{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T09:54:56Z","timestamp":1776765296042,"version":"3.51.2"},"reference-count":21,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Polish National Science Centre","award":["DEC-2016\/21\/B\/ST8\/00496"],"award-info":[{"award-number":["DEC-2016\/21\/B\/ST8\/00496"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An analysis is presented of the irreversibility of flow and thermal phenomena in innovative streamlined structured packing of catalytic chemical reactors. The fundamental equations of irreversible thermodynamics defining entropy production as a result of flow friction and heat transport are formulated. The parameters describing the flow and heat transport in these equations are determined using the Computational Fluid Dynamics (CFD) methodology. Local entropy production due to flow friction and heat transport in the channel structure is plotted and compared with flow-temperature maps and relations for flow resistance, pressure gradient, and Nusselt number derived from CFD. The calculations were performed for three gas velocities: 0.3; 2.0, and 6.0 ms\u22121. It was found that the entropy due to flow friction increases strongly with increasing gas velocity, while the entropy due to heat transport decreases with gas velocity, but to a limited extent. These opposing tendencies mean that there is always a minimum of the total entropy production (including these due to flow friction and heat transport), usually for moderate gas velocity. This minimum constitutes the optimum operating point of the reactor from the thermodynamic point of view.<\/jats:p>","DOI":"10.3390\/e27070675","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T03:53:02Z","timestamp":1750823582000},"page":"675","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Thermodynamic Irreversibility of the Flow and Transfer Phenomena Within Streamlined Structures of the Catalytic Reactors"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7126-2839","authenticated-orcid":false,"given":"Mateusz","family":"Korpy\u015b","sequence":"first","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2882-0345","authenticated-orcid":false,"given":"Adam","family":"Rotkegel","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2847-8992","authenticated-orcid":false,"given":"Anna","family":"Gancarczyk","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3966-5205","authenticated-orcid":false,"given":"Marzena","family":"Iwaniszyn","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8089-9946","authenticated-orcid":false,"given":"Katarzyna","family":"Sindera","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0998-8989","authenticated-orcid":false,"given":"Miko\u0142aj","family":"Suwak","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej","family":"Ko\u0142odziej","sequence":"additional","affiliation":[{"name":"Institute of Chemical Engineering, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"},{"name":"Faculty of Civil Engineering and Architecture, Opole University of Technology, Katowicka 48, 45-061 Opole, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1080\/01614949408013925","article-title":"Monoliths in heterogeneous catalysis","volume":"36","author":"Cybulski","year":"1994","journal-title":"Catal. Rev."},{"key":"ref_2","unstructured":"Irvine, T., and Hartnett, J.P. (1978). Laminar Flow Forced Convection in Ducts, Academic Press. [1st ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/j.cep.2011.05.003","article-title":"Short-channel structured reactor: Experiments versus previous theoretical design","volume":"50","year":"2011","journal-title":"Chem. Eng. Process. Process Intensif."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.cej.2013.07.068","article-title":"A compact highly efficient multichannel reactor with a fixed catalyst bed to produce hydrogen via methanol steam reforming","volume":"231","author":"Gribovskiy","year":"2013","journal-title":"Chem. Eng. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.apcata.2008.07.033","article-title":"Design of novel Pt-structured catalyst on anodic aluminum support for VOC\u2019s catalytic combustion","volume":"350","author":"Wang","year":"2008","journal-title":"Appl. Catal. A Gen."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103504","DOI":"10.1016\/j.tsep.2025.103504","article-title":"Convective heat transfer enhancement by combination effect of twist and helix in helical twisted tubes","volume":"60","author":"Wang","year":"2025","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"138297","DOI":"10.1016\/j.cej.2022.138297","article-title":"New streamlined catalytic carriers of enhanced transport properties: Experiments vs CFD","volume":"450","author":"Sindera","year":"2022","journal-title":"Chem. Eng. J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Korpy\u015b, M., Iwaniszyn, M., Sindera, K., Suwak, M., Gancarczyk, A., and Ko\u0142odziej, A. (2023). Flow phenomena in laminar flow through streamlined and sharp-edged short monolithic structures. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-42568-2"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1002\/andp.18822540106","article-title":"Ueber die W\u00e4rmeleitungsf\u00e4higkeit von Fl\u00fcssigkeiten","volume":"254","author":"Graetz","year":"1882","journal-title":"Ann. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1002\/andp.18852610702","article-title":"Ueber die W\u00e4rmeleitungsf\u00e4higkeit von Fl\u00fcssigkeiten","volume":"261","author":"Graetz","year":"1885","journal-title":"Ann. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kong, R., Chen, L., Xia, S., Li, P., and Ge, Y. (2021). Minimization of entropy generation rate in hydrogen iodide decomposition reactor heated by high-temperature helium. Entropy, 23.","DOI":"10.3390\/e23010082"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1134\/S0869864324030211","article-title":"Numerical investigation of entropy generation induced by assisted mixed convection in a vertical convergent channel: Effects of geometric parameters","volume":"31","author":"Hadjadj","year":"2024","journal-title":"Thermophys. Aeromech."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kizilova, N., Shankar, A., and Kjelstrup, S. (2024). A minimum entropy production approach to optimization of tubular chemical reactors with nature-inspired design. Energies, 17.","DOI":"10.3390\/en17020432"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, Y., Wang, T., Wang, Z., Zhu, C., Yang, J., and Yang, B. (2024). Thermal\u2013hydraulic performance analysis of combined heat sink with open microchannels and embedded pin fins. Energies, 17.","DOI":"10.3390\/en17215301"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Saboj, J.H., Nag, P., Saha, G., and Saha, S.C. (2023). Entropy production analysis in an octagonal cavity with an inner cold cylinder: A thermodynamic aspect. Energies, 16.","DOI":"10.3390\/en16145487"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7811","DOI":"10.1007\/s10973-023-12253-7","article-title":"Performance and entropy production analysis of angle blade turbulators used to increase heat transfer","volume":"148","author":"Firat","year":"2023","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Korpy\u015b, M., Gancarczyk, A., Iwaniszyn, M., Sindera, K., Jod\u0142owski, P.J., and Ko\u0142odziej, A. (2020). Analysis of entropy production in structured chemical reactors: Optimization for catalytic combustion of air pollutants. Entropy, 22.","DOI":"10.3390\/e22091017"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1021\/ie50682a010","article-title":"Irreversible thermodynamics in engineering","volume":"58","author":"Wei","year":"1966","journal-title":"Ind. Eng. Chem."},{"key":"ref_19","unstructured":"de Groot, S.R., and Mazur, P. (1969). Non-Equilibrium Thermodynamics, North-Holland."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Herwig, H. (2016). What exactly is the Nusselt number in convective heat transfer problems and are there alternatives?. Entropy, 18.","DOI":"10.3390\/e18050198"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Schlichting, H., and Gersten, K. (2017). Boundary-Layer Theory, Springer. [9th ed.].","DOI":"10.1007\/978-3-662-52919-5"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/675\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:58:03Z","timestamp":1760032683000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/675"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,25]]},"references-count":21,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["e27070675"],"URL":"https:\/\/doi.org\/10.3390\/e27070675","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,25]]}}}