9-020-S-HeatDiffusion

By Kimberly Spayd1, James Puckett2

1. Mathematics, Gettysburg College, Gettysburg PA USA 2. Physics, Gettysburg College, Gettysburg PA USA

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Modeling Scenarios

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Abstract

This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin metal rod that has one of its ends submerged in hot water and the other end in room-temperature water. Students then investigate the subtleties of analytical and numerical techniques used to solve the initial boundary value problem. Finally, the experimental data can be used to compare the theoretical model with the physical phenomenon.

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Researchers should cite this work as follows:

  • Kimberly Spayd; James Puckett (2019), "9-020-S-HeatDiffusion," https://www.simiode.org/resources/6451.

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Tags

  1. boundary
  2. collect
  3. data
  4. Dirichlet
  5. experiment
  6. heat
  7. homogeneous
  8. initial condition
  9. Longer Duration (Week or more project)
  10. MatLab
  11. modeling
  12. Newton
  13. non-homogeneous
  14. numerical
  15. partial differential equation
  16. physics
  17. project
  18. Python
  19. Raspberry Pi
  20. separation