Kraus and Kern derived for heat exchangers a relationship between the temperature effectiveness of the tube side stream,the number of heat transfer units based on the tube-side heat capacity rate and the heat capacity ratio of the tube to the shell. This paper is aimed at further simplification of the Kraus-Kern formula and provides analytical proof for a limiting process for the effectiveness of heat exchangers that was intuitively considered in various texts but whose analytical proof was not available in the literature.