Heat Equation Solution (partial Fourier series)
This is a partial Fourier series solution of the the one-dimensional heat equation with a zero left boundary and a Newton's Law of Cooling style right boundary condition. The sliders allow one to vary a few important physical parameters. Once the parameters are chosen, one can advance the solution in time with the slider.
The problem is based on Example 7.1 from Farlow's "Partial Differential Equations for Scientists and Engineers".
What is the effect of varying ?
In the "three dot" menu at the upper right most corner of the page, click on "Open with GeoGebra App". This will allow you to modify elements of the visualization. Click on the definition of in the left hand panel and change it to . What's interesting about the behavior of the temperature at the right end as time moves forward? How is this behavior affected by the value of ? Explain the behavior from a physical perspective.