Refer to the solution of Example 3 in the class notes (the transient heat diffusion problem). Take α = 0.1 m^2/s, l = 1 m and:
1. Plot the temperature distribution in the slab at t = 0, 10, 20, 50 s.
2. The heat flux q is given by Fourier's law of heat conduction:
q = -k ∂T/∂x, where k is the thermal conductivity of the slab material.
Calculate the heat flux q at the slab boundaries (i.e., at x = 0, 1 m). Take k = 50 W/m·K and plot q vs. t for 0 ≤ t ≤ 20.