The black box model of a double-tube counter-flow heat exchanger

Abstract

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 difference between the hot fluid outlet temperature and the cold fluid inlet temperature List of symbolsThe difference between the hot fluid inlet temperature and the cold fluid outlet temperatureAbstract 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 R. Laskowski (*)

Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

“…Based on Table 1 of [26] and Table 4 of the present study, the average of absolute error is 3.3% in [26] and 2.6% with the LR model. While the precision of the compared models are essentially the same, the LR model based on linear regression is considerably easier to derive than the models worked out in [26], where complex physical relations and mathematical calculations (with iterative process) were needed to gain the proposed relations. Furthermore, thermodynamic properties (like the NTU) were needed to identify in [26] by means of a special heat exchanger simulator (because of the complex and iterative derivations of the thermodynamic properties).…”

“…If the outer pipe is cold and the interaction with the environment (heat gain) is lower (m=0.93 is closer to 1), the difference between the E and ME models in modelling out h T , is negligible (the error is 0.6% and 0.7%, respectively). In addition, the results of the LR model can be compared with the ones published in [26], where also linear relations have been derived for the outlet temperature of the cold side. More particularly, the comparison has been carried out for out c T , in case of DPHEs, under the following circumstances: hot fluid is in the inner pipe and both flow rates are constant but different (this is the case of the first nine rows in Table 1 of [26]).…”

“…In addition, the results of the LR model can be compared with the ones published in [26], where also linear relations have been derived for the outlet temperature of the cold side. More particularly, the comparison has been carried out for out c T , in case of DPHEs, under the following circumstances: hot fluid is in the inner pipe and both flow rates are constant but different (this is the case of the first nine rows in Table 1 of [26]). Based on Table 1 of [26] and Table 4 of the present study, the average of absolute error is 3.3% in [26] and 2.6% with the LR model.…”

“…More particularly, the comparison has been carried out for out c T , in case of DPHEs, under the following circumstances: hot fluid is in the inner pipe and both flow rates are constant but different (this is the case of the first nine rows in Table 1 of [26]). Based on Table 1 of [26] and Table 4 of the present study, the average of absolute error is 3.3% in [26] and 2.6% with the LR model. While the precision of the compared models are essentially the same, the LR model based on linear regression is considerably easier to derive than the models worked out in [26], where complex physical relations and mathematical calculations (with iterative process) were needed to gain the proposed relations.…”

“…Section 5 presents the detailed comparison of the E, ME and LR models in view of accuracy completed with the discussion of the results. Furthermore, the LR model is compared with another linear model published in [26], based on which the advantages of the LR model are shown. In Section 6, summarizing conclusions can be found with recommendations on future research.…”