Effectiveness-NTU relations for parallel flow heat exchangers subjected to heat leak from outside

The effectiveness-NTU relations are a valuable piece of information for designing and rating of heat exchangers when heat leaks are significant. In this paper, the closed-form relations for parallel flow heat exchangers when the heat leak is either on the cold or hot side of the heat exchanger are presented. The results are also presented in a graphical form to illustrate dependence of the fluid capacity ratio as well as the dimensionless heat leak parameter. It is demonstrated that when the dimensionless heat leak term approaches zero, the solution reduces to the classical effectiveness-NTU relations for parallel-flow configurations. In addition, when the ratio approaches zero, the analytical solutions reduce to the cases of condenser and evaporator applications.