Counterflow, crossflow and cocurrent flow heat transfer in heat exchangers: analytical solution based on transfer units

Bradley, Joel C.

doi:10.1007/s00231-010-0579-5

Cited by 11 publications

(7 citation statements)

References 2 publications

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“…in (hydraulic) heating systems like central [1], district [2] or solar heating systems [3,4], etc.). Many modelling approaches like the ones based on the most commonly used [5] effectiveness-number of transfer units (effectiveness-NTU) method [6,7] and the logarithmic mean temperature difference (LMTD) approach [8] assume energy balance between the two sides (that is between the fluids in the two sides) of a heat exchanger without any heat gain/loss to the environment. In [9], the LMTD is used to model the effect of a heat exchanger coil in a water storage tank.…”

Section: Introductionmentioning

confidence: 99%

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

2018

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Developing mathematical models for describing heat exchanger outlet temperatures is of great importance for the practice, since heat exchangers are unavoidable elements in any applications, where heat transfer is needed between hydraulically separated fluid parts. The conventional, well-tried physically-based E model (standing for the known effectiveness-NTU approach) is recalled. This model assumes energy balance between the two sides of a heat exchanger (without any interaction with the environment). Based on studies in the literature, mathematical models with similar simplicity and usability to that of the E model, but under heat gain/loss to the environment, are still lacking in the field. This work intends to contribute to filling this gap with two proposed models, called ME and LR models. Based on measured data, all three models are accurate enough for general engineering/modelling purposes, nevertheless, the partly physically-based, partly empirical ME model is more precise than the E model if the heat gain/loss to the environment is considerable, and the empirical (black-box type) LR model is more precise than both the E and ME models if the heat gain/loss is not negligible. Furthermore, the outlet temperatures can be explicitly expressed from the simple linear algebraic relations characterizing all models alike.

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Section: Introductionmentioning

confidence: 99%

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

2018

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“…Co-current flow heat exchangers involve the transfer of heat between two fluids travelling in the same direction (Figure 3) and were modelled as ( [22]):…”

Section: Co-current Flow Heat Exchangersmentioning

confidence: 99%

Thermal and Economic Analysis of Heat Exchangers as Part of a Geothermal District Heating Scheme in the Cheshire Basin, UK

et al. 2022

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Heat exchangers are vital to any geothermal system looking to use direct heat supplied via a district heat network. Attention on geothermal schemes in the UK has been growing, with minimal attention on the performance of heat exchangers. In this study, different types of heat exchangers are analysed for the Cheshire Basin as a case study, specifically the Crewe area, to establish their effectiveness and optimal heat transfer area. The results indicate that counter-current flow heat exchangers have a higher effectiveness than co-current heat exchangers. Optimisation of the heat exchange area can produce total savings of £43.06 million and £71.5 million, over a 25-year lifetime, in comparison with a fossil-fuelled district heat network using geothermal fluid input temperatures of 67 °C and 86 °C, respectively.

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“…The relation for the temperature difference (ΔT 2 ) as a function of the inlet temperatures (T h1 ; T c1 ) is linear (13). However, it was difficult to find appropriate functions to describe the relation for the temperature difference (ΔT 2 ) as a function of mass flow rates (ṁ h ,ṁ c ).…”

Section: The Black Box Model Of the Heat Exchangermentioning

confidence: 99%

“…the heat exchanger efficiency defined as the ratio of the actual to the optimum rate of heat transfer [10][11][12]. To determine the performance of heat exchangers, the required, or obtained, heat transfer units [13] were also proposed. For a counter-flow heat exchanger, the heat transfer effectiveness is a function of two parameters: NTU and C; it has the following form [1][2][3][4][5]:…”

Section: Introductionmentioning

confidence: 99%

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

Laskowski

2014

Heat Mass Transfer

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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 (*)

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Counterflow, crossflow and cocurrent flow heat transfer in heat exchangers: analytical solution based on transfer units

Cited by 11 publications

References 2 publications

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

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

Thermal and Economic Analysis of Heat Exchangers as Part of a Geothermal District Heating Scheme in the Cheshire Basin, UK

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

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