On the Impact of the Dynamics of Heat Transfer of the Thermal Machine Working Fluid and Heat Sources on the Shape of the Boundary of the Set of Realizable Regimes

Abstract

From the point of view of finite time thermodynamics, the performance boundaries of thermal machines are considered, taking into account the irreversibility of the heat exchange processes of the working fluid with hot and cold sources. We show how the dynamics of heat exchange affects the shape of the optimal cycle of a heat engine and its performance, in particular, energy conversion efficiency in the maximum power mode. This energy conversion efficiency can depend only on the ratio of the heat transfer coefficients to the sources, or not depend on them at all. A class of dynamic functions corresponding to “natural” requirements is introduced and it is shown that, for any dynamics from this class, the optimal cycle consists of two isotherms and two adiabats, not only for the maximum power problem, but also for the problem of maximum energy conversion efficiency at a given power. Examples are given for calculating the parameters of the optimal cycle for the cases when the heat transfer coefficient to the cold source is arbitrarily large, and for dynamics in the form of a linear phenomenological (Fourier heat transfer) law.