Optimization of energy expenses at convective and conductive heating of the liquid in cylindrical capacity

Abstract

The mathematical model (MM) is developed for the description of evaporation process of model liquid with a surface of the cylindrical capacity (CC) for application of power expenses optimization at convective and conductive influence. Also processes of the changes of liquid and steam-gas mixture (SGM) temperature were considered in the MM. The optimization of power expenses was based on the Pontryagin maximum principle with application to process of liquid evaporation. For the modeling of heat and mass transfer processes with evaporation in cylindrical capacity at the combined influence, the system of the ordinary differential equations was used. At some admission, the MM allows to perform optimization of the cyclogram of a convective expulsion (and heating systems operation and to define a tendency of power expenses reduction at consecutive inclusions and switching off the SGM expulsion and heating of walls of cylindrical capacity with a liquid film on its walls. Power expenses of conductive heating of liquid and a expulsion of SGM from cylindrical capacity are accepted for an optimality criterion. Time intervals of heating the walls with liquid and expulsions of SGM providing minimization of power expenses for evaporation of the set mass of liquid are defined with the help of numerical modeling. The result of calculations without optimization show the increased power expenses are carried out.