Relationships between temperature differences in heat exchangers of heat transformation devices

The temperatures which are present in a heat transformation device play a very important part: at first, the temperatures determine the maximum performance or efficiency of the cycle via the first and second laws of thermodynamics. Secondly, the temperatures determine the heat transfer area which is required to put a given heat flux through the system. Consequently, they relate power to investment cost. In order to elaborate further on these interdependencies, in this paper basic relationships between technically and thermodynamically relevant temperatures, as they are present in the heat exchangers, are being derived. To this end, we will define several temperature differences as usual: the temperature glide, the driving mean temperature difference and the thermodynamic or entropic mean temperature difference. The logarithmic temperature mean is significant for determining the heat transfer. It will be shown that, as long as the temperature gradient between external and internal fluids is larger than the difference in glide of both fluids, the log-mean can be substituted by the difference of the arithmetic mean temperatures. Consequently, it is almost identical to the entropic temperature difference. The entropic temperature difference is a measure of efficiency whereas the logarithmic temperature difference is a measure of first cost. As both temperature differences deviate only marginally from each other in most technical applications it will easily be possible to establish a relationship between performance and investment.