{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T19:13:54Z","timestamp":1762542834926,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T00:00:00Z","timestamp":1522627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004412","name":"T\u00fcrkiye Bilimler Akademisi","doi-asserted-by":"publisher","award":["GEBIP"],"award-info":[{"award-number":["GEBIP"]}],"id":[{"id":"10.13039\/501100004412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>During the last decade, second law analysis via entropy generation has become important in terms of entropy generation minimization (EGM), thermal engineering system design, irreversibility, and energy saving. In this study, heat transfer and entropy generation characteristics of flows of multi-walled carbon nanotube-based nanofluids were investigated in horizontal minitubes with outer and inner diameters of ~1067 and ~889 \u00b5m, respectively. Carbon nanotubes (CNTs) with outer diameter of 10\u201320 nm and length of 1\u20132 \u00b5m were used for nanofluid preparation, and water was considered as the base fluid. The entropy generation based on the experimental data, a significant parameter in thermal design system, was examined for CNTs\/water nanofluids. The change in the entropy generation was only seen at low mass fractions (0.25 wt.% and 0.5 wt.%). Moreover, to have more insight on the entropy generation of nanofluids based on the experimental data, a further analysis was performed on Al2O3 and TiO2 nanoparticles\/water nanofluids from the experimental database of the previous study of the authors. The corresponding results disclosed a remarkable increase in the entropy generation rate when Al2O3 and TiO2 nanoparticles were added to the base fluid.<\/jats:p>","DOI":"10.3390\/e20040242","type":"journal-article","created":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T12:32:20Z","timestamp":1522672340000},"page":"242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Entropy Generation Analysis of Laminar Flows of Water-Based Nanofluids in Horizontal Minitubes under Constant Heat Flux Conditions"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2712-1908","authenticated-orcid":false,"given":"Mehrdad","family":"Karimzadehkhouei","sequence":"first","affiliation":[{"name":"Mechatronics Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Shojaeian","sequence":"additional","affiliation":[{"name":"Mechatronics Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdolali","family":"Sadaghiani","sequence":"additional","affiliation":[{"name":"Mechatronics Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K\u00fcr\u015fat","family":"\u015eendur","sequence":"additional","affiliation":[{"name":"Mechatronics Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey"},{"name":"Center of Excellence for Functional Surfaces and Interfaces for Nano Diagnostics (EFSUN), Sabanci University Nanotechnology and Applications Center (SUNUM), Sabanci University, Tuzla, Istanbul 34956, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Meng\u00fc\u00e7","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Ozyegin University, Cekmekoy, Istanbul 34782, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6283-6717","authenticated-orcid":false,"given":"Ali","family":"Ko\u015far","sequence":"additional","affiliation":[{"name":"Mechatronics Engineering Program, Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey"},{"name":"Center of Excellence for Functional Surfaces and Interfaces for Nano Diagnostics (EFSUN), Sabanci University Nanotechnology and Applications Center (SUNUM), Sabanci University, Tuzla, Istanbul 34956, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.1016\/j.applthermaleng.2010.06.023","article-title":"Convective Performance of Nanofluids in Commercial Electronics Cooling Systems","volume":"30","author":"Roberts","year":"2010","journal-title":"Appl. Therm. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1016\/j.ijheatfluidflow.2007.01.007","article-title":"Performance analysis of nanofluid-cooled microchannel heat sinks","volume":"28","author":"Tsai","year":"2007","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.renene.2017.09.067","article-title":"Numerical analysis of the Al2O3-water nanofluid forced laminar convection in an asymmetric heated channel for application in flat plate PV\/T collector","volume":"116","author":"Bianco","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_4","unstructured":"Choi, S.U.S., and Eastman, J.A. (1995, January 12\u201317). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the 1995 International mechanical engineering congress and exhibition, San Francisco, CA, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.colsurfa.2013.10.026","article-title":"Stable colloidal copper nanoparticles for a nanofluid: Production and application","volume":"441","author":"Gurav","year":"2014","journal-title":"Colloids Surf. A Physicochem. Eng. Asp."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4063","DOI":"10.1016\/j.ijheatmasstransfer.2012.03.048","article-title":"A review and analysis on influence of temperature and concentration of nanofluids on thermophysical properties, heat transfer and pumping power","volume":"55","author":"Vajjha","year":"2012","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.expthermflusci.2011.11.007","article-title":"Effect of Al2O3\u2013Cu\/water hybrid nanofluid in heat transfer","volume":"38","author":"Suresh","year":"2012","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14304","DOI":"10.1063\/1.3155999","article-title":"Particle shape effects on thermophysical properties of alumina nanofluids","volume":"106","author":"Timofeeva","year":"2009","journal-title":"J. Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"91001","DOI":"10.1115\/1.4024354","article-title":"Heat transfer in microchannels\u20142012 Status and research needs","volume":"135","author":"Kandlikar","year":"2013","journal-title":"J. Heat Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.ijheatmasstransfer.2006.08.001","article-title":"Assessment of the effectiveness of nanofluids for single-phase and two-phase heat transfer in micro-channels","volume":"50","author":"Lee","year":"2007","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1016\/j.nucengdes.2010.01.020","article-title":"Subcooled flow boiling heat transfer of dilute alumina, zinc oxide, and diamond nanofluids at atmospheric pressure","volume":"240","author":"Kim","year":"2010","journal-title":"Nucl. Eng. Des."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1016\/j.ijheatmasstransfer.2009.11.011","article-title":"An experimental study on CHF enhancement in flow boiling using Al2O3 nano-fluid","volume":"53","author":"Kim","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ijmultiphaseflow.2010.01.004","article-title":"Experimental study of critical heat flux enhancement during forced convective flow boiling of nanofluid on a short heated surface","volume":"36","author":"Ahn","year":"2010","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.expthermflusci.2014.10.013","article-title":"Pressure drop and heat transfer characteristics of nanofluids in horizontal microtubes under thermally developing flow conditions","volume":"67","author":"Karimzadehkhouei","year":"2015","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1016\/j.ijrefrig.2009.01.025","article-title":"Heat transfer characteristics of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube","volume":"32","author":"Peng","year":"2009","journal-title":"Int. J. Refrig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1016\/j.ijrefrig.2009.06.005","article-title":"Measurement and correlation of frictional pressure drop of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube","volume":"32","author":"Peng","year":"2009","journal-title":"Int. J. Refrig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1016\/j.ijheatmasstransfer.2009.11.026","article-title":"Flow-boiling heat transfer of R-134a-based nanofluids in a horizontal tube","volume":"53","author":"Henderson","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0021-9797(02)00176-5","article-title":"Production of aqueous colloidal dispersions of carbon nanotubes","volume":"260","author":"Jiang","year":"2003","journal-title":"J. Colloid Interface Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.icheatmasstransfer.2005.05.005","article-title":"Enhancement of thermal conductivity with carbon nanotube for nanofluids","volume":"32","author":"Liu","year":"2005","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.ijheatmasstransfer.2013.01.021","article-title":"Convective heat transfer characteristics of CNT nanofluids in a tubular heat exchanger of various lengths for energy efficient cooling\/heating system","volume":"60","author":"Kumaresan","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.ijheatmasstransfer.2005.07.009","article-title":"Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids)","volume":"49","author":"Ding","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.ijheatmasstransfer.2012.11.074","article-title":"The influence of multi-walled carbon nanotubes on single-phase heat transfer and pressure drop characteristics in the transitional flow regime of smooth tubes","volume":"58","author":"Meyer","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00231-013-1226-8","article-title":"Experimental characterization of convective heat transfer with MWCNT based nanofluids under laminar flow conditions","volume":"50","author":"Abreu","year":"2014","journal-title":"Heat Mass Transf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.expthermflusci.2014.06.003","article-title":"Comparing the thermal performance of water, Ethylene Glycol, Alumina and CNT nanofluids in CPU cooling: Experimental study","volume":"57","author":"Nazari","year":"2014","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1007\/s00231-013-1212-1","article-title":"Heat transfer characteristics of multi-walled carbon nanotubes suspension in a developing channel flow","volume":"49","author":"Elnajjar","year":"2013","journal-title":"Heat Mass Transf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.003","article-title":"The effect of nanoparticles on laminar heat transfer in a horizontal tube","volume":"69","author":"Utomo","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1016\/j.icheatmasstransfer.2012.07.017","article-title":"An experimental investigation on heat transfer characteristics of multi-walled CNT-heat transfer oil nanofluid flow inside flattened tubes under uniform wall temperature condition","volume":"39","author":"Ashtiani","year":"2012","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1016\/j.energy.2013.10.064","article-title":"Entropy generation of nanofluid flow with streamwise conduction inmicrochannels","volume":"64","author":"Ting","year":"2014","journal-title":"Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1016\/j.energy.2015.10.100","article-title":"Numerical investigation of flow characteristics, heat transfer and entropy generation of nanofluid flow inside an annular pipe partially or completely filled with porous media using two-phase mixture model","volume":"93","author":"Siavashi","year":"2015","journal-title":"Energy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.energy.2016.01.102","article-title":"Heat transfer and entropy generation in a microchannel with longitudinal vortex generators using nanofluids","volume":"101","author":"Ebrahimi","year":"2016","journal-title":"Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.ijheatmasstransfer.2016.04.089","article-title":"Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation","volume":"100","author":"Pantoja","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ijheatmasstransfer.2014.06.051","article-title":"Entropy generation during Al2O3\/water nanofluid flow in a solar collector: Effects of tube roughness, nanoparticle size, and different thermophysical models","volume":"78","author":"Mahian","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.enconman.2013.09.049","article-title":"Entropy generation analysis of turbulent convection flow of Al2O3\u2013water nanofluid in a circular tube subjected to constant wall heat flux","volume":"77","author":"Bianco","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4757","DOI":"10.1016\/j.ijheatmasstransfer.2010.06.016","article-title":"Entropy generation due to flow and heat transfer in nanofluids","volume":"53","author":"Singh","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ji, Y., Zhang, H.-C., Yang, X., and Shi, L. (2017). Entropy Generation Analysis and Performance Evaluation of Turbulent Forced Convective Heat Transfer to Nanofluids. Entropy, 19.","DOI":"10.3390\/e19030108"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"122401","DOI":"10.1115\/1.4002395","article-title":"Entropy Generation Analysis for Nanofluid Flow in Microchannels","volume":"132","author":"Li","year":"2010","journal-title":"J. Heat Transf."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.physa.2014.09.053","article-title":"Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method","volume":"417","author":"Sheikholeslami","year":"2014","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.ijheatmasstransfer.2014.10.041","article-title":"Shape effects of nanosize particles in Cu-H2O nanofluid on entropy generation","volume":"81","author":"Ellahi","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1016\/j.icheatmasstransfer.2011.04.008","article-title":"Entropy generation due to natural convection cooling of a nanofluid","volume":"38","author":"Shahi","year":"2011","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.energy.2012.06.009","article-title":"Analysis of entropy generation between co-rotating cylinders using nanofluids","volume":"44","author":"Mahian","year":"2012","journal-title":"Energy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.ijheatmasstransfer.2016.08.053","article-title":"Heat transfer and entropy generation analysis of HFE 7000 based nanorefrigerants","volume":"104","author":"Helvaci","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.ijheatmasstransfer.2013.06.010","article-title":"A review of entropy generation in nanofluid flow","volume":"65","author":"Mahian","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Singh, P.K., Ahmed, N.Z., Das, S.K., and Shatilla, Y. (2011, January 19\u201322). Exergy analysis of nanofluids in microchannel. Proceedings of the ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels, Edmonton, AB, Canada.","DOI":"10.1115\/ICNMM2011-58120"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/435873","article-title":"A review on nanofluids: Preparation, stability mechanisms, and applications","volume":"2012","author":"Yu","year":"2012","journal-title":"J. Nanomater."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3639","DOI":"10.1016\/S0017-9310(03)00156-X","article-title":"Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids","volume":"46","author":"Khanafer","year":"2003","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5090","DOI":"10.1016\/j.ijheatmasstransfer.2009.04.029","article-title":"An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids","volume":"52","author":"Garg","year":"2009","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.expthermflusci.2012.01.033","article-title":"Convective performance of CuO\/water nanofluid in an electronic heat sink","volume":"40","author":"Selvakumar","year":"2012","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1080\/08916159808946559","article-title":"Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles","volume":"11","author":"Pak","year":"1998","journal-title":"Exp. Heat Transf."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2115\/fiber.26.61","article-title":"Measurement of Specific Heat of Polyethylene","volume":"26","author":"Maeda","year":"1970","journal-title":"Sen\u2019i Gakkaishi"},{"key":"ref_50","first-page":"3","article-title":"Describing uncertainties in single-sample experiments","volume":"75","author":"Kline","year":"1953","journal-title":"Mech. Eng."},{"key":"ref_51","unstructured":"Bejan, A. (1982). Entropy Generation through Heat and Fluid Flow, Wiley."},{"key":"ref_52","unstructured":"Shah, R.K., and Alexander, L.L. (1971). Laminar Flow Forced Convection Heat Transfer and Flow Friction in Straight and Curved Ducts-A Summary of Analytical Solutions, Stanford University. No. TR-75."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ijthermalsci.2016.05.022","article-title":"Numerical modeling of convective heat transfer of thermally developing nanofluid flows in a horizontal microtube","volume":"109","author":"Sadaghiani","year":"2016","journal-title":"Int. J. Therm. Sci."},{"key":"ref_54","unstructured":"Bejan, A. (1995). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, CRC Press."},{"key":"ref_55","first-page":"89","article-title":"A prediction of the drop size distribution in a spray from first principles","volume":"1","author":"Sellens","year":"1985","journal-title":"At. Spray Technol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1080\/00102208808923992","article-title":"Derivation of droplet size distribution in sprays by using information theory","volume":"60","author":"Li","year":"1988","journal-title":"Combust. Sci. Technol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:59:21Z","timestamp":1760194761000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,2]]},"references-count":56,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["e20040242"],"URL":"https:\/\/doi.org\/10.3390\/e20040242","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,4,2]]}}}