# Numerical modeling of hot magma

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1. May 15, 2015

### PinkGeologist

Ok, I've built a numerical model to show the cooling of hot magma sills entered into the crust over time. The results show that the volume of the "hot" zone when the emplacement of a constant volume of hot sills is all done will vary as a matter of two things: the overall rate at which the magma is emplaced (duh) and the thickness of the sills of magma (they are all wafer- or cylinder-shaped).

You can see from the attached figure that the volume shows a maximum and then decreases from that maximum as sills get shorter and taller.

My intuition suggests this is because du/dx and du/dy shrink with the thinner sills until du/dz is the only heat transfer of note (at the peak, the ratio of radius to height is ~300:1). That means heat is only escaping in effectively in one direction and thus more heat is retained in the zone.

I guess as the sills get "too" thin, they simply lose heat to quickly between sill-emplacement events to keep the heat in the zone.

I need to develop this for a journal paper I am working on, so is this sounding like the plausible cause of the curve shapes in my figure, or might there be an effect I am missing or not taking into account?

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2. May 15, 2015

### Staff: Mentor

I remember your previous thread, and I still don't understand what you are plotting as function of what, under which conditions.

Your initial condition is some magma cylinder and colder material around? We have the height in the plot, how does the width get determined? How do you fill in more magma over time?
How do you measure a volume? Volume of what, and how does it depend on the cooling process?