Modeling Electrical Wire Heat Transfer
In this project I set out to model the rate at which an electrical wire with a constant applied wattage in a closed environment changes temperature. The thing that makes this problem complicated is the closed environment -- any heat that leaves the wire enters and stays in the surroundings, changing the rate at which the next heat will leave heat wire. After creating some analytical and numerical models, I did real experiments. The first experiment involved a constant temperature wire heating up a variable temperature pool of oil. The second experiment involved a constant wattage but variable temperature wire heating up a variable temperature pool of oil. For experiments that required a constant temperature wire I implemented a PID temperature control system which is explained below.
The Experiments
For all of the numerical approximations and PID algorithms used in this experiment, check out my github reposiory
Experiment #1: A wire with a constant applied power is placed in an insulated pool of oil. The water temperature and wire temperature are measured via thermistors embedded in the wire and placed in the oil. These temperature readings are compared with the predictions of a numerical model.
Experiment #2: A wire is held at a constant temperature with a PID controller that modulates power input to the wire. The wire is placed in the same insulated container with oil set up described in experiment #1 and the temperature readings are compared with the predictions of a numerical model.
PID Controller
The below video is an explanation of my PID controlled constant temperature wire set up.
Tuning The Thermistor
I heated up the thermistors in a beaker of water and measured the water temperature using a thermometer. I then plotted the temperatures of the water and resistance readings of the thermistors (taken with an Arduino), creating a standard curve for the temperature of the thermistor surroundings based on their resistances.
Results
Experiment #1:
Experiment #2:
Discussion
The estimated temperatures and actual temperatures were very close. Since this experiment was really difficult to do and took a long time to run, I was not able to do multiple trials. For that reason, the experiment was more of an educational demonstration than a scientific inquiry. The numerical methods I used were based in well proven heat transfer laws, so I do not find it surprising that the approximation is close to the actual results. Still, without more trials I cannot say if my results support my models and methods. I can say, however, that my results look really cool and that I had fun gathering them.