In this paper, the concept of exergy transfer effectiveness is put forward firstly and the expressions involving relevant variables for the exergy transfer effectiveness, the heat transfer units number and the ratio of cold and hot fluids heat capacity rate have been derived for the high and low temperature heat exchangers. Taking the parallel flow, counter flow and cross flow heat exchangers as examples, the numerical results of exergy transfer effectiveness are given and the comparison of exergy transfer effectiveness with heat transfer effectiveness is analyzed.

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