2D heat diffusion simulation with thermal insulators

1. Aug 3, 2011

fmilano

Hi. I don't know if this is the correct place to ask this, but prefer you to suggest me where I should ask. I'm starting with numerical simulation and I've been playing with the finite differences method to solve the heat equation on 1D, 2D and 3D uniform grids. This was really simple. Now I want to introduce some thermal insulator elements in my simulation, let's say I have a 2D rectangular surface with some squared thermal insulators embedded in it. What should I do with the nodes that are located in the insulator region? How should I calculate them? Maybe it's a really simple problem, but it's been puzzling me for some time now and I don't know where should I start looking for an answer.

Federico

2. Aug 3, 2011

xts

if it is ideal insulator - just ignore them
If your insulator has small, but non-zero conductivity - allow your simulation to compute their temp.

Generally, in order to avoid stupid programming errors, it may be easier to specify your insulator as conductive with very-very-small conductance and not to make any computational exceptions, additional boundary conditions, etc. (Remember about Murphy's laws)

3. Aug 3, 2011

fmilano

Thanks xts. So, just to clarify, it's an ideal insulator; so if I ignore it I should never touch its initial value and I should use this initial value to update the neighboring nodes value. Is this right?

4. Aug 3, 2011

xts

No!!! You must set their temperature as equal to neighbouring 'true' node. Or you must program the conditional statement, making no heat flow on boundary true-insulating node.
That's why I told you that setting it to small, but non-zero conductivity may help to avoid programming pitfalls...

What you've proposed is not an insulator, but just contrary: superconducting isothermic source/sink of heat.