Thermodynamic Optimization with a Finite Number of Heat Intercepts for Cryogenic Systems with Parameters Stepwise Continuous

Some authors assume that the second law efficiency of reversed cryogenic cycles is independent of the minimum temperature of the working fluid. On the contrary Bejan shows, by empirical and theoretical arguments, that exergy efficiency values decrease as the minimum temperature goes down. However, there is no guaranteeing that exergy efficiency vs. minimum temperature is continuous with its derivatives.

The aim of this paper is to study the thermodynamic optimization by the variation of the heat transfer rate in a finite number of points through insulation for the general case of one-dimensional heat transfer (flat plate, hollow cylinder and hollow sphere) in systems, consisting of different materials in series, whose thermal conductivity is a function of temperature and of the coordinate in the heat flux direction. Besides, some parameters or their first derivative are assumed stepwise continuous.

For this purpose, the results of some researches by the author pertinent to the properties of entropy production rate in the one-dimensional heat transfer are utilized.