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Purpose The paper aims to present the mathematical modeling of plate fin and tube heat exchanger at small Reynolds numbers on the water side. The Reynolds number of the water flowing inside the tubes was varied in the range from 4,000 to 12,000. Design/methodology/approach A detailed analysis of transient response was modeled for the following changes in the operating parameters of the heat exchanger: a reduction in the water volume flow, an increase in the water volume flow and an increase in the water volume flow with a simultaneous reduction in the air flow velocity. Findings The results of the numerical simulation of a heat exchanger by using experimentally determined water-side heat transfer correlation and theoretical correlation derived for the transition tube flow agree very well. The relationship to calculate the air-side Nusselt number was determined experimentally. The correlation for the air-side Nusselt number was the same for the theoretical and experimental water side correlation. Research limitations/implications The correlation for the air-side Nusselt number as a function of the Reynolds and Prandtl numbers is based on the experimental data and was determined using the least squares method. Originality/value The form of the relationship that was used to approximate experimentally determined water-side Nusselt numbers is identical to the theoretically derived formula for the transition range. The experiments show that the relationship for the water-side Nusselt number in transition and turbulent flow regime that was obtained using theoretical analysis gives quite satisfactory results.

Hybrid hydro energy systems are usually analysed with pumped hydro storage systems, which can facilitate energy accumulation from other sources. Despite the lack of water storage, run-of-the-river hydropower plants are also attractive for hybrid systems owing to their low investment cost, short construction time, and small environmental impact. In this study, a hybrid system that contains run-of-the-river small hydro power plants (SHPs), PV systems, and batteries to serve local loads is examined. Low-power and low-head schemes that use variable-speed operation are considered. The novelty of this study is the proposal of a dedicated steady-state model of the run-of-the-river hydropower plant that is suitable for energy production analysis under different hydrological conditions. The presented calculations based on a real SHP of 150 kW capacity have shown that a simplified method can result in a 43% overestimation of the produced energy. Moreover, a one-year analysis of a hybrid system operation using real river flow data showed that the flow averaging period has a significant influence on the energy balance results. The system energy deficiency and surplus can be underestimated by approximately 25% by increasing the averaging time from day to month.

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