The Local Distribution of Temperatures and Entropy Generation Rate in an Ideal Counterflow Heat Exchanger

Abstract

The process of heat exchange between two fluids of different temperatures and separated by a solid wall occurs in many engineering applications. Log mean temperature difference and effectiveness-NTU methods are widely used to assist in the design of heat exchangers. However, the two methods focus on overall analysis and cannot show the local temperature distributions. This paper obtains the mathematical solutions to the temperature profiles in an ideal counterflow heat exchanger. The aim of this research is to explain the phenomenon called the “entropy generation paradox”, which indicates a discrepancy between effectiveness and optimal entropy generation. The theoretical analysis reveals that the temperature curves are exponential functions when the heat capacity rates of the two streams are different; otherwise, the curves are linear functions. A heat exchanger is demonstrated to draw the temperature profiles under different working conditions. Local entropy generation rates are determined by the ratio of local stream temperatures in the form of a hook function. To realize a certain heat duty, there are many stream flow rate couples, and each couple results in a different entropy generation profile and obtains a corresponding total entropy generation. The helical steam generator of a high-temperature gas-cooled reactor is analyzed in this article and the principle of equipartition of entropy generation is confirmed. This principle indicates that, among the many working conditions to achieve a certain heat duty, a heat exchanger characterized by a nearly constant entropy production gives the best second law efficiency possible in order to achieve the best energy conversion.