ME 701 - Project 1

Description

For this project, your team (of $\leq 3$ students) will adapt the open-source code in fd2d_heat_steady.py to produce an easy-to-use program for modeling 2-d heat conduction. Because the numerical methods needed are completely implemented in the given code, the challenges for your team are (1) to understand how the existing code works and (2) to craft a new interface that takes a given "input" and provides a desired "output." You are free to change code in fd2d_heat_steady.py, or you may import only those pieces you want or need. You should avoid simply copying code from fd2d_heat_steady.py into new functions that do basically the same thing.

What You are Given

This project repository contains several files that define your path forward:

• heat2d/fd2d_heat_steady.py is the same file we saw earlier in class (unmodified from its original source as of 10/05/2022.

• heat2d/__init__.py is used to perform imports and other operations needed to set up the module. In particular, this imports the solve function defined in driver.

• heat2d/driver.py defines the solve function and the plot function.

• examples/simple_box.py defines a very simple, 2-d heat conduction problem without any heat sources. This is equivalent to the example given in fd2d_heat_steady.py. However, note that the inputs to solve differ from the fd2d_heat_steady function defined in fd2d_heat_steady.py.

• examples/simple_box_ref.png is identical to the image that should be produced by heat2d.plot.

• examples/simple_box_ref.out is identical to the text-based output that should be saved to file. Hint: np.savetxt is your friend.

• examples/refrigerator.py defines a more realistic application.
  Although refrigeration units rely on convection for removing heat, we can approximate the heat exchanger with a fixed, negative heat source.

Tasks

• Fully implement the solve and plot functions. You may add additional functions to the driver.py module as needed. All development should be clearly shown in git logs. Development should include multiple pull-request and review cycles.

• Run the code to produce simple_box.png and simple_box.out.

• Implement the q and k functions needed for the refrigerator "default" example. Run and save your png and out files.
  Note the temperatures within the refrigerator region.

• Create a Jupyter notebook that demonstrates your tool by "optimizing" the refrigerator materials or heat sink to ensure the maximum temperature inside the refrigerator is equal to or below 4 $^{\circle}$ C. Show the results first for the "default" configuration. Then describe your optimization process and the final "design." Compare your results to real fridges; are they even remotely comparable?

  Warnings:

  • The "default" fridge geometry has 1 cm-thick walls. Hence, please don't divide the 50 cm of space into 11 or 21 or whatever cells.
    Make sure you use a grid that can actually capture the geometry!
  • You may wish to test how sensitive things like "minimum temperature" are to the "delta" used to discretize the domain.
  • As "delta" gets small, the matrix gets big.

Deliverable

• Your group repository must contain all of the files and output noted above. Your Jupyter notebook should be committed in an "executed" state, i.e., all your results should be visible from GitHub.

Extra Credit Opportunities

• What happens if k depends on the temperature?