In an earlier contribution it was shown that the Continuous-Properties Model (CPM) is an ideal theoretical model to calculate melting of ice slurries. Now with a shock-theoretical approach, it is proven that the CPM - in the limit toward a discontinuous melting - just yields the Stefan problem. This limit corresponds to the case when the additive content in an ice slurry tends toward zero. In heat exchangers the ice fraction of an ice slurry is a decreasing function of the downstream space coordinate. The specific pressure drop R=-dp/dx can differ from the inlet to the outlet by more than a factor ten, because the viscosity and the critical shear stress decrease with increasing temperature. A simple analytical model to calculate the overall pressure drop of a cylindrical heat exchanger (with different boundary conditions) is presented.