Dynamic Thermal Performance of a Plate Heat Exchanger Under Viscosity–Velocity Combined: Implications for Seawater-Source Heat Pump Systems

Abstract

To address the difficulty of predicting plate heat exchanger performance under variable-flow and fouling-prone coastal conditions, this study developed a novel combined framework for a BR50 plate heat exchanger by integrating a steady-state heat transfer model with a transfer-function-based dynamic wall-temperature model. The main innovation is that the framework simultaneously captures steady thermal performance and transient wall-temperature response, while explicitly quantifying the coupled effects of flow velocity and kinematic viscosity. The model was evaluated for sewage-side velocities of 0.8–1.5 m/s and viscosities up to ten times that of clean water. Results show that wall temperature increases slightly with velocity and can be described by a fourth-order polynomial. Its transient response follows first-order inertia, and the time constant decreases as velocity increases, indicating faster thermal response at higher flow rates. Both the sewage-side heat transfer coefficient and the overall heat transfer coefficient increase with velocity but decrease with viscosity; increasing velocity from 0.8 to 1.5 m/s raises the sewage-side coefficient by 49.2%. Sensitivity analysis identifies kinematic viscosity as the dominant factor affecting thermal performance, followed by flow velocity and wall temperature. The framework provides a practical basis for seawater-source heat pumps and coastal heat recovery systems under fouling-influenced conditions.

Keywords

Plate heat exchanger / Viscosity-velocity combined / Dynamic wall temperature / Heat transfer prediction / Seawater-source heat pump / Coastal heat recovery

Author Contributions

Conceptualization, C.L.; Methodology, C.L.; Software, C.L., N.Q., W.H. and S.Q.; Validation, W.H. and S.Q.; Formal Analysis, C.L. and N.Q.; Investigation, C.L., N.Q., W.H. and S.Q.; Resources, C.L.; Data Curation, N.Q.; Writing—Original Draft Preparation, C.L.; Writing—Review & Editing, N.Q.; Visualization, N.Q.; Supervision, N.Q.; Project Administration, N.Q.; Funding Acquisition, N.Q.

Ethics Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be made available on request.

Funding

This work was supported by the Tianjin Youth Fund Project [grant number 15JCQNJC06800], University-level College Students’ Innovation and Entrepreneurship Training Program of Tianjin University of Technology [grant number 202510060172].

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

[1] Liu M, Jin Z, Zhang J, Yuan Y, Ma Q, Mo X, et al. Large—Scale Language Model Assisted Construction of Multi—Source Heterogeneous Knowledge Graphs for Marine Renewable Energy. Mar. Energy Res. 2026, 3, 10002. DOI: 10.70322/mer.2026.10002

[2] Chen R, Samuelson H, Zou Y, Zheng X, Cao Y. Improving building resilience in the face of future climate uncertainty: A comprehensive framework for enhancing building life cycle performance. Energy Build. 2024, 302, 113761. DOI: 10.1016/j.enbuild.2023.113761

[3] Tomrukcu G, Ashrafian T. Climate—resilient building energy efficiency retrofit: Evaluating climate change impacts on residential buildings. Energy Build. 2024, 316, 114315. DOI: 10.1016/j.enbuild.2024.114315

[4] Wang Z, Akbarzadeh M, Aviv D. Multi—objective design exploration for integrated structural—environmental performance of buildings: A review. Energy Build. 2024, 322, 114638. DOI: 10.1016/j.enbuild.2024.114638

[5] Al—Zahrani S. Plate heat exchangers: A state—of—the—art review. Renew. Sustain. Energy Rev. 2026, 227, 116502. DOI: 10.1016/j.rser.2025.116502

[6] Lian JJ, Cui L, Fu Q. Offshore Renewable Energy Advance. Mar. Energy Res. 2024, 7, 10006. DOI: 10.70322/mer.2024.10006

[7] Ma J, Zhang X, Yu J, Wei P. Thermo—economic assessments on building heating by a sewage source heat pump coupled with heat storage system. Therm. Sci. Eng. Prog. 2024, 53, 102756. DOI: 10.1016/j.tsep.2024.102756

[8] Chadly A, Urs RR, Wei M, Maalouf M, Mayyas A. Techno—economic assessment of energy storage systems in green buildings while considering demand uncertainty. Energy Build. 2023, 291, 113130. DOI: 10.1016/j.enbuild.2023.113130

[9] Nikman SA, Mortazavi M, Li D. Additively manufactured heat exchangers: A review on opportunities and challenges. Int. J. Adv. Manuf. Technol. 2021, 112, 601-618. DOI: 10.1007/s00170—020—06372—w

[10] Shah RK. Advances in science and technology of compact heat exchangers. Heat Transf. Eng. 2006, 27, 3-22. DOI: 10.1080/01457630600559462

[11] Clark D. Plate Heat Exchanger Design and Development ; Brewer: London, UK, 1976.

[12] Wang M, Liu W. Thermal performance analysis of a new multiple flat—plate latent heat storage heat exchanger. J. Energy Storage 2024, 98, 113035. DOI: 10.1016/j.est.2024.113035

[13] Wang M. Experimental Study on Special Heat Exchanger for Waste Heat Recovery of Sewage. Master’s Thesis, Harbin Institute of Technology, Harbin, China, 2020. DOI: 10.27061/d.cnki.ghgdu.2020.001564

[14] Pardiñas ÁÁ, Kauko H, Hazarika MM, Selvnes H, Banasiak K, Hafner A. Two—stage evaporator for R744 heat pumps using greywater as heat source. Energy Build. 2023, 289, 113047. DOI: 10.1016/j.enbuild.2023.113047

[15] Wehbi Z, Taher R, Faraj J, Ramadan M, Castelain C, Khaled M. A short review of recent studies on wastewater heat recovery systems: Types and applications. Energy Rep. 2022, 8, 896-907. DOI: 10.1016/j.egyr.2022.07.104

[16] Wang Y, You S, Zheng W, Zhang H, Zheng X, Miao Q. State space model and robust control of plate heat exchanger for dynamic performance improvement. Appl. Therm. Eng. 2018, 128, 1588-1604. DOI: 10.1016/j.applthermaleng.2017.09.120

[17] Wu X, Wang F, Sun D, Yang W. Rheology and flow characteristic of urban untreated sewage for cooling and heating source. Exp. Therm. Fluid Sci. 2011, 35, 508-514. DOI: 10.1016/j.expthermflusci.2010.11.009

[18] Rios—Iribe EY, Cervantes—Gaxiola ME, Rubio—Castro E, Hernández—Calderón OM. Heat transfer analysis of a non—Newtonian fluid flowing through a plate heat exchanger using CFD. Int. J. Appl. Therm. Eng. 2016, 101, 262-272. DOI: 10.1016/j.applthermaleng.2016.02.094

[19] Fernandes S, Gomes IB, Simões LC, Simões M. Overview on the hydrodynamic conditions found in industrial systems and its impact in (bio)fouling formation. Chem. Eng. J. 2021, 418, 129348. DOI: 10.1016/j.cej.2021.129348

[20] Liang B, Chen M, Fu BA, Guan J. Thermal and flow characteristics in a vertical spiral—type ground heat exchanger based on linear non—equilibrium thermodynamic principle. Energy Build. 2022, 266, 112111. DOI: 10.1016/j.enbuild.2022.112111

[21] Vavřička R, Boháč J, Matuška T. Experimental development of the plate shower heat exchanger to reduce the domestic hot water energy demand. Energy Build. 2021, 254, 111536. DOI: 10.1016/j.enbuild.2021.111536

[22] Wang K, Peng Y, Chen J, Wu P. Investigating subcooled flow boiling heat transfer and fluid dynamics within a shell—and—plate heat exchanger. Appl. Therm. Eng. 2025, 258, 124679. DOI: 10.1016/j.applthermaleng.2024.124679

[23] Xu Z, Jia Y, Wang B, Zhang Y, Liu Z, Wang J. Experimental analysis on bio—fouling of iron bacteria on plate heat exchanger. CIESC J. 2013, 64, 3178-3182. DOI: 10.3969/j.issn.0438—1157.2014.08.045

[24] Zhang Z. Experimental Study on Sewage Flow and Heat Transfer Characteristics in Tube with Unsymmetrically Heated Walls. Master’s Thesis, Dalian University of Technology, Dalian, China, 2018. Available online: https://kns.cnki.net/reader/flowpdf?invoice=dRsJFdfqdeDD9b88tHUMe7VCWiqBHoe%2FAtiNqBioP0Ph24juB%2FWfezUjJv2cNUsPjppKt%2B9j2rcFRqAVig36RA8cny4vQFDaG37WztOTKMcBd2UsSdRwWhCSiRzb2CKLCDFy3u8mseUbXdGnhoJyxwFENG8LvM2gvKW7PfymyE4%3D&platform=NZKPT&sourcetype=nxgp&product=CMFD&filename=1018869934.nh&tablename=cmfd201901&type=DISSERTATION&scope=trial&cflag=overlay&dflag=pdf&pages=&language=CHS&trial=&nonce=2E12B094D2144E5CA0025A851CE8FED7 (accessed on 7 June 2018).

[25] Niezgoda—Żelasko B, Kuchmacz J. CFD modelling of the flow of ice slurry in plate heat exchanger channels. Energy 2025, 317, 134700. DOI: 10.1016/j.energy.2025.134700

[26] Yang Q, Tong Z, Tong S, Wang Z, Wang H, Wang Y, et al. Collaborative optimization of high—efficiency and anti—fouling for pillow plate heat exchangers in waste heat recovery. Appl. Therm. Eng. 2025, 276, 126985. DOI: 10.1016/j.applthermaleng.2025.126985

[27] Zhu C, Wang Z, Tian Z, Duan H, Luo S, Cai R. Research on Heat Transfer Characteristics of Parallel Plate Heat Exchanger Clusters for District Cooling Systems. J. Tianjin Univ. Sci. Technol. 2025, 58, 1031-1044. Available online: https://kns.cnki.net/nzkhtml/xmlRead/trialRead.html?dbCode=CJFD&tableName=cjfdlast2025&fileName=TJDX202510004&fileSourceType=1&appId=KNS_BASIC_PSMC&invoice=Wb3jACcZuOfC9f5ea7pUgpPmfDc9ei4TSKuDfh/7ECIKaDpm9e0NL4v/jeaKlrS9tr8HDbhab/c6BtcYBHW01gpHecUWoHmRkYj4jFGzpYejB8LitxVdGOP+dQ2D4WnEodFpdcbewr++Uytb/Ms0S1dJPWIUNKVYWAv6vkIeyo=&platform=NZKPT&type=JOURNAL&cflag=html&trial=&nonce=691AB1521DA245FA9E1517602D55105B (accessed on 24 December 2024).

[28] Xu H, Liu Q, Qiu H, Ni S, Yang C, Wu Y, et al. Numerical investigation on the nonuniform flow distribution and its impact on the heat transfer performance in the microchannel plate heat exchanger. Appl. Therm. Eng. 2026, 284, 129157. DOI: 10.1016/j.applthermaleng.2025.129157

[29] Shi Q, Song C, Pan W, Lei Y. Flow and heat transfer characteristics and comprehensive evaluation of asymmetric plate heat exchangers for centralized heat supply. Appl. Therm. Eng. 2024, 257, 124306. DOI: 10.1016/j.applthermaleng.2024.124306

[30] Wan X, Song K, Dong H, Hou Q, Wu X, He A, et al. Performance improvement of wavy—plate heat exchanger by vortex generators with adjacent—reverse arrangement. Int. J. Therm. Sci. 2025, 215, 109982. DOI: 10.1016/j.ijthermalsci.2025.109982

[31] Prabakaran R, Mohanraj T, Dhamodharan P, Kim SC. Comparative condensation analysis of low—GWP refrigerants in a plate heat exchanger with response surface methodology optimization. Int. Commun. Heat Mass Transf. 2025, 169, 109653. DOI: 10.1016/j.icheatmasstransfer.2025.109653

[32] Berce J, Zupančič M, Može M, Golobič I. Local temperature distribution of a plate heat exchanger undergoing crystallization fouling. Heat Mass Transf. 2025, 61, 68. DOI: 10.1007/s00231—025—03593—1

[33] Wang Q, Zhang X, Geng X, Chen X, Xing M. Experiments on the characteristics of a sewage water source heat pump system for heat recovery from bath waste. Appl. Therm. Eng. 2022, 204, 117956. DOI: 10.1016/j.applthermaleng.2021.117956

[34] Hirokawa T, Imamura T, Kawanami O. Local heat transfer and dryout behavior in a plate heat exchanger using a thin—wall measurement method. Appl. Therm. Eng. 2025, 281, 128708. DOI: 10.1016/j.applthermaleng.2025.128708

[35] Li Y, Lü Y, Wang F. Study on heat transfer enhancement of supercritical CO₂ in printed circuit plate heat exchangers . Cryogenics Supercond. 2025, 53, 36-45. DOI: 10.16711/j.1001—7100.2025.09.009

[36] Krishnan EN, Muneeshwaran M, Rendall J, Brechtl J, Nawaz K. Experimental investigation on heat transfer performance of drain water heat recovery heat exchangers. Energy Build. 2025, 346, 116213. DOI: 10.1016/j.enbuild.2025.116213

[37] Ma D. Study on Heat Transfer Characteristics of Heat Exchangers Under Fluctuating Reclaimed Water Flow and Its Impact on Heat Transfer Performance. Master’s Thesis, Xi’an University of Architecture and Technology, Xi’an, China, 2017. Available online: https://kns.cnki.net/reader/flowpdf?invoice=P%2FwtyZcZpXiGa5tnCtZym8EXs2NPFbW43l0VK8DzQUSzAr8D35CuMKOJBuE6R0G9dR%2FivL5McvVkoSHd7LLtL72Nq8cszqD8jyl90hvw4lY4CXz2Vpe%2FJ6Q5v%2FEWKHbUzPwWE lz%2B%2BJmI4smHK9hg3%2FCa5KWbD7%2FVWVjzr%2FFonJQ%3D&platform=NZKPT&sourcetype=nxgp&product=CMFD&filename=1017737158.nh&tablename=cmfd201802&type=DISSERTATION&scope=trial&cflag=overlay&dflag=pdf&pages=&language=CHS&trial=&nonce=579BA95590B34DFF8E9625FA203290E7 (accessed on 4 June 2017).

[38] Zeng Q, Zhou W, Xu H, Yu J, Wang Z, Zhang Y, et al. Impact of fouling in the thin—plate cut tobacco dryer on equipment process performance. J. Zhengzhou Univ. Light Ind. Nat. Sci. Ed. 2025, 40, 58-63. DOI: 10.12187/2025.01.007

[39] Du Y, Wei W, Xu C, Wang Y, Li X. Heat transfer characteristics of single—phase flow through dimple plate heat exchanger. Appl. Therm. Eng. 2025, 273, 126499. DOI: 10.1016/j.applthermaleng.2025.126499

[40] Yang J, Jacobi A, Liu W. Heat transfer correlations for single—phase flow in plate heat exchangers based on experimental data. Appl. Therm. Eng. 2017, 113, 1547-1557. DOI: 10.1016/j.applthermaleng.2016.10.147

[41] Xuan W, Xu C, Qian C, Wang J, Jiang Z, Ma R, et al. Numerical simulation and thermodynamic test analysis of plate heat exchanger based on topology optimization. Appl. Therm. Eng. 2024, 255, 123882. DOI: 10.1016/j.applthermaleng.2024.123882

[42] Piper M, Zibart A, Djakow E, Springer R, Homberg W, Kenig EY. Heat transfer enhancement in pillow—plate heat exchangers with dimpled surfaces: A numerical study. Appl. Therm. Eng. 2019, 153, 142-146. DOI: 10.1016/j.applthermaleng.2019.02.082

[43] Joybari MM, Selvnes H, Sevault A, Hafner A. Potentials and challenges for pillow—plate heat exchangers: State—of—the—art review. Appl. Therm. Eng. 2022, 214, 118739. DOI: 10.1016/j.applthermaleng.2022.118739

[44] Few J, Manouseli D, McKenna E, Pullinger M, Zapata—Webborn E, Elam S, et al. The over—prediction of energy use by EPCs in Great Britain: A comparison of EPC—modelled and metered primary energy use intensity. Energy Build. 2023, 288, 113024. DOI: 10.1016/j.enbuild.2023.113024

[45] Sun Y, Zhai P, Ning J, Zheng C, Zhang S, Liu C, et al. An integrated system of sinusoidal—corrugated plate heat exchanger and thermoelectric modules for wastewater heat recovery. Energy Convers. Manag. 2022, 267, 115885. DOI: 10.1016/j.enconman.2022.115885

[46] Strobel M, Beckedorff LE, Martins GSM, Oliveira JLG, Paiva KV. Experiments on Gasketed Plate Heat Exchangers with Segmented Corrugation Pattern. ASME J. Heat Transf. 2024, 146, 101901. DOI: 10.1115/1.4065453

[47] Martins GSM, Zanzi MS, de Paiva KV, de Oliveira AAM, Oliveira JLG. Mechanical stress analysis of various GPHE corrugated plates during the assembly and in working conditions. Int. J. Press. Vessel. Pip. 2023, 206, 105013. DOI: 10.1016/j.ijpvp.2023.105013

[48] Arsenyeva O, Tovazhnyansky L, Kapustenko P, Klemeš JJ, Varbanov PS. Review of Developments in Plate Heat Exchanger Heat Transfer Enhancement for Single—Phase Applications in Process Industries. Energies 2023, 16, 4976. DOI: 10.3390/en16134976

[49] dos Santos FJ, Silva RPP, de Paiva KV, Oliveira JLG. Evaluation of plate heat exchangers comprising sections with different chevron angle arrangements. Appl. Therm. Eng. 2024, 249, 123452. DOI: 10.1016/j.applthermaleng.2024.123452

[50] Zahan I, Nasrin R, Jakia NJ. Data analysis for performance index of plate heat exchanger filled by ionanofluid—oil: Parallel versus counterflow. Sci. Rep. 2025, 15, 4688. DOI: 10.1038/s41598—025—88851—2

[51] Muneeshwaran M, Kim HJ, Tayyab M, Tayyab M, Li W, Nawaz K, et al. Flow maldistribution in plate heat exchangers—Impact, analysis, and solutions. Renew. Sustain. Energy Rev. 2025, 207, 114905. DOI: 10.1016/j.rser.2024.114905