<p>Of course there is, and in not that complex. Is called the <a href="https://en.wikipedia.org/wiki/Heat_equation" rel="nofollow noreferrer">heat equation</a>, and is a type of <a href="https://en.wikipedia.org/wiki/Diffusion_equation" rel="nofollow noreferrer">diffusion equation</a> that can be easily solved numerically or analytically in some simple geometries.</p>

<p>If you don't want to get involved in the math, you can use one of mane heat transfer simulation software, there are even online version that run in your browser like <a href="http://energy.concord.org/energy2d/compare-capacity.html" rel="nofollow noreferrer">Energy2D</a>, in which you can configure the geometry and thermal properties of your materials and let the simulation run.</p>

<p>The screenshot below is a problem with the geometry you suggest. But you would need to set the correct thermal properties of air and basalt.</p>

<p>If you are looking for a customized equation, you have to constrain the geometry of the problem. For instance: the cooling of a laterally infinite layer of material at 1000 °C of thickness X with a medium (air in your case) above it, at constant temperature of 10°C and a medium below it (bedrock) at initial temperature 5°C, you can look at engineering formulas handbooks, or post the question on the Engineering or Math Stack Exchange sites. 
<a href="https://i.sstatic.net/t8IjL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/t8IjL.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2018-02-07T23:16:32.930Z
it is not that simple actually.. if the problem involves phase change you need to consider the Stefan Problem, i.e. the heat equation with a moving phase boundary
ye-ti-800
CC BY-SA 3.0
2018-02-08T00:04:16.440Z
@ye-ti-800 I agree of the increased complexity of considering phase transitions. However, I don't think it is the case in this question, as it is asking about the cooling of basalt, no the solidification of basalt from lava. So, as I understand it, the material to be considered is a solid throughout the cooling process.
Camilo Rada
CC BY-SA 3.0
2018-02-07T22:26:42.757Z
2018-02-07T22:26:42.757Z
Camilo Rada
<p>In places like the Giant's causeway in Ireland (Antrim basalts) there are columnar basalt flows of 100 metres or more. I'm aware that the cooling mechanism is complex, but is there any rough and ready equation for estimating the cooling time of such a basalt flow?</p>

CC BY-SA 3.0
2018-02-07T23:05:29.817Z
i assume with cooling you mean cooling including solidification?
ye-ti-800
CC BY-SA 3.0
2017-03-05T20:29:32.940Z
I have some notes from a Geodynamics module that cover cooling by conduction (the most simplest case) that by using the right approximations (boundary conditions, temperatures etc.) the cooling time can be estimated by a variation of the 1D heat equation. I will look this up for you tomorrow!
Conquistador
<geophysics><magmatism>
Cooling time of basalt flows?
Gordon Stanger
# Cooling time of basalt flows?

(Asked by: username_0 on 2017-03-04)

In places like the Giant's causeway in Ireland (Antrim basalts) there are columnar basalt flows of 100 metres or more. I'm aware that the cooling mechanism is complex, but is there any rough and ready equation for estimating the cooling time of such a basalt flow?

**Tags:** geophysics, magmatism

> **Comments:**
> **username_2**: I have some notes from a Geodynamics module that cover cooling by conduction (the most simplest case) that by using the right approximations (boundary conditions, temperatures etc.) the cooling time can be estimated by a variation of the 1D heat equation. I will look this up for you tomorrow!  
> **username_1**: i assume with cooling you mean cooling including solidification?  

---

## 1 answers

### Answer by username_3 on 2018-02-07. Score: 2

Of course there is, and in not that complex. Is called the [heat equation](https://en.wikipedia.org/wiki/Heat_equation), and is a type of [diffusion equation](https://en.wikipedia.org/wiki/Diffusion_equation) that can be easily solved numerically or analytically in some simple geometries.

If you don't want to get involved in the math, you can use one of mane heat transfer simulation software, there are even online version that run in your browser like [Energy2D](http://energy.concord.org/energy2d/compare-capacity.html), in which you can configure the geometry and thermal properties of your materials and let the simulation run.

The screenshot below is a problem with the geometry you suggest. But you would need to set the correct thermal properties of air and basalt.

If you are looking for a customized equation, you have to constrain the geometry of the problem. For instance: the cooling of a laterally infinite layer of material at 1000 °C of thickness X with a medium (air in your case) above it, at constant temperature of 10°C and a medium below it (bedrock) at initial temperature 5°C, you can look at engineering formulas handbooks, or post the question on the Engineering or Math Stack Exchange sites.
[![enter image description here](https://i.sstatic.net/t8IjL.png)](https://i.sstatic.net/t8IjL.png)

> **Comments:**
> **username_1**: it is not that simple actually.. if the problem involves phase change you need to consider the Stefan Problem, i.e. the heat equation with a moving phase boundary  
> **username_3**: @username_1 I agree of the increased complexity of considering phase transitions. However, I don't think it is the case in this question, as it is asking about the cooling of basalt, no the solidification of basalt from lava. So, as I understand it, the material to be considered is a solid throughout the cooling process.  

---

