1D heat conduction equation - Your turn

A rod of length \(2\) has the following initial and boundary temperature conditions:

\[ T(x,0) = 50; \quad T(0,t) = 0 \quad \text{and} \quad T(2,t) = 100 \]

The solution to the heat conduction equation \(\lambda \dfrac{\partial^2 T}{\partial x^2} + q = \dfrac{\partial T}{\partial t}\) with \(\lambda=1\), is:

\[ T(x,t) = 50x + \sum_{n=\text{even},\neq 0}^{\infty} \dfrac{200}{n \pi} \sin \left( \dfrac{n\pi x}{2} \right) e^{-\frac{n^2 \pi^2}{4}t} \]

Plot the temperature distribution of the rod at \(t = 0\), \(0.05\), \(0.1\), and \(0.5\).

# TODO: Write your solution below

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