{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:19:28Z","timestamp":1773152368886,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2010,7,26]],"date-time":"2010-07-26T00:00:00Z","timestamp":1280102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper discusses a simple multi-variable optimization problem: the bifurcation of a branch of a pipe of circular cross-section with a given initial radius r0 and delivering a given mass flow rate m0.The optimization is performed using an objective function that prescribes the minimization of the entropy generation rate due \u2014 in this simple case \u2014 only to viscous flow effects within the tubes. Several fundamental simplifying assumptions are made to reduce the problem to a multi-variable optimization in three independent variables: the aspect ratio of the domain served by the flow, the diameter ratio of the primary and secondary branches, and the length of the secondary branch (the location of both the \u201csource\u201d of the fluid and the \u201csink\u201d, i.e., the place of desired delivery of the fluid, being a datum).It is shown that the solution is strongly dependent both on the aspect ratio and on the diameter ratio, and that the \"optimal\" configurations display some resemblance to the branching patterns observed in natural structures. The study poses a challenge both to Designers and to Natural Scientists: are the optima suggested by the present procedure compatible with the structures currently used in heat exchangers and flow devices? Are they compatible with the structures observed in nature? No final answer is provided in this preliminary study, but a possible \"falsification\" procedure is outlined in the conclusions.<\/jats:p>","DOI":"10.3390\/e12081855","type":"journal-article","created":{"date-parts":[[2010,7,26]],"date-time":"2010-07-26T10:36:08Z","timestamp":1280140568000},"page":"1855-1866","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Entropy Generation Minima in Different Configurations of the Branching of a Fluid-Carrying Pipe in Laminar Isothermal Flow"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2220-1762","authenticated-orcid":false,"given":"Enrico","family":"Sciubba","sequence":"first","affiliation":[{"name":"Dept. of Mechanical & Aeronautical Engineering, University of Roma 1 \u201cLa Sapienza\u201d, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cano-Andrade, S., Hernandez-Guerrero, A., von Spakovsky, M.R., Damian-Ascencio, C.E., and Rubio-Arana, J.C. (2010). Current density and polarization curves for radial flow field patterns applied to PEMFCs. Energy, in press.","DOI":"10.1016\/j.energy.2009.07.045"},{"key":"ref_2","first-page":"48","article-title":"Efficiency of optimized bifurcating tree-like and parallel microchannel networks in the cooling of electronics","volume":"07","author":"Escher","year":"2008","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_3","unstructured":"Ramos-Alvarado, B., Hernandez-Guerrero, A., Juarez-Robles, D., Li, P., and Rubio-Arana, J.C. (, January November). Parametric study of a symmetric flow distributor. Proceedings of ASME-IMECE, Lake Buena Vista, FL, USA."},{"key":"ref_4","unstructured":"Bejan, A. (1995). Entropy Generation Minimization, CRC Press."},{"key":"ref_5","unstructured":"Robbe, M., and Sciubba, E. (, January May). A 2-D constructal configuration genetic optimization method. 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Abteil.)"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1073\/pnas.12.3.207","article-title":"The physiological principle of minimum work: I. The vascular system and the cost of blood","volume":"12","author":"Murray","year":"1926","journal-title":"Natl. Acad. Sci."},{"key":"ref_15","unstructured":"Rubio-Jimenez, C.A., Hernandez-Guerrero, A., Rubio-Arana, J.C., and Kandlinkar, S. (, January November). Natural patterns applied to the design of microchannel heat sinks. Proceedings of ASME-IMECE, Lake Buena Vista, Florida, USA."},{"key":"ref_16","unstructured":"Robbe, M. (2007). CFD Analysis of the Thermo-Fluidynamic Performance of Constructal Structures. [Ph.D. Thesis, University of Roma 1]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/0017-9310(96)00175-5","article-title":"Constructal-theory network of conducting paths for cooling a heat generating volume","volume":"40","author":"Bejan","year":"1997","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_18","unstructured":"Bejan, A. (2000). Shape and Structure from Engineering to Nature, Cambridge U. Press."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1016\/S1290-0729(00)01176-5","article-title":"Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluids streams","volume":"39","author":"Bejan","year":"2000","journal-title":"Int. J. Therm. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3203","DOI":"10.1016\/j.ijheatmasstransfer.2004.02.007","article-title":"The constructal law and the thermodynamics of flow systems with configuration","volume":"47","author":"Bejan","year":"2004","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_21","unstructured":"Sciubba, E. (, January March). Constructal theory & variational principles for the Navier-Stokes equations: Is there a link?. Proceedings of Workshop on Constructal Theory of the Generation of Optimal Flow Configuration, Rome, Italy."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/8\/1855\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:59Z","timestamp":1760220179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/8\/1855"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,26]]},"references-count":21,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2010,8]]}},"alternative-id":["e12081855"],"URL":"https:\/\/doi.org\/10.3390\/e12081855","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,26]]}}}