Consider a slab of thickness 2W that is initially at a temperature TH. The slab is in contact with a cold reservoir at some temperature TC < TH. The slab has a thermal conductivity k and the heat transfer coefficient h is infinitely large. Starting from the unsteady heat equation, find an appropriate set of dimensionless variables so that you can convert this problem into the form

subject to the initial condition T(x, 0) = 1 and the boundary conditions T(0, t) = 0 and T(1, t) = 0.