Effectiveness-NTU relations for counterflow heat exchangers: The effect of kinetic energy variation and heat leak from outside

The effectiveness-number of transfer units (NTU) relations are useful data for designing and performance evaluation of heat exchangers with fluids having considerable variation in velocities in the presence of heat leak. In this article, the closed-form (benchmark) solutions for counterflow heat exchangers, when the heat leak is either on the hot or cold side of the heat exchanger in the presence of kinetic energy variation, are presented. It was found that the effectiveness depends on NTU and fluid capacity ratio along with six other dimensionless variables that reflect the magnitude and axial distribution of the kinetic energy and heat leak on the hot and cold sides of the heat exchanger. The results are also presented in a graphical form exhibiting the variation of effectiveness of the heat exchanger with the already-mentioned parameters. It was demonstrated that when the dimensionless heat leak and kinetic energy terms approach zero, the solution reduces to the classical effectiveness-NTU relations for counterflow heat exchangers.