3. Unsteady-State Conduction in a Slab. Part III A homogeneous and isotropic slab of length L with insulated sides is initially held at a constant temperature of 100 C everywhere. Then, for t > 0 its end at a: = 0 is held at zero temperature, while its right end at 3: = L has a temperature of 100 exp(-t) at time t. The surface of the slab is large enough that only heat conduction in the thin direction is important. (a) Identify the eigenvalue problem and, therefore, the eigenfunctions and eigenvalues. (1)) Use nite Fourier-transform method to derive the complete solution