On optimal heating and cooling strategies for melting and freezing

For a one-dimensional liquid or solid slab that undergoes freezing or melting, we solve for the cooling or heating strategy that, subject to certain constraints and approximations, minimizes entropy production and hence maximizes potentially available work. The key constraint is that the freezing or melting process must be completed in a given fixed time. This constraint can correspond, for example, to a fixed production rate in an industrial process. The validity of this optimal strategy and its practical significance are discussed.