README.md

# TransientConduction
 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


## Results
 
Heat equation 

 ![3 dimensional Heat eq](mathcad/imgs/3d-heattransfereq.png)
 
 Which can be simplified to the following for one dimension
 
 ![1 dimensional Heat eq](mathcad/imgs/1d-heattransereq.png)
 
 
 
### Python Implementation

#### Dependencies
 - python2.7 or 3
 - matplotlib
 - numpy

![Comparison](imgs/Comparison.png)

### MathCAD Implementation

![Forward Euler](mathcad/imgs/ForwardEuler.png)
![Crank Nicholson](mathcad/imgs/CrankNicholson.png)

### SMath Studio Implementation

![Transient Conduction](smath/Screenshot%202022-09-22%20191601.png)

## Sources
 - [Wikipedia: Transient Conduction](https://en.wikipedia.org/wiki/Thermal_conduction)
 - [Wikipedia: Crank-Nicolson](https://en.wikipedia.org/wiki/Crank%E2%80%93Nicolson_method)
 - [Hackaday Article by Matt Moses](https://hackaday.io/project/21642-repkiln/log/65537-numerically-solving-the-1d-transient-heat-equation)
 - [In depth comparison from Tennessee Technological University](https://www.cae.tntech.edu/~shan/numerical%20heat%20transfer%20note(ME4730_5730)/transient%201-D%20conduction(2013).pdf)
 - [Another Comparison by Hans Petter Langtangen](http://hplgit.github.io/num-methods-for-PDEs/doc/pub/diffu/sphinx/._main_diffu001.html)
 - [Hindered Settling python implimentation](https://hinderedsettling.com/2015/02/06/exploring-the-diffusion-equation-with-python/)
 - [Another Python implimentation Claudio Bellei](http://www.claudiobellei.com/2016/11/10/crank-nicolson/)
 - [Video Explanation by Sam R](https://www.youtube.com/watch?v=LihC0DzIibo&t=399s)