A system of uniform temperature in contact with a thermal bath must be heated in a fixed time interval between given initial and final temperatures. Several ways of defining the lost work associated with the heating process are presented. The minimum entropy generation is generally not equivalent to the minimum lost available work. Two optimal control problems are defined and solved for various heat transfer mechanisms, among them Newtonian heat convection and radiative heat transfer. The optimal paths are obtained for both objective functions (i.e., entropy generation and lost available work). The results of the optimal strategies are di¤erent from those associated with the usual industrial heating strategy that keeps a constant heat reservoir temperature. Much better results are obtained by using another simple heating procedure, namely the constant heat flux strategy. The di¤erence between various heating strategies is higher in the case of Newtonian convection than in the case of radiative heat transfer and increases by increasing the final temperature of the heating process. The analytical expressions of the optimal paths are presented in dimensionless form, allowing easy implementation.The energy transport coe‰cient between heat reservoir and system (sometimes called thermal conductance or heat transfer coe‰cient) is denoted by k n , where n is shorthand for the mechanism of heat transfer. One assumes that k n is constant in time and 54 V. Badescu

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