mantle. Experiments show that mantle-material becomes transparent to infrared radiation at increasing pressures (http://www.esrf.eu/news/general-old/general-2004/earthbadro/index_html).

I would also say that the mantle is currently not understood in a way where estimates of heat-conduction-type versus depth can be accurately made. The heterogeneity of heat transfer (Cold detached subduction-slabs sinking to various depths and hot plumes quickly rising from the D''-layer) makes the question even more difficult.