How equation-of-state choice and property uncertainty influence numerical heat exchanger design: A case study of an n-butane/CO₂ mixture
Open accessAbstract
Numerical design of heat transfer and pressure loss in heat exchangers depends strongly on the thermophysical property models used for the working fluid. This is particularly relevant for zeotropic mixtures, where saturation behavior, temperature glide, and transport properties determine local driving temperature differences during phase change. This work analyzes the interplay between heat exchanger modeling and thermophysical property models from user and developer perspectives, examining how model choice affects engineering predictions and analyzing how uncertainties in individual fluid properties propagate into application-level results. A one-dimensional spatially resolved double-pipe condenser model is applied to a zeotropic n -butane/CO₂ mixture with water as secondary fluid. The equations of state GERG-2008, Peng–Robinson, and a molecular-simulation-based Helmholtz model are combined with transport-property models based on the extended corresponding states principle and residual entropy scaling. Local heat-transfer coefficients and pressure gradients are evaluated using correlations suitable for zeotropic mixtures. Results show that fluid-model choice substantially affects temperature profiles and heat-exchanger sizing, mainly through differences in saturation states. Predicted heat exchanger lengths vary from −7.3% to + 11.8% relative to the mean; in a limiting case with small temperature difference full condensation is not always reached. Sensitivity analyses show that uncertainties in thermal conductivity, dynamic viscosity, and isobaric heat capacity dominate fluid-property uncertainty propagation into heat-transfer predictions, whereas pressure-drop-related properties have only minor influence on exchanger length under present conditions with relatively large tube diameters. Including empirical correlation uncertainties for heat-transfer coefficients and pressure loss makes them dominate the total output uncertainty; nevertheless, fluid-property uncertainties remain a relevant secondary contribution.
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Cites
SciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2020) · Nature Methods · doi:10.1038/s41592-019-0686-2 · Cited by 38,430 · see citing works
A New Two-Constant Equation of State
Peng, D., & Robinson, D. B. (1976) · Industrial & Engineering Chemistry Fundamentals · doi:10.1021/i160057a011 · Cited by 13,111 · see citing works
Wagner, W., & Pruß, A. (2002) · Journal of Physical and Chemical Reference Data · doi:10.1063/1.1461829 · Cited by 4,964 · see citing works
SALib: An open-source Python library for Sensitivity Analysis
Herman, J. D., & Usher, W. (2017) · The Journal of Open Source Software · doi:10.21105/joss.00097 · Cited by 1,549 · see citing works
Kunz, O., & Wagner, W. (2012) · Journal of Chemical & Engineering Data · doi:10.1021/je300655b · Cited by 1,341 · see citing works
Relation between the transport coefficients and the internal entropy of simple systems
Rosenfeld, Y. (1977) · Physical Review A · doi:10.1103/physreva.15.2545 · Cited by 691 · see citing works
Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes
Thome, J. R., Hajal, J. E., & Cavallini, A. (2003) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(03)00140-6 · Cited by 592 · see citing works
Condensation in Horizontal Smooth Tubes: A New Heat Transfer Model for Heat Exchanger Design
Cavallini, A., COL, D. D., Doretti, L., Matkovič, M., Rossetto, L., Zilio, C., & Censi, G. (2006) · Heat Transfer Engineering · doi:10.1080/01457630600793970 · Cited by 545 · see citing works
Condensation in horizontal tubes, part 1: two-phase flow pattern map
Hajal, J. E., Thome, J. R., & Cavallini, A. (2003) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(03)00139-x · Cited by 536 · see citing works
New International Formulation for the Viscosity of H2O
Huber, M. L., Perkins, R. A., Laesecke, A., Friend, D. G., Sengers, J. V., ASSAEL, M. J., Metaxa, I. N., Vogel, E., Mareš, R., & Miyagawa, K. (2009) · Journal of Physical and Chemical Reference Data · doi:10.1063/1.3088050 · Cited by 514 · see citing works
A quasi-universal scaling law for atomic transport in simple fluids
Rosenfeld, Y. (1999) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/11/28/303 · Cited by 501 · see citing works
Prediction of transport properties. 1. Viscosity of fluids and mixtures
Ely, J. F., & Hanley, H. J. M. (1981) · Industrial & Engineering Chemistry Fundamentals · doi:10.1021/i100004a004 · Cited by 430 · see citing works
Surface Tensions of Methane-Propane Mixtures
Weinaug, C. F., & Katz, D. L. (1943) · Industrial & Engineering Chemistry · doi:10.1021/ie50398a028 · Cited by 347 · see citing works
New International Formulation for the Thermal Conductivity of H2O
Huber, M. L., Perkins, R. A., Friend, D. G., Sengers, J. V., ASSAEL, M. J., Metaxa, I. N., Miyagawa, K., Hellmann, R., & Vogel, E. (2012) · Journal of Physical and Chemical Reference Data · doi:10.1063/1.4738955 · Cited by 265 · see citing works
Zühlsdorf, B., Jensen, J. K., Cignitti, S., Madsen, C., & Elmegaard, B. (2018) · Energy · doi:10.1016/j.energy.2018.04.048 · Cited by 157 · see citing works
Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid
Bell, I. H., Messerly, R. A., Thol, M., Costigliola, L., & Dyre, J. C. (2019) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.9b05808 · Cited by 144 · see citing works
Self-citationKlein, S. A., McLinden, M. O., & Laesecke, A. (1997) · International Journal of Refrigeration · doi:10.1016/s0140-7007(96)00073-4 · Cited by 122 · see citing works
In-tube condensation of zeotropic fluid mixtures: A review
Fronk, B. M., & Garimella, S. (2012) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2012.11.030 · Cited by 116 · see citing works
Prediction of the thermal conductivity of refrigerants and refrigerant mixtures
Huber, M. L., Friend, D. G., & Ely, J. F. (1992) · Fluid Phase Equilibria · doi:10.1016/0378-3812(92)87072-u · Cited by 97 · see citing works
COL, D. D., Cavallini, A., & Thome, J. R. (2005) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.1857951 · Cited by 88 · see citing works
Surface tension: a simple correlation for natural gas + conensate systems
Hugill, J. A., & van Welsenes, A. J. (1986) · Fluid Phase Equilibria · doi:10.1016/0378-3812(86)85038-5 · Cited by 87 · see citing works
Entropy Scaling of Viscosity—III: Application to Refrigerants and Their Mixtures
Yang, X., Xiao, X., May, E. F., & Bell, I. H. (2021) · Journal of Chemical & Engineering Data · doi:10.1021/acs.jced.0c01009 · Cited by 86 · see citing works
High-pressure vapor-liquid equilibria involving mixtures of nitrogen, carbon dioxide, and n-butane
Shibata, S. K., & Sandler, S. I. (1989) · Journal of Chemical & Engineering Data · doi:10.1021/je00057a011 · Cited by 82 · see citing works
(Vapor + liquid) equilibria and coexisting densities of (carbon dioxide + n-butane) at 311 to 395 K
Niesen, V. G. (1989) · The Journal of Chemical Thermodynamics · doi:10.1016/0021-9614(89)90150-x · Cited by 82 · see citing works
Dai, B., Zhao, P., Liu, S., Su, M., Zhong, D., Qian, J., Hu, X., & Hao, Y. (2020) · Energy Conversion and Management · doi:10.1016/j.enconman.2020.113225 · Cited by 81 · see citing works
Yelishala, S. C., Kannaiyan, K., Sadr, R., Wang, Z., Levendis, Y. A., & Metghalchi, H. (2020) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2020.08.006 · Cited by 67 · see citing works
Lu, P., Luo, X., Wang, J., Chen, J., Liang, Y., Yang, Z., He, J., Wang, C., & Chen, Y. (2022) · Energy Conversion and Management · doi:10.1016/j.enconman.2022.116117 · Cited by 57 · see citing works
Entropy Scaling of Thermal Conductivity: Application to Refrigerants and Their Mixtures
Yang, X., Kim, D., May, E. F., & Bell, I. H. (2021) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.1c02154 · Cited by 52 · see citing works
Sensitivity and uncertainty analysis of heat-exchanger designs to physical properties estimation
Clarke, D. D., Vásquez, V. R., Whiting, W. B., & Greiner, M. (2001) · Applied Thermal Engineering · doi:10.1016/s1359-4311(00)00101-0 · Cited by 50 · see citing works
Linking Viscosity to Equations of State Using Residual Entropy Scaling Theory
Yang, X., Xiao, X., Thol, M., Richter, M. J., & Bell, I. H. (2022) · International Journal of Thermophysics · doi:10.1007/s10765-022-03096-9 · Cited by 47 · see citing works
Self-citationCondensation of zeotropic mixtures of low-pressure hydrocarbons and synthetic refrigerants
Garimella, S., Milkie, J. A., & Macdonald, M. P. (2020) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2020.120301 · Cited by 46 · see citing works
Zhao, Q., Mecheri, M., Neveux, T., Privat, R., & Jaubert, J. (2017) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.7b00917 · Cited by 45 · see citing works
A new simplified model for condensation heat transfer of zeotropic mixtures inside horizontal tubes
Deng, H., Rossato, M., Fernandino, M., & COL, D. D. (2019) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2019.02.128 · Cited by 44 · see citing works
A low-temperature glide cycle for pumped thermal energy storage
Koen, A., Farres-Antunez, P., Macnaghten, J., & White, A. J. (2021) · Journal of Energy Storage · doi:10.1016/j.est.2021.103038 · Cited by 39 · see citing works
Surface Tension of Refrigerants—Selection of Data and Recommended Correlations
Cachadiña, I., Mulero, A., & Tian, J. (2015) · Journal of Physical and Chemical Reference Data · doi:10.1063/1.4921749 · Cited by 35 · see citing works
Performance enhancement of thermal-integrated Carnot battery through zeotropic mixtures
Zhou, T., Shi, L., Sun, X., Zhang, M., Zhang, Y., Yao, Y. F., Pan, Z., Hu, Q., Jiang, Z., Tian, H., et al. (2024) · Energy · doi:10.1016/j.energy.2024.133328 · Cited by 31 · see citing works
Huang, B., Fang, Y., Miao, Z., & Xu, J. (2024) · Journal of Energy Storage · doi:10.1016/j.est.2024.113669 · Cited by 23 · see citing works
Entropy Scaling of Viscosity IV─Application to 124 Industrially Important Fluids
Martinek, V., Bell, I. H., Herzog, R., Richter, M. J., & Yang, X. (2025) · Journal of Chemical & Engineering Data · doi:10.1021/acs.jced.4c00451 · Cited by 22 · see citing works
Sensitivity analysis of heat exchanger design to uncertainties of correlations
Lambert, J., & Gosselin, L. (2018) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2018.03.037 · Cited by 20 · see citing works
Stochastic modeling of heat exchanger response to data uncertainties
Prasad, R. C., Karmeshu, & Bharadwaj, K. K. (2002) · Applied Mathematical Modelling · doi:10.1016/s0307-904x(01)00082-8 · Cited by 18 · see citing works
Sieres, J., & Campo, A. (2018) · International Journal of Thermal Sciences · doi:10.1016/j.ijthermalsci.2018.03.019 · Cited by 16 · see citing works
Multi-criteria decision-making under uncertainty conditions of a shell-and-tube heat exchanger
Saldanha, W. H., Arrieta, F. R. P., Ekel, P., Machado-Coelho, T. M., & Soares, G. L. (2020) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2020.119716 · Cited by 16 · see citing works
Håkansson, A. (2019) · Journal of Food Engineering · doi:10.1016/j.jfoodeng.2019.05.031 · Cited by 14 · see citing works
Yu, Y., Wang, S., Niu, F., Lai, Y., & Kuang, Z. (2014) · Progress in Nuclear Energy · doi:10.1016/j.pnucene.2014.10.014 · Cited by 9 · see citing works
Babuska, I. M., & Silva, R. S. (2010) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.3012 · Cited by 8 · see citing works
ZeoPTES: Zeotropic Pumped Thermal Energy Storage with an Ammonia–Water Mixture as Working Fluid
Bernehed, A. (2021) · Energy Technology · doi:10.1002/ente.202100470 · Cited by 7 · see citing works
Fang, X., Qiu, G., Chen, J., Liu, K., Li, Q., & Cai, W. (2024) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2024.11.024 · Cited by 7 · see citing works
Qiao, H., Lu, X., Yuan, L., Wang, H., Yang, B., & Yu, X. (2025) · Energy Conversion and Management · doi:10.1016/j.enconman.2025.121009 · Cited by 4 · see citing works
Li, H. B., Sun, Q., Ding, M., & Guo, Z. (2024) · Nuclear Engineering and Design · doi:10.1016/j.nucengdes.2024.113585 · Cited by 3 · see citing works
Šarić, D., Pohl, S. M., Fiedler, F., Guevara‐Carrion, G., Span, R., Thol, M., & Vrabec, J. (2026) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.6c00459 · Cited by 2 · see citing works
Self-citationBerger, C., Schnelting, L., Raabe, G., Welzl, M., Heberle, F., & Brüggemann, D. (2026) · Experimental Thermal and Fluid Science · doi:10.1016/j.expthermflusci.2026.111760 · Cited by 1 · see citing works
Sabbaghnia, M. Z., & Atakan, B. (2026) · Energy Technology · doi:10.1002/ente.202502620 · Cited by 1 · see citing works
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- Authors
- Welp, A., Buchenfeld, J., Saric, D., Sabozin, F., Thol, M., Vrabec, J., Span, R., & Atakan, B.
- Affiliations
- University of Duisburg-Essen (DE)
- Ruhr University Bochum (DE)
- Technische Universität Berlin (DE)
- Corresponding author
- Welp, Alexandra
- ORCID
- Venue
- International Journal of Heat and Mass Transfer
- Publisher
- Elsevier BV
- Published
- 2027-01
- Volume
- 272
- Pages
- 129557
- ISSN
- 0017-9310 (ISSN-L)
- OpenAlex
- W7213953988
- Cited by
- 0
- References
- 52
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- International Journal of Heat and Mass Transfer (publishedVersion, cc-by)
- Universitätsbibliographie, Universität Duisburg-Essen (submittedVersion)
- Funders
- German Research Foundation (526086126, 525876331, 525971077)
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Refrigeration and Air Conditioning Technologies
- Physical Sciences › Engineering › Biomedical Engineering › Phase Equilibria and Thermodynamics
- Physical Sciences › Engineering › Mechanical Engineering › Heat Transfer and Boiling Studies
- Keywords
- heat exchanger design, equation of state, zeotropic mixtures, GERG-2008, Peng-Robinson equation of state, Helmholtz equation of state, heat transfer coefficient, pressure drop, saturation behavior, temperature glide, error propagation, heat exchanger length
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