Hi Tony,
Let me find some values. ( are we assuming pulverized Cu mixed with pulverized Pb or large chunks? or what? and what mix ratio?)
It will be strips of 10 cms wide, 3mm thick lead sheeting, wrapped around a core of 2mm diameter bare copper wire folded lengthwise into a 10cm long stick. Pb/Cu ratio by weight = 70%:30%. So, the lead melts first, then rises up to copper's melting point of 1084 degrees Celsius, and finally both metals melt and alloy together.
Thermal diffusivity, α is a measure of how quickly heat propagates through a material per unit of depth over time, [m²/s]....
Good analysis, but you are assuming that the primary heat transfer mechanism is thermal diffusion. What I'm saying is that in the skin depth zone, heat is being generated instantaneously, and before this heat can diffuse inwards into the rest of the metal, due to lead's poor thermal diffusion coefficient, the heat stays in the skin depth zone of the lead and melts it. The molten lead pools at the bottom of the crucible and gets heated along with the now exposed inner sections of the heterogeneous Pb/Cu composite slug. The skin depth region repeats its magic, more molten lead pools at the bottom of the crucible and so on.
And hence, the key to the entire process is to maximise skin depth.