Advice on software for solving transient heat conduction? The temperature of the material that is cooling is not uniform

I'm interested in chemical reactions. There's a reaction that only takes place above a certain temperature. I would like to figure out how long a solid material can stay above that temperature under two end-member circumstances (described below).

I am not an engineer, but took basic heat transport a long time ago. I would be very grateful if someone would point me to any software/downloadable code that might be useful for solving my problem. So far I have searched extensively on the Matlab file exchange board, but don't see anything that seems relevant. I don't have access to ANSYS, but would be willing to get access to COMSOL or some other commercial software and figure out how to use it.

I want to know approximately how long it would take for a 2D, rectangular sheet to cool below a certain temperature when:

1. There is one hot rectangular area in the middle of the sheet (I'm pretty sure I can figure this one out in Matlab), and

2. When there are multiple hot vertical areas in the sheet (the sheet is "striped" with hot and cold areas). This is the tough one for me that I'd like to solve with already-prepared code.

Thank you.

1 Answer

The basic approach for both MatLab, and other tools such as NumPy, is to use Finite Element Method. This approach would be to divide your material into a number of grid squares, (the number depending on the desired accuracy and the computer time that you are prepared to devote), each with a temperature value and use the materials heat transfer characteristics to iteratively calculate, say once per (simulated) second the amount of heat energy that is lost & gained from each square to all of the adjacent squares. At the edges you have the environment temperature and plus a transfer function for how much heat is lost to the environment, usually you assume that the environment is an infinite sink, i.e. though they receive energy based on the temperature of the adjacent cells they do not gain in temperature.

For externally applied heat sources you simply supply at each iteration an input of the amount of energy to those areas that are receiving heat.

The only difference between a single hot spot and multiple is the values that you populate your starting conditions with and/or the number and position of the cells that are receiving external energy.