Variable working conditions of a double-tube counter-flow heat exchanger were analysed. During operation of the heat exchanger, the parameters (temperatures and mass flow rates) of both fluids at its inlet change, which leads to a change in its performance. Heat transfer effectiveness is commonly used to assess the heat exchanger performance, defined as the ratio of the actual to the maximum heat flow rate. In the present paper, the heat exchanger was considered to be a ‘black box’, and the aim was to investigate how the inlet parameters (temperatures and mass flow rates of both fluids) affect the outlet ones (temperatures of both fluids), and thus to attempt to introduce a new relation for the heat transfer effectiveness of a counter-flow heat exchanger as a function of only inlet parameters. Following the analysis, a relation for the heat transfer effectiveness as a function of inlet parameters with five constant coefficients was obtained. These coefficients depend on the heat exchanger geometry and on the properties of the heat transfer fluids; they are not general-purpose, but specific to a counter-flow heat exchanger. The form of the proposed relation for the heat transfer effectiveness of a counter-flow heat exchanger is not satisfactory as it involves five constant coefficients; therefore, a new approach was chosen, consisting in analysing a parameter defined as the ratio of the minimum to the actual arithmetic mean temperature difference. Using the parameter defined in this way, the relation for the heat transfer effectiveness of a counter-flow heat exchanger was obtained as a function of two parameters: the ratio of the heat capacity rates of both fluids, and NTU, with no constant coefficients. The proposed relations were verified against the data produced by a simulator of a double-tube counter-flow heat exchanger.

The diameter and configuration of tubes are important design parameters of power condensers. If a proper tube diameter is applied during the design of a power unit, a high energy efficiency of the condenser itself can be achieved and the performance of the whole power generation unit can be improved. If a tube assembly is to be replaced, one should verify whether the chosen condenser tube diameter is correct. Using a diameter that is too large increases the heat transfer area, leading to over-dimensioning and higher costs of building the condenser. On the other hand, if the diameter is too small, water flows faster through the tubes, which results in larger flow resistance and larger pumping power of the cooling-water pump. Both simple and complex methods can be applied to determine the condenser tube diameter. The paper proposes a method of technical and economic optimisation taking into account the performance of a condenser, the low-pressure (LP) part of a turbine, and a cooling-water pump as well as the profit from electric power generation and costs of building the condenser and pumping cooling water. The results obtained by this method were compared with those provided by the following simpler methods: minimization of the entropy generation rate per unit length of a condenser tube (considering entropy generation due to heat transfer and resistance of cooling-water flow), minimization of the total entropy generation rate (considering entropy generation for the system comprising the LP part of the turbine, the condenser, and the cooling-water pump), and maximization of the power unit’s output. The proposed methods were used to verify diameters of tubes in power condensers in a200-MW and a 500-MW power units.