Imagine you inject a 16km high stack of magma in the Earth's crust continuously over X years and then analyze the size and shape of the final "hot zone" as your "result" ... let's say you want to quantify the volume of crust at a temperature (T) greater than 1000 Kelvin (K). In case 1, that volime is (X1 m^-3) Not, imagine you insert the same amount of magma over the same amount of time but not continuously - you insert 40 sills of magma, each 400m in height. The fial volume you get for that is ... (X2 m^-3) Then you insert 160 sills in the crust, each 100m tall and get a final V = X3 m^-3 Then you insert 320 sills in the crust, each 50m tall and get a final V = X4 m^-3 Then you insert 640 sills in the crust, each 25m tall and get a final V = X5 m^-3 I did this with a numerical model (COMSOL multi-physics) where the cooling is by conduction with some latent heat added to the system as minerals in the magma crystallize out and freeze while it cools. What is weird is that the final V does not just get larger or smaller as the sills gets shorter (and the time between their injection obviously gets shorter). You can SEE the results here (a picture is worth 1000 words and all that): https://www.dropbox.com/s/irzgjkoj78czb78/Screen Shot 2015-04-29 at 9.30.13 PM.png?dl=0 https://www.dropbox.com/s/9wdpd3hlg3x80iu/Screen Shot 2015-04-29 at 9.30.03 PM.png?dl=0 https://www.dropbox.com/s/q2mrfkilkgme5p1/Screen Shot 2015-04-29 at 9.29.52 PM.png?dl=0 https://www.dropbox.com/s/ruemoh8wc4mr043/Screen Shot 2015-04-29 at 9.29.40 PM.png?dl=0 At each total rate I choose, somewhere in the 100m to 50m sills height range I get the highest final volume. I need to describe this quantitatively rather than just qualitatively and was hoping for the insight of someone who works with thermodynamic problems to actually elucidate the finer points of what is happening. I know there must be a "sweet spot" where the retained heat between injections and the added heat of the injections combined and amplify, but I'm not sure how to make a finer discussion.