I wrote a simple script to calculate and display 1 dimensional plane wall transient thermal conduction. Originally for an in-depth analysis of an insulation wall of a solder reflow oven for a thermodynamic project. Instead of going into how it works, I am going to just dump some of the results on this page and link a few good resources that already exist for explaining the methods (and probably do better that I can).

Source Code

Heat equation

Which can be simplified to the following for one dimension

Results

Python Implementation

Mathcad Implementation

Resources

• phcreery/TransientConduction
• Wikipedia: Transient Conduction
• Wikipedia: Crank-Nicolson
• Hackaday Article by Matt Moses
• In depth comparison from Tennessee Technological University
• Another Comparison by Hans Petter Langtangen
• Hindered Settling python implimentation
• Another Python implimentation Claudio Bellei
• Video Explanation by Sam R