Analysis of heat transfer and fluid flow thermodynamic irreversibilities is realized on an example of a counter flow double pipe heat exchanger utilizing turbulent air flow as a working fluid. During the process of mathematical model creation and for different working and constructing limitations, total thermodynamic irreversibility is studied. The present work proves that the irreversibility occurred due to unequal capacity flow rates (flow imbalance irreversibility). It is concluded that the heat exchanger should be operated at effectiveness, $ε$, greater than 0.5 and the well operating conditions will be achieved when $ε$ approaches one where low irreversibility is expected. A new equation is adopted to express the entropy generation numbers for imbalanced heat exchangers of similar design with smallest deviation from the exact value. The results obtained from the new equation are compared with the exact values and with those obtained by Bejan (Bejan, A., 1997, Advanced Engineering Thermodynamics, Wiley, New York).

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