The heat diffusion equation is u_t = Du_{xx}. A rectangular block of dimensions 0 \leq x \leq L, 0 \leq y \leq W \ \text{and} \ 0 \leq z \leq H has an initial temperature profile of f(x,y,z). If all sides are held at a fixed temperature u = 0, find a formal expression for the temperature at later times.
For the case f(x,y,z) = C obtain an explicit expression for the coefficients in the Fourier series.