Numerical and thermodynamic analyses have been undertaken in this study to examine energy and exergy efficiencies of in-line tube banks for unsteady cross-flow. Pitch ratio (PR) and the number of in-line tubes are varied for Reynolds numbers of 500 and 10,000, and artificial heat leakages are modeled as a source term. Numerical results are compared with published values, and good agreements are obtained regarding Nusselt number and pressure drop. Whereas the energy efficiency varied between 72% and 99%, the exergy efficiency ranged from 40% to 70%. It was found that while viscous dissipation has a low effect on energy and exergy efficiencies for the lower Reynolds number, it has a significant effect for the higher Reynolds number. On the other hand, heat leakage had a greater effect on exergy efficiency compared to energy efficiency, especially for the lower Reynolds number case. Overall, this study verified how heat leakage could play a vital role on efficiency for low-inlet temperature heat recovery systems.