Heat Transfer in Camilla's Apartment
This is a group project I worked on for Graduate Level Mathematical Modeling Case Studies. My partner, Camilla, and I had two weeks to complete this project.
In this project we modeled heat transfer in an apartment in Socorro, NM. We used temperature data from personal data collection and from wunderground.com. We used a 2D representation of the apartment to model heat transfer through the walls. We made the assumption that each XY slice of the apartment is identical. We solved the partial differential equation using Matlab’s PDE Toolbox. We created a model with geometry representative of the real apartment and coefficients representative of the materials in the real apartment. Our recorded time lag between minimum temperatures was 20,700 seconds. We calculated the temperature of a node near where the thermometer was, and the time lag between minimum temperatures was 43,000 seconds. We suspect this difference is caused by our model having thicker walls than the real apartment and by the temperature outside constantly being the minimum outside temperature. Overall, we believe that our model shows behavior representative of the real apartment. The accuracy could be increased in future research by creating thinner walls.