This repository contains two jupyter notebooks for the lecture on transport phenomena.
Please open the file named TransportPhenomenaLab.ipynb first. It contains the interactive assigment. To gain a deeper understanding of the contents shown in the lecture with more examples, look at TransportPhenomenaLab-Addition.ipynb. Below is a short theoretical recap of solving the heat equation with finite differences.
This repo was made by Artur M. Schweidtmann and Maximilian Theisen
As you will see, the notebook consists of four parts:
- Real data for comparison
- A finite-differences implementation to solve the Partial Differential Equation (PDE) and animate the results
- A section to define the thermal diffusivity
- A comparison between real values and calculated ones
First, choose a value for the thermal diffusivity, here called , for Section 2. Then, run all Sections 0 to 4 to get a result. If you want to change the parameter alpha afterwards, rerun Section 2-4 after changing alpha
You can run the cells either by clicking on the cell and then on Run or press shift+enter
To solve this partial differential equation (PDE), we need to define one initial condition (accounting for time) and four boundary conditions (accounting for space)
Initial condition:
The plate is assumed to be adiabatic. Hence, the temperature function's change on the edges of the plate is zero. This can be formulated into the following boundary conditions:
Boundary conditions:
To account for the isothermal left side, we will furthermore define a constraint:
: We assume that at all time, the left edge of the plate is at temperature
For a the temperature
at the next time step is approximated by:
