Thermodynamic optimization for cryogenic systems with a finite number of heat intercepts

Thermodynamic optimization by varying through the use of insulation the heat-transfer rate at finite number of points is studied for one-dimensional heat transfer in systems consisting of different materials in series, whose equivalent conductivity is a function of temperature. For this purpose the results of previous research by the author (Proc. 23rd Intersociety Energy Conversion Conf., p.67-73, 1988), in particular, on the rate of entropy production in regarding one-dimensional heat transfer, are utilized. Four possible cases are considered: (a) shield temperatures are known a prior and the shield positions that minimize the total entropy production rate are required; (b) shield positions are known and the shield temperature are required for which, were these chosen a priori, the shields would be in the most convenient position; (c) shield positions are known and the shield temperatures that minimize the total entropy production rate are required; (d) neither shield temperatures nor shield locations are given and it is required to optimize both simultaneously. It is found that, with certain exceptions, there is almost always one and only one minimum of the total entropy production rate