2D heat diffusion simulation with thermal insulators

[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.

Thanks in advance,

Federico

 

[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)

 

[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?

 

[xts]

I should use this initial value to update the neighboring nodes value. Is this right?

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.

 

[sardar]

Hello Federico,

Thank you for reaching out and seeking assistance with your simulation. I am happy to help guide you in the right direction.

In order to accurately simulate heat diffusion with thermal insulators, you will need to take into account the thermal conductivity and thickness of the insulator material. These properties will affect how heat is transferred through the material and how it affects the surrounding nodes.

One approach you can take is to assign a separate thermal conductivity and thickness value to the insulator material in your simulation. This will allow you to accurately calculate the heat transfer through the insulator and how it affects the nodes in the surrounding region.

Another approach is to treat the insulator as a boundary condition in your simulation. This means that you can set the temperature of the nodes in the insulator region to a constant value, as the insulator will not allow heat to pass through it. This will also affect the surrounding nodes and can be taken into account in your calculations.

I recommend consulting with a numerical simulation expert or reviewing literature on heat diffusion simulations with thermal insulators for more in-depth guidance. Good luck with your simulation and don't hesitate to reach out if you have any further questions.

Best,