{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T14:32:54Z","timestamp":1768487574568,"version":"3.49.0"},"reference-count":58,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,7]],"date-time":"2020-01-07T00:00:00Z","timestamp":1578355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Al2O3\/water nanofluid conjugate heat transfer inside a microchannel is studied numerically. The fluid flow is laminar and a constant heat flux is applied to the axisymmetric microchannel\u2019s outer wall, and the two ends of the microchannel\u2019s wall are considered adiabatic. The problem is inherently three-dimensional, however, in order to reduce the computational cost of the solution, it is rational to consider only a half portion of the axisymmetric microchannel and the domain is revolved through its axis. Hence. the problem is reduced to a two-dimensional domain, leading to less computational grid. At the centerline (r = 0), as the flow is axisymmetric, there is no radial gradient (\u2202u\/\u2202r = 0, v = 0, \u2202T\/\u2202r = 0). The effects of four Reynolds numbers of 500, 1000, 1500, and 2000; particle volume fractions of 0% (pure water), 2%, 4%, and 6%; and nanoparticles diameters in the range of 10 nm, 30 nm, 50 nm, and 70 nm on forced convective heat transfer as well as performance evaluation criterion are studied. The parameter of performance evaluation criterion provides valuable information related to heat transfer augmentation together with pressure losses and pumping power needed in a system. One goal of the study is to address the expense of increased pressure loss for the increment of the heat transfer coefficient. Furthermore, it is shown that, despite the macro-scale problem, in microchannels, the viscous dissipation effect cannot be ignored and is like an energy source in the fluid, affecting temperature distribution as well as the heat transfer coefficient. In fact, it is explained that, in the micro-scale, an increase in inlet velocity leads to more viscous dissipation rates and, as the friction between the wall and fluid is considerable, the temperature of the wall grows more intensely compared with the bulk temperature of the fluid. Consequently, in microchannels, the thermal behavior of the fluid would be totally different from that of the macro-scale.<\/jats:p>","DOI":"10.3390\/sym12010120","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T03:59:57Z","timestamp":1578455997000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":76,"title":["Numerical Investigation of Forced Convective Heat Transfer and Performance Evaluation Criterion of Al2O3\/Water Nanofluid Flow inside an Axisymmetric Microchannel"],"prefix":"10.3390","volume":"12","author":[{"given":"Misagh","family":"Irandoost Shahrestani","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, University of Tehran, Tehran 14155-6619, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5830-4934","authenticated-orcid":false,"given":"Akbar","family":"Maleki","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0631-3046","authenticated-orcid":false,"given":"Mostafa","family":"Safdari Shadloo","sequence":"additional","affiliation":[{"name":"CORIA-UMR 6614, Normandie University, CNRS-University &amp; INSA, 76000 Rouen, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iskander","family":"Tlili","sequence":"additional","affiliation":[{"name":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,7]]},"reference":[{"key":"ref_1","first-page":"827","article-title":"A review on the applications of intelligence methods in predicting thermal conductivity of nanofluids","volume":"138","author":"Ramezanizadeh","year":"2019","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109345","DOI":"10.1016\/j.rser.2019.109345","article-title":"A review on the utilized machine learning approaches for modeling the dynamic viscosity of nanofluids","volume":"114","author":"Ramezanizadeh","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.ijheatmasstransfer.2019.05.032","article-title":"A review on the approaches applied for cooling fuel cells","volume":"139","author":"Ramezanizadeh","year":"2019","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.18280\/mmep.050402","article-title":"Applications of nanofluids in geothermal: A review","volume":"5","author":"Ahmadi","year":"2018","journal-title":"Math. Model. Eng. Probl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Abdollahzadeh Jamalabadi, M., Ghasemi, M., Alamian, R., Wongwises, S., Afrand, M., and Shadloo, M. (2019). Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field. Symmetry, 11.","DOI":"10.3390\/sym11101275"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Abdollahzadeh Jamalabadi, M.Y., Alamian, R., Yan, W.-M., Li, L.K.B., Leveneur, S., and Safdari Shadloo, M. (2019). Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers. Symmetry, 11.","DOI":"10.3390\/sym11111353"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.physe.2016.10.015","article-title":"The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump","volume":"86","author":"Karimipour","year":"2017","journal-title":"Phys. E Low-Dimens. Syst. Nanostruct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"168781401667356","DOI":"10.1177\/1687814016673569","article-title":"A survey on experimental and numerical studies of convection heat transfer of nanofluids inside closed conduits","volume":"8","author":"Safaei","year":"2016","journal-title":"Adv. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tso, C.P., Hor, C.H., Chen, G.M., and Kok, C.K. (2018). Heat induction by viscous dissipation subjected to symmetric and asymmetric boundary conditions on a small oscillating flow in a microchannel. Symmetry, 10.","DOI":"10.3390\/sym10100499"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3447","DOI":"10.1016\/j.ijheatmasstransfer.2007.01.016","article-title":"Experimental and numerical studies of liquid flow and heat transfer in microtubes","volume":"50","author":"Li","year":"2007","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1115\/1.2825978","article-title":"Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles","volume":"121","author":"Lee","year":"1999","journal-title":"J. Heat Transf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1063\/1.1341218","article-title":"Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles","volume":"78","author":"Eastman","year":"2001","journal-title":"Appl. Phys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/j.applthermaleng.2013.08.005","article-title":"Optimization of thermal performances and pressure drop of rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid","volume":"62","author":"Halelfadl","year":"2014","journal-title":"Appl. Therm. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.molliq.2018.05.124","article-title":"A review of thermal conductivity of various nanofluids","volume":"265","author":"Ahmadi","year":"2018","journal-title":"J. Mol. Liq."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jalali, E., Akbari, O.A., Sarafraz, M.M., Abbas, T., and Safaei, M.R. (2019). Heat transfer of oil\/MWCNT nanofluid jet injection inside a rectangular microchannel. Symmetry, 11.","DOI":"10.3390\/sym11060757"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1080\/10407782.2014.916101","article-title":"Investigation of Heat Transfer Enhancement in a Forward-Facing Contracting Channel Using FMWCNT Nanofluids","volume":"66","author":"Safaei","year":"2014","journal-title":"Numer. Heat Transf. Part A Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.physe.2017.04.006","article-title":"Analysis of heat transfer and nanofluid fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs","volume":"91","author":"Behnampour","year":"2017","journal-title":"Phys. E Low-Dimens. Syst. Nanostruct."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Tian, C., Maleki, A., Motie, S., Yavarinasab, A., and Afrand, M. (2019). Generation expansion planning by considering wind resource in a competitive environment. J. Therm. Anal. Calorim.","DOI":"10.1007\/s10973-019-09139-y"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117920","DOI":"10.1016\/j.jclepro.2019.117920","article-title":"A heuristic-based approach for optimizing a small independent solar and wind hybrid power scheme incorporating load forecasting","volume":"241","author":"Zhang","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ijepes.2015.11.107","article-title":"Generation expansion planning by considering energy-efficiency programs in a competitive environment","volume":"80","author":"Motie","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, J., Mohammadi, A., and Maleki, A. (2019). Techno-economic analysis of new integrated system of humid air turbine, organic Rankine cycle, and parabolic trough collector. J. Therm. Anal. Calorim.","DOI":"10.1007\/s10973-019-08855-9"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"15973","DOI":"10.1016\/j.ijhydene.2017.01.169","article-title":"Design of a cost-effective on-grid hybrid wind\u2013hydrogen based CHP system using a modified heuristic approach","volume":"42","author":"Maleki","year":"2017","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3538","DOI":"10.1016\/j.ijheatmasstransfer.2006.03.004","article-title":"Microtube liquid single-phase heat transfer in laminar flow","volume":"49","author":"Celata","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_24","unstructured":"Bergman, T.L., and Incropera, F.P. (2011). Fundamentals of Heat and Mass Transfer, Wiley."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.applthermaleng.2012.07.040","article-title":"Analytical analysis of heat transfer and pumping power of laminar nanofluid developing flow in microchannels","volume":"50","author":"Mital","year":"2013","journal-title":"Appl. Therm. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1115\/1.3244249","article-title":"Simultaneous Wall and Fluid Axial Conduction in Laminar Pipe-Flow Heat Transfer","volume":"102","author":"Faghri","year":"1980","journal-title":"J. Heat Transf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1016\/j.ijheatfluidflow.2009.03.009","article-title":"Conjugate forced convection and heat conduction in circular microchannels","volume":"30","author":"Nonino","year":"2009","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1108\/09615530610649717","article-title":"Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension","volume":"16","author":"Galanis","year":"2006","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1108\/09615530710761216","article-title":"Developing mixed convection of a nanofluid in a horizontal tube with uniform heat flux","volume":"17","author":"Akbari","year":"2007","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.colsurfa.2018.01.030","article-title":"Thermal conductivity ratio prediction of Al2O3\/water nanofluid by applying connectionist methods","volume":"541","author":"Ahmadi","year":"2018","journal-title":"Colloids Surf. A Physicochem. Eng. Asp."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Ahmadi, M.H., Ahmadi, M.A., Nazari, M.A., Mahian, O., and Ghasempour, R. (2018). A proposed model to predict thermal conductivity ratio of Al2O3\/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach. J. Therm. Anal. Calorim.","DOI":"10.1007\/s10973-018-7035-z"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s10973-018-7916-1","article-title":"Rigorous smart model for predicting dynamic viscosity of Al2O3\/water nanofluid","volume":"137","author":"Ramezanizadeh","year":"2019","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1093\/ijlct\/ctz030","article-title":"Modeling thermal conductivity of Ag\/water nanofluid by applying a mathematical correlation and artificial neural network","volume":"14","author":"Ramezanizadeh","year":"2019","journal-title":"Int. J. Low-Carbon Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1007\/s10973-015-4565-5","article-title":"Evaluation of thermal conductivity of COOH-functionalized MWCNTs\/water via temperature and solid volume fraction by using experimental data and ANN methods","volume":"121","author":"Naderi","year":"2015","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Komeilibirjandi, A., Raffiee, A.H., Maleki, A., Alhuyi Nazari, M., and Safdari Shadloo, M. (2019). Thermal conductivity prediction of nanofluids containing CuO nanoparticles by using correlation and artificial neural network. J. Therm. Anal. Calorim.","DOI":"10.1007\/s10973-019-08838-w"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"121056","DOI":"10.1016\/j.physa.2019.121056","article-title":"Minimize pressure drop and maximize heat transfer coefficient by the new proposed multi-objective optimization\/statistical model composed of \u201cANN + Genetic Algorithm\u201d based on empirical data of CuO\/paraffin nanofluid in a pipe","volume":"527","author":"Bagherzadeh","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.icheatmasstransfer.2015.05.014","article-title":"Thermal conductivity of Cu\/TiO2\u2013water\/EG hybrid nanofluid: Experimental data and modeling using artificial neural network and correlation","volume":"66","author":"Wongwises","year":"2015","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s11051-004-3170-5","article-title":"A new thermal conductivity model for nanofluids","volume":"6","author":"Koo","year":"2004","journal-title":"J. Nanopart. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"153107","DOI":"10.1063\/1.2093936","article-title":"Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement","volume":"87","author":"Chon","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.applthermaleng.2006.04.011","article-title":"Effect of uncertainties in physical properties on forced convection heat transfer with nanofluids","volume":"27","author":"Galanis","year":"2007","journal-title":"Appl. Therm. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4215","DOI":"10.1016\/j.ijheatmasstransfer.2004.04.018","article-title":"Three-dimensional analysis of heat transfer in a micro-heat sink with single phase flow","volume":"47","author":"Li","year":"2004","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.icheatmasstransfer.2009.09.005","article-title":"Effects of temperature dependent thermal conductivity on Nu number behavior in micro-tubes","volume":"37","author":"Lelea","year":"2010","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1016\/S0017-9310(99)00241-0","article-title":"Experimental verification of the role of Brinkman number in microchannels using local parameters","volume":"43","author":"Tso","year":"2000","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1016\/S0017-9310(98)00276-2","article-title":"The role of the Brinkman number in analysing flow transitions in microchannels","volume":"42","author":"Tso","year":"1999","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1016\/S0017-9310(97)00232-9","article-title":"The use of the Brinkman number for single phase forced convective heat transfer in microchannels","volume":"41","author":"Tso","year":"1998","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1080\/01457630500523865","article-title":"Scaling Effects for Liquid Flows in Microchannels","volume":"27","author":"Morini","year":"2006","journal-title":"Heat Transf. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"740578","DOI":"10.1155\/2014\/740578","article-title":"Investigation of micro- and nanosized particle erosion in a 90\u00b0 pipe bend using a two-phase discrete phase model","volume":"2014","author":"Safaei","year":"2014","journal-title":"Sci. World J."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Lin, C. (2019). Application of the Symmetric Model to the Design Optimization of Fan Outlet Grills. Symmetry, 11.","DOI":"10.3390\/sym11080959"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Chen, C.-W., and Lu, Y.-F. (2019). Computational Fluid Dynamics Study of Water Entry Impact Forces of an Airborne-Launched, Axisymmetric, Disk-Type Autonomous Underwater Hovering Vehicle. Symmetry, 11.","DOI":"10.3390\/sym11091100"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.ijheatmasstransfer.2016.02.032","article-title":"Pavement surface maximum temperature increases linearly with solar absorption and reciprocal thermal inertial","volume":"97","author":"Qin","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.enbuild.2016.05.026","article-title":"Theory and procedure for measuring the solar reflectance of urban prototypes","volume":"126","author":"Qin","year":"2016","journal-title":"Energy Build."},{"key":"ref_52","unstructured":"Versteeg, H., and Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Prentice Hall."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Patankar, S. (2018). Numerical Heat Transfer and Fluid Flow, CRC Press.","DOI":"10.1201\/9781482234213"},{"key":"ref_54","unstructured":"Perry, R.H., and Green, D.W. (2008). Perry\u2019s Chemical Engineers\u2019 Handbook, McGraw-Hill."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1017\/S0022112077001062","article-title":"The effect of Brownian motion on the bulk stress in a suspension of spherical particles","volume":"83","author":"Batchelor","year":"1977","journal-title":"J. Fluid Mech."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ijthermalsci.2012.03.009","article-title":"Heat transfer performance and hydrodynamic behavior of turbulent nanofluid radial flows","volume":"58","author":"Roy","year":"2012","journal-title":"Int. J. Therm. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/j.icheatmasstransfer.2011.04.002","article-title":"The micro-tube heat transfer and fluid flow of water based Al2O3 nanofluid with viscous dissipation","volume":"38","author":"Lelea","year":"2011","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.ijheatmasstransfer.2008.03.033","article-title":"Forced convective heat transfer of nanofluids in microchannels","volume":"52","author":"Jung","year":"2009","journal-title":"Int. J. Heat Mass Transf."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:04:12Z","timestamp":1760364252000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,7]]},"references-count":58,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["sym12010120"],"URL":"https:\/\/doi.org\/10.3390\/sym12010120","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,7]]}}}