{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:19Z","timestamp":1760243179887,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,12,15]],"date-time":"2015-12-15T00:00:00Z","timestamp":1450137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The present paper analyzes numerically the entropy generation induced by forced convection in a canonical configuration. The configuration itself includes two well known fluid dynamic problems: (1) an external flow (flow around a cylinder, K\u00e1rm\u00e1n flow); and (2) an internal flow (flow between two concentric rotating cylinders, Couette flow). In many daily engineering issues (e.g., cooling of electric machines), a combination of these problems occurs and has to be investigated. Using the canonical configuration, the fields of entropy generation are analyzed in this work for a constant wall heat flux but varying two key parameters (Reynolds numbers                                        Re\u221e and                                        Re0). The entropy generation due to conduction shows an absolute minimum around                                                         Re0 =               10,000. The same minima can be found by a detailed analysis of the temperature profile. Thus, entropy generation seems to be a suitable indicator for optimizing heat exchange processes and delivers a large amount of information concerning fluid and heat transport.<\/jats:p>","DOI":"10.3390\/e17127874","type":"journal-article","created":{"date-parts":[[2015,12,15]],"date-time":"2015-12-15T10:09:11Z","timestamp":1450174151000},"page":"8187-8206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Preliminary Numerical Investigations of Entropy Generation in Electric Machines Based on a Canonical Configuration"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5785-1231","authenticated-orcid":false,"given":"Toni","family":"Eger","sequence":"first","affiliation":[{"name":"Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg \u201cOtto von Guericke\u201d, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"},{"name":"Starter Motors and Generators, Robert Bosch GmbH, Robert-Bosch Strasse 2, 71701 Schwieberdingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Bol","sequence":"additional","affiliation":[{"name":"Starter Motors and Generators, Robert Bosch GmbH, Robert-Bosch Strasse 2, 71701 Schwieberdingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7599-9574","authenticated-orcid":false,"given":"Dominique","family":"Th\u00e9venin","sequence":"additional","affiliation":[{"name":"Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg \u201cOtto von Guericke\u201d, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00fcdiger","family":"Schroth","sequence":"additional","affiliation":[{"name":"Starter Motors and Generators, Robert Bosch GmbH, Robert-Bosch Strasse 2, 71701 Schwieberdingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4560-9640","authenticated-orcid":false,"given":"G\u00e1bor","family":"Janiga","sequence":"additional","affiliation":[{"name":"Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg \u201cOtto von Guericke\u201d, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Th\u00e9venin, D., and Janiga, G. (2008). Optimization and Computational Fluid Dynamics, Springer-Verlag.","DOI":"10.1007\/978-3-540-72153-6"},{"key":"ref_2","unstructured":"Bejan, A. (1995). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, CRC Press."},{"key":"ref_3","first-page":"209","article-title":"The constructal law and the evolution of design in nature","volume":"8","author":"Bejan","year":"2011","journal-title":"Phys. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/j.rser.2014.11.104","article-title":"Entropy generation analysis as a design tool\u2014A review","volume":"43","author":"Sciacovelli","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1115\/1.3245176","article-title":"Fin Geometry for Minimum Entropy Generation in Forced Convection","volume":"104","author":"Poulikakos","year":"1982","journal-title":"J. Heat Transf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0735-1933(94)90080-9","article-title":"Correlation of optimal sizes of bodies with external forced convection heat transfer","volume":"21","author":"Fowler","year":"1994","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.3390\/e16042071","article-title":"The Entropic Potential Concept: A New Way to Look at Energy Transfer Operations","volume":"16","author":"Wenterodt","year":"2014","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0142-727X(92)90060-M","article-title":"Second law analysis of combined heat and mass transfer in internal and external flows","volume":"13","author":"Carrington","year":"1992","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"055507","DOI":"10.1088\/0169-5983\/45\/5\/055507","article-title":"Drag with external and pressure drop with internal flows: A new and unifying look at losses in the flow field based on the second law of thermodynamics","volume":"45","author":"Herwig","year":"2013","journal-title":"Fluid Dyn. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.ijthermalsci.2005.01.010","article-title":"Entropy generation and optimal analysis for laminar forced convection in curved rectangular ducts: A numerical study","volume":"45","author":"Ko","year":"2006","journal-title":"Int. J. Therm. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/S0360-5442(98)00010-3","article-title":"Irreversibilities in various duct geometries with constant wall heat flux and laminar flow","volume":"23","year":"1998","journal-title":"Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S1290-0729(02)00051-0","article-title":"Analysis of entropy generation inside concentric cylindrical annuli with relative rotation","volume":"42","author":"Mahmud","year":"2003","journal-title":"Int. J. Therm. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/j.ijthermalsci.2007.11.002","article-title":"Entropy analysis for non-linear viscoelastic fluid in concentric rotating cylinders","volume":"47","author":"Mirzazadeh","year":"2008","journal-title":"Int. J. Therm. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/S1164-0235(01)00011-5","article-title":"Entropy analysis of concentric annuli with rotating outer cylinder","volume":"1","author":"Yilbas","year":"2001","journal-title":"Exergy Int. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.physa.2015.02.062","article-title":"Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface","volume":"432","author":"Adesanya","year":"2015","journal-title":"Physica A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.crme.2014.09.002","article-title":"Entropy generation in a variable viscosity channel flow of nanofluids with convective cooling","volume":"343","author":"Mkwizu","year":"2015","journal-title":"Comptes Rendus M\u00e9canique"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.3390\/e15062081","article-title":"Analysis of entropy generation rate in an unsteady porous channel flow with Navier slip and convective cooling","volume":"15","author":"Chinyoka","year":"2013","journal-title":"Entropy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.3390\/e13071212","article-title":"Application of the EGM Method to a LED-Based Spotlight: A Constrained Pseudo-Optimization Design Process Based on the Analysis of the Local Entropy Generation Maps","volume":"13","author":"Giangaspero","year":"2011","journal-title":"Entropy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.energy.2013.01.069","article-title":"Application of the entropy generation minimization method to a solar heat exchanger: A pseudo-optimization design process based on the analysis of the local entropy generation maps","volume":"58","author":"Giangaspero","year":"2013","journal-title":"Energy"},{"key":"ref_20","unstructured":"Khan, W., Yovanovich, M., and Culham, J. (2006, January 14\u201316). Optimization of microchannel heat sinks using entropy generation minimization method. Proceedings of the 2006 IEEE Twenty-Second Annual IEEE Semiconductor Thermal Measurement and Management Symposium, Dallas, TX, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4038","DOI":"10.1016\/j.ijheatmasstransfer.2007.11.041","article-title":"Optimal package design of stacks of convection-cooled printed circuit boards using entropy generation minimization method","volume":"51","author":"Yang","year":"2008","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/TCAPT.2004.831812","article-title":"Optimal design methodology of plate-fin heat sinks for electronic cooling using entropy generation strategy","volume":"27","author":"Shih","year":"2004","journal-title":"IEEE Trans. Compon. Packag. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1109\/6144.926378","article-title":"Optimization of plate fin heat sinks using entropy generation minimization","volume":"24","author":"Culham","year":"2001","journal-title":"IEEE Trans. Compon. Packag. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.jtice.2012.11.012","article-title":"Multi-objective optimization design of plate-fin heat sinks using a direction-based genetic algorithm","volume":"44","author":"Chen","year":"2013","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s11630-006-0159-7","article-title":"Local entropy production in turbulent shear flows: A tool for evaluating heat transfer performance","volume":"15","author":"Herwig","year":"2006","journal-title":"J. Therm. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00231-006-0086-x","article-title":"Direct and indirect methods of calculating entropy generation rates in turbulent convective heat transfer problems","volume":"43","author":"Herwig","year":"2007","journal-title":"Heat Mass Transf."},{"key":"ref_27","unstructured":"Kock, F. (2003). Bestimmung der Lokalen Entropieproduktion in Turbulenten Str\u00f6mungen und Deren Nutzung zur Bewertung Konvektiver Transportprozesse, Shaker. (In German)."},{"key":"ref_28","unstructured":"Eger, T., Th\u00e9venin, D., Janiga, G., Bol, T., and Schroth, R. (2014). Energy and Sustainability V, WIT Press."},{"key":"ref_29","unstructured":"Menter, F. (2008). Improved Two-Equation K-Omega Turbulence Models for Aerodynamic Flows, Technical Report for NASA Technical Memorandum."},{"key":"ref_30","unstructured":"(2015). CFX-Solver Modeling Guide, Release 16.2, ANSYS Inc.. Software for fluid dynamics program."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/S0035-3159(96)80059-6","article-title":"Method of entropy generation minimization, or modeling and optimization based on combined heat transfer and thermodynamics","volume":"35","author":"Bejan","year":"1996","journal-title":"Rev. G\u00e9n\u00e9rale Therm."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zierep, J., and B\u00fchler, K. (2014). Grundz\u00fcge der Str\u00f6mungslehre: Grundlagen, Statik und Dynamik der Fluide, Springer Fachmedien. (In German).","DOI":"10.1007\/978-3-658-01606-7"},{"key":"ref_33","first-page":"21","article-title":"Calculation of Exergetic Losses in Compact Heat Exchanger Passages","volume":"10","author":"Paoletti","year":"1989","journal-title":"ASME AES"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/12\/7874\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:54:04Z","timestamp":1760216044000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/12\/7874"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,15]]},"references-count":33,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["e17127874"],"URL":"https:\/\/doi.org\/10.3390\/e17127874","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,12,15]]}}}