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Abstract
Based on constructal theory, entropy generation minimization, and second law efficiency, equations are formulated for tree-shaped counterflow-imbalanced heat exchanger for fully developed laminar and turbulent fluid flow. Entropy generation number, rational efficiency, and effectiveness behavior with respect to changes in number of pairing levels and different tube length-to-diameter ratios of constructal heat exchanger are analyzed analytically. Different values of capacity ratio and Reynolds number for fully developed laminar and turbulent fluid flow are considered to study the influence of pressure drop and flow imbalance irreversibilities of constructal heat exchanger. Values of tube length-to-diameter ratio and number of pairing levels of constructal heat exchanger can be obtained for lower entropy generation number and higher second law efficiency which includes both irreversibilities due heat transfer and pressure drop. The analysis reveals the improvements in the performance of constructal heat exchanger compared to conventional single-tube-dimensioned heat exchanger.