Another confirmation that counter-current logarithmic mean is upper bound and a note on approximations

The paper presents modifications on published demonstration that the counter-current logarithmic-mean-temperature-difference (ΔTLM) is upper bound compared with the co-current ΔTLM. In the published demonstration, an approach was proposed but it suffered from wrong assumption. In this paper, corrections to the wrong assumption and a property of a curve derived from the ΔTLM curve have been used to propose another demonstration that counter-current ΔTLM is upper bound. Optimization problems have been formulated to verify the proposed developments and demonstrate the results obtained.A class of ΔTLM approximations including two accurate approximations proposed by the author are discussed. The selected approximations are designated as Underwood's class. This class generates accurate results over the problem temperature-difference-ratio range and has the advantage of direct use of the heat exchanger (HEX) terminal temperature differences.

► Demonstration of the counter-current logarithmic mean temperature difference is upper bound. ► A curve derived from ΔTLM curve is used in the development of the proposed demonstration. ► Optimization problems are used to verify the developments and demonstrate the results. ► The paper includes corrections to a published demonstration by other investigators. ► The paper concludes by discussing a class of ΔTLM approximations labeled Underwood's class.