*figure, not a case* — framing physics anchor for the lecture

q = -k∇T. The mathematical backbone of the entire one-dimensional heat-intensity argument.

What do I mean by fundamental heat flow? Anybody know what Forte's [Fourier's] law of heat conduction is? You've never heard of it before? The heat flux is equal to minus K, the thermal conductivity of the material, times the gradient of temperature with distance. Watts per square centimeter equals minus the thermal conductivity times delta T over delta X, if you want to get out of calculus and go to algebra. If I have less than 300 watts per square centimeter, I can't get a delta T hot enough to melt steel. It doesn't really matter what X is — the steel has enough thermal conductivity to carry the heat away. If I tried to melt copper, which has about four or five times the thermal conductivity of steel, I'd have a hard time doing it with an oxy-acetylene flame. Copper, aluminum — hard to do; I really need two or three thousand watts per square centimeter. But an electric arc, I can melt them within a fraction of a second depending on how many amps I have in my arc. With a laser and electron beam at the other end of the spectrum.