{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T18:02:40Z","timestamp":1778954560820,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,6,2]],"date-time":"2017-06-02T00:00:00Z","timestamp":1496361600000},"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>To intensify heat transfer within the complex three-dimensional flow field found in technical devices, all relevant transport phenomena have to be taken into account. In this work, a generic procedure based on a detailed analysis of entropy generation is developed to improve heat sinks found in electric machines. It enables a simultaneous consideration of temperature and velocity distributions, lumped into a single, scalar value, which can be used to directly identify regions with a high potential for heat transfer improvement. By analyzing the resulting entropy fields, it is demonstrated that the improved design obtained by this procedure is noticeably better, compared to those obtained with a classical analysis considering separately temperature and velocity distributions. This opens the door for an efficient, computer-based optimization of heat transfer in real applications.<\/jats:p>","DOI":"10.3390\/e19060255","type":"journal-article","created":{"date-parts":[[2017,6,2]],"date-time":"2017-06-02T10:20:44Z","timestamp":1496398844000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Application of Entropy Generation to Improve Heat Transfer of Heat Sinks in Electric Machines"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5785-1231","authenticated-orcid":false,"given":"Toni","family":"Eger","sequence":"first","affiliation":[{"name":"Robert Bosch SG GmbH, Robert-Bosch Strasse 2, 71701 Schwieberdingen, Germany"},{"name":"Laboratory of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Bol","sequence":"additional","affiliation":[{"name":"Robert Bosch SG GmbH, Robert-Bosch Strasse 2, 71701 Schwieberdingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ayothi","family":"Thanu","sequence":"additional","affiliation":[{"name":"Robert Bosch Engineering and Business Solutions Limited, CHIL-SEZ Keeranatham Village, 641035 Tamil Nadu Coimbatore, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00e1szl\u00f3","family":"Dar\u00f3czy","sequence":"additional","affiliation":[{"name":"Laboratory of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, 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, Otto von Guericke University Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00fcdiger","family":"Schroth","sequence":"additional","affiliation":[{"name":"Robert Bosch SG 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, Otto von Guericke University Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,2]]},"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","doi-asserted-by":"crossref","first-page":"8187","DOI":"10.3390\/e17127874","article-title":"Preliminary numerical investigations of entropy generation in electric machines based on a canonical configuration","volume":"17","author":"Eger","year":"2015","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1016\/j.ijheatmasstransfer.2016.07.023","article-title":"Numerical investigations of entropy generation to analyze and improve heat transfer processes in electric machines","volume":"102","author":"Eger","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","first-page":"751","article-title":"Identification of a Canonical Configuration for a Quantitative Analysis of Transport Phenomena in Electric Machines Based on Entropy Generation","volume":"Volume 186","author":"Brebbia","year":"2014","journal-title":"Energy and Sustainability V"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Eger, T., Th\u00e9venin, D., Janiga, G., Bol, T., and Schroth, R. (2015, January 1\u20134). Numerical investigations of residence time distribution of air in electric machines based on a canonical configuration. Proceedings of the Conference on Modelling Fluid Flow, Budapest, Hungary.","DOI":"10.3390\/e17127874"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite size devices and finite time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_7","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":"Revue G\u00e9n\u00e9rale de Thermique"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.plrev.2011.05.010","article-title":"The constructal law and the evolution of design in nature","volume":"8","author":"Bejan","year":"2011","journal-title":"Phys. Life Rev."},{"key":"ref_9","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_10","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_11","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_12","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_13","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_14","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_15","doi-asserted-by":"crossref","first-page":"7211","DOI":"10.1007\/s13369-014-1253-x","article-title":"Optimization of a rectangular microchannel heat sink using entropy generation minimization (EGM) and genetic algorithm (GA)","volume":"39","author":"Adham","year":"2014","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1016\/j.ijheatmasstransfer.2010.11.055","article-title":"Second law analysis of momentum and heat transfer in unit operations","volume":"54","author":"Herwig","year":"2011","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.063","article-title":"Turbulent flow and heat transfer in channels with shark skin surfaces: Entropy generation and its physical significance","volume":"70","author":"Jin","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"2205","DOI":"10.1016\/j.ijheatmasstransfer.2003.11.025","article-title":"Local entropy production in turbulent shear flows: A high-Reynolds number model with wall functions","volume":"47","author":"Kock","year":"2004","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.ijheatfluidflow.2005.03.005","article-title":"Entropy production calculation for turbulent shear flows and their implementation in CFD codes","volume":"26","author":"Kock","year":"2005","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_21","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_22","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_23","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 Semiconductor Thermal Measurement and Management Symposium, Dallas, TX, USA."},{"key":"ref_24","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_25","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_26","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_27","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_28","unstructured":"Kock, F. (2003). Bestimmung der Lokalen Entropieproduktion in Turbulenten Str\u00f6mungen und deren Nutzung zur Bewertung Konvektiver Transportprozesse. [Ph.D. Thesis, Technische Universit\u00e4t Hamburg-Harburg]. (In German)."},{"key":"ref_29","unstructured":"Bejan, A. (1995). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes. Mechanical and Aerospace Engineering Series, CRC Press."},{"key":"ref_30","unstructured":"Gesellschaft, V. (2010). VDI Heat Atlas, Springer."},{"key":"ref_31","unstructured":"Menter, F. (2008). Improved Two-Equation k-Mmega Turbulence Models for Aerodynamic Flows, Technical Report."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.energy.2013.11.035","article-title":"Systematic analysis of the heat exchanger arrangement problem using multi-objective genetic optimization","volume":"65","author":"Janiga","year":"2014","journal-title":"Energy"},{"key":"ref_33","unstructured":"Dar\u00f3czy, L. (2016). Practical Issues in the Optimization of CFD Based Engineering Problems. [Ph.D. Thesis, Otto von Guericke University Magdeburg]. Available online: http:\/\/edoc2.bibliothek.uni-halle.de\/hs\/content\/titleinfo\/61051."},{"key":"ref_34","first-page":"115","article-title":"Simulated binary crossover for continuous search space","volume":"9","author":"Deb","year":"1995","journal-title":"Complex Syst."},{"key":"ref_35","unstructured":"Shi, K. (2016). Integrale Analyse der W\u00e4rme\u00fcbertragung in Elektrischen Generatoren. [Master\u2019s Thesis, Karlsruhe Institute of Technology]. (In German)."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/6\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:37:48Z","timestamp":1760207868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/6\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,2]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["e19060255"],"URL":"https:\/\/doi.org\/10.3390\/e19060255","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,2]]}}}