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Energies
Volume 18
Issue 17
10.3390/en18174760
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Article

Experimental-Numerical Method for Determining Heat Transfer Correlations in the Plate-and-Frame Heat Exchanger

by
Dawid Taler
1,
Ewelina Ziółkowska
2,
Jan Taler
3,*,
Tomasz Sobota
1,
Magdalena Jaremkiewicz
1,
Mateusz Marcinkowski
1 and
Tomasz Cieślik
1
1
Department of Thermal Processes, Air Protection, and Waste Utilisation, Cracow University of Technology, ul. Warszawska 24, 31-155 Cracow, Poland
2
Department of Energy, CUT Doctoral School, Cracow University of Technology, al. Jana Pawła II 37, 31-864 Cracow, Poland
3
Department of Energy, Cracow University of Technology, al. Jana Pawła II 37, 31-864 Cracow, Poland
*
Author to whom correspondence should be addressed.
Energies 2025, 18(17), 4760; https://doi.org/10.3390/en18174760 (registering DOI)
Submission received: 1 August 2025 / Revised: 1 September 2025 / Accepted: 5 September 2025 / Published: 7 September 2025
(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications)
Versions Notes

Abstract

Plate heat exchangers are used in heat substations for domestic hot water preparation and building heating in municipal central heating systems. Water from the municipal water supply is heated by hot water from a district heating network. This paper presents a numerical method for simultaneously determining heat transfer correlations on the cold and hot water sides based on flow-thermal measurements of the plate heat exchanger. The unknown parameters in the functions approximating the Nusselt numbers, which depend on the Reynolds and Prandtl numbers, are determined using the least-squares method, so the sum of the squares of the differences in the calculated and measured temperatures at the heat exchanger outlet reaches a minimum. One or two correlations were sought for a plate heat exchanger, and the total number of parameters sought is between three and six. The limits of the 95% confidence intervals for all estimated parameters were also determined. Correlations for Nusselt numbers determined experimentally for a clean plate heat exchanger can be used in the online monitoring of the degree of fouling of plate heat exchangers installed in the substations of a large urban district heating network.
Keywords: plate-and-frame heat exchanger; thermal substation; heat transfer correlations; experimental testing; numerical method; scale deposits plate-and-frame heat exchanger; thermal substation; heat transfer correlations; experimental testing; numerical method; scale deposits

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MDPI and ACS Style

Taler, D.; Ziółkowska, E.; Taler, J.; Sobota, T.; Jaremkiewicz, M.; Marcinkowski, M.; Cieślik, T. Experimental-Numerical Method for Determining Heat Transfer Correlations in the Plate-and-Frame Heat Exchanger. Energies 2025, 18, 4760. https://doi.org/10.3390/en18174760

AMA Style

Taler D, Ziółkowska E, Taler J, Sobota T, Jaremkiewicz M, Marcinkowski M, Cieślik T. Experimental-Numerical Method for Determining Heat Transfer Correlations in the Plate-and-Frame Heat Exchanger. Energies. 2025; 18(17):4760. https://doi.org/10.3390/en18174760

Chicago/Turabian Style

Taler, Dawid, Ewelina Ziółkowska, Jan Taler, Tomasz Sobota, Magdalena Jaremkiewicz, Mateusz Marcinkowski, and Tomasz Cieślik. 2025. "Experimental-Numerical Method for Determining Heat Transfer Correlations in the Plate-and-Frame Heat Exchanger" Energies 18, no. 17: 4760. https://doi.org/10.3390/en18174760

APA Style

Taler, D., Ziółkowska, E., Taler, J., Sobota, T., Jaremkiewicz, M., Marcinkowski, M., & Cieślik, T. (2025). Experimental-Numerical Method for Determining Heat Transfer Correlations in the Plate-and-Frame Heat Exchanger. Energies, 18(17), 4760. https://doi.org/10.3390/en18174760

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