Entransy Dissipation Minimization for Isothermal Crystallization Processes with Diffusive Mass Transfer Law

Abstract

A class of isothermal crystallization process with the given total mass of crystals is investigated. The mass transfer process is assumed to obey the diffusive mass transfer law [ g∝Δ(c)], and the optimal concentration configuration for the minimum entransy dissipation of the crystallization process is obtained by applying optimal control theory. Numerical examples are provided, and the obtained results are also compared to those of the minimum entropy generation, constant concentration and constant mass flux operations. The results show that 2/3 power of the net mass of crystals for the minimum entransy dissipation of the process change with the time linearly, and the entransy dissipation rate of the process keeps constant, which coincides with the principle of equipartition of entransy dissipation and is significant different from that obtained for the minimum entropy generation of the process; the entransy dissipation for the mass transfer strategy of constant concentration is smaller than that for the mass transfer strategy of constant mass flux; both the entransy dissipation and the entropy generation for the two mass transfer strategies of the minimum entransy dissipation and the minimum entropy generation are smaller than those for the other two mass transfer strategies. The entropy generation characterizes the irreversibility of energy conversion processes, and the mass entransy dissipation characterizes the irreversibility of mass transfer processes. Since the crystallization process is independent of the energy conversion, so the optimization principle should be entransy dissipation minimization.