{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T20:49:35Z","timestamp":1762375775279,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T00:00:00Z","timestamp":1383177600000},"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>Application requirements for avionics are often very strict. For example, the heat sinks of avionics need very good temperature uniformity, but the flow rate of coolant is very restricted. In addition, the use of micro-channels is not recommended due to the potential clogging issue. Considering these design requirements, we will discuss a multiple-objective optimal design method to obtain a good stacked mini-channel structure for avionics applications. In our thermal design, the design variables are the mini-channel geometry parameters. Temperature uniformity, entropy generation, max temperature of heat sink and pump work are chosen as the objective functions. A Multi Objective Genetic Algorithm (MOGA) and Fluent solver are used together to minimize multiple objective functions subject to constraints, and locate the Pareto front. By analyzing the multiple objective optimal results, we can draw the conclusion that the objective functions of Tmax and sg have same effect on the optimization, and the multiple optimal results are a set and not a single value. If mostly focusing on the temperature uniformity, we can recommend some optimal structures to design a stacked mini-channel heat sink.<\/jats:p>","DOI":"10.3390\/e15114716","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T11:49:09Z","timestamp":1383220149000},"page":"4716-4731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Optimal Thermal Design of a Stacked Mini-Channel Heat Sink Cooled by a Low Flow Rate Coolant"],"prefix":"10.3390","volume":"15","author":[{"given":"Liping","family":"Pang","sequence":"first","affiliation":[{"name":"School of Aviation Science and Engineering, Beijing University of Aeronautics and Astronautics, Xueyuan Road 37, Haidian District, Beijing 100191, China"}]},{"given":"Minxing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aviation Science and Engineering, Beijing University of Aeronautics and Astronautics, Xueyuan Road 37, Haidian District, Beijing 100191, China"}]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aviation Science and Engineering, Beijing University of Aeronautics and Astronautics, Xueyuan Road 37, Haidian District, Beijing 100191, China"}]},{"given":"Meng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Aviation Science and Engineering, Beijing University of Aeronautics and Astronautics, Xueyuan Road 37, Haidian District, Beijing 100191, China"}]},{"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aviation Science and Engineering, Beijing University of Aeronautics and Astronautics, Xueyuan Road 37, Haidian District, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2013,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"413","DOI":"10.3390\/e6050413","article-title":"Entropy generation due to laminar incompressible forced convection flow through parallel-plates minichannel","volume":"6","author":"Haddad","year":"2004","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1108\/09615530510571921","article-title":"Analysis and optimization of the thermal performance of minichannel heat sinks","volume":"15","author":"Liu","year":"2005","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_3","first-page":"1","article-title":"Multi-layer mini-channel and ribbed mini-channel based high performance cooling configurations for automotive inverters\u2014Part A: Design and evaluation","volume":"5","author":"Pritish","year":"2013","journal-title":"J. Therm. Sci. Eng. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1016\/j.icheatmasstransfer.2012.10.008","article-title":"Optimal thermal design of microchannel heat sinks with different geometric configurations","volume":"39","author":"Hung","year":"2012","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_5","first-page":"1","article-title":"Analysis of multi-layer mini- and micro-channel heat sinks in single phase flow using one and two equation porous media models","volume":"32","author":"Hassel","year":"2011","journal-title":"Heat Transf. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0017-9310(94)90103-1","article-title":"High flux boiling in low flow rate, low pressure drop mini-channel and micro-channel heat sinks","volume":"37","author":"Bowers","year":"1994","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1115\/1.1647124","article-title":"Stacked microchannel heat sinks for liquid cooling of microelectronic components","volume":"126","author":"Wei","year":"2004","journal-title":"J. Electron. Package"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TCAPT.2003.811473","article-title":"Optimization study of stacked mini-channel heat sinks for mini-electronic cooling","volume":"26","author":"Wei","year":"2003","journal-title":"IEEE Trans. Compon. Package Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3262","DOI":"10.1016\/j.ijheatmasstransfer.2012.02.059","article-title":"Optimal design of geometric parameters of double-layered microchannel heat sinks","volume":"55","author":"Hung","year":"2012","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3090","DOI":"10.1016\/j.ijheatmasstransfer.2012.02.038","article-title":"Analysis of heat transfer characteristics of double-layered microchannel heat sink","volume":"55","author":"Hung","year":"2012","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","unstructured":"Dixit, P., Lin, N., Miao, J., Wong, W.K., and Teo, K.C. (June, January 29). Concept and Analytical Analysis of Silicon Mini\/Nanopillars Based 3-D Stacked Minichannel Heat Sink for Advanced Heat Dissipation Applications. Proceedings of the Electronic Components and Technology Conference, Sparks, NV, USA."},{"key":"ref_12","first-page":"22","article-title":"Cooling behavior in a novel heat sink based on multilayer staggered honeycomb structure","volume":"4","author":"Liu","year":"2010","journal-title":"J. Energy Power Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5133","DOI":"10.1016\/S0017-9310(02)00223-5","article-title":"Numerical computation of fluid flow and heat transfer in minichannels","volume":"45","author":"Toh","year":"2002","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1016\/j.proeng.2012.01.1123","article-title":"Optimization and numerical simulation of multi-layer minichannel heat sink","volume":"31","author":"Shao","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1115\/1.2159007","article-title":"Numerical analysis of blockage and optimization of heat transfer performance of fractal-like microchannel nets","volume":"128","author":"Wang","year":"2006","journal-title":"J. Electron. Packag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1108\/09615530510571930","article-title":"Optimization of thermal resistance of stacked micro-channel using genetic algorithms","volume":"15","author":"Jeevan","year":"2005","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1108\/09615531111108512","article-title":"Multi-objective optimization design of a mini-channel heat sink using adaptive genetic algorithm","volume":"21","author":"Shao","year":"2011","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1016\/j.ijheatmasstransfer.2005.08.032","article-title":"Optimization of mini heat exchanger: CFD, analytical approach and multi-objective evolutionary algorithms","volume":"49","author":"Foli","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/j.applthermaleng.2012.06.034","article-title":"Multi-objective design optimization of a mini heat sink for Concentrating Photovoltaic\/Thermal (CPVT) systems using a genetic algorithm","volume":"59","author":"Karathanassis","year":"2013","journal-title":"Appl. Therm. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1016\/j.applthermaleng.2010.03.027","article-title":"Enhanced multi-objective optimization of a minichannel heat sink through evolutionary algorithm coupled with multiple surrogate models","volume":"30","author":"Husain","year":"2010","journal-title":"Appl. Therm. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"144","DOI":"10.3390\/e15010144","article-title":"Numerical study of entropy generation in a flowing nanofluid used in micro- and mini-channels","volume":"15","author":"Hassan","year":"2013","journal-title":"Entropy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TCAPT.2010.2070874","article-title":"Multiobjective optimization of a grooved mini-channel heat sink","volume":"15","author":"Ansari","year":"2010","journal-title":"IEEE Trans. Compon. Package Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1109\/TCAPT.2009.2022586","article-title":"Optimization of minichnnel heat sinks using entropy generation minimization method","volume":"32","author":"Khan","year":"2009","journal-title":"IEEE Trans. Compon. Package Technol."},{"key":"ref_24","unstructured":"Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms, Wiley."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1016\/j.applthermaleng.2008.01.008","article-title":"Simulation-based optimization of thermal systems","volume":"29","author":"Jaluria","year":"2009","journal-title":"Appl. Therm. Eng."},{"key":"ref_26","unstructured":"Poles, S., Geremia, P., Campos, F., Weston, S., and Islam, M. (March, January 5). MOGA-II for an Automotive Cooling Duct Optimization on Distributed Resources. Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO\u201907), Matsushima, Japan."},{"key":"ref_27","unstructured":"(2006). Fluent, Inc.. Software for fluid simulation."},{"key":"ref_28","unstructured":"Shah, R.K., and London, A.L. (1978). Laminar Flow Forced Convection in Ducts, Academic Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4716\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:18Z","timestamp":1760219418000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4716"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,31]]},"references-count":28,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2013,11]]}},"alternative-id":["e15114716"],"URL":"https:\/\/doi.org\/10.3390\/e15114716","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2013,10,31]]}}}