{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T19:21:17Z","timestamp":1779909677000,"version":"3.53.1"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,18]],"date-time":"2020-10-18T00:00:00Z","timestamp":1602979200000},"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>Magnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles\u2014sphere, blade and lamina\u2014are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.<\/jats:p>","DOI":"10.3390\/e22101171","type":"journal-article","created":{"date-parts":[[2020,10,18]],"date-time":"2020-10-18T21:26:06Z","timestamp":1603056366000},"page":"1171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Shape Effect of Nanosize Particles on Magnetohydrodynamic Nanofluid Flow and Heat Transfer over a Stretching Sheet with Entropy Generation"],"prefix":"10.3390","volume":"22","author":[{"given":"Umair","family":"Rashid","sequence":"first","affiliation":[{"name":"Department of Modern Mechanics, CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, Turkey"},{"name":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan"},{"name":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5103-6092","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0491-1528","authenticated-orcid":false,"given":"Muhammd","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.joems.2014.04.005","article-title":"Entropy generation analysis of magneto hydrodynamic flow of a nanofluid over a stretching sheet","volume":"23","author":"Govindaraju","year":"2015","journal-title":"J. Egypt Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012010","DOI":"10.1088\/1742-6596\/1139\/1\/012010","article-title":"Analysis of entropy generation for nanofluid flow over a stretching sheet with an inclined magnetic field and uniform heat source\/sink","volume":"1139","author":"Govindaraju","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2037","DOI":"10.2298\/TSCI151112070S","article-title":"Analytical study of parameters affecting entropy generation of nanofluid turbulent flow in channel and micro-channel","volume":"20","author":"Sheikhzadeh","year":"2016","journal-title":"Therm. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1016\/j.icheatmasstransfer.2007.05.021","article-title":"Numerical investigation on developing laminar forced convection and entropy generation in a wavy channel","volume":"34","author":"Ko","year":"2007","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_5","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_6","first-page":"6053","article-title":"Analysis of entropy generation in a variable viscosity fluid flow between two concentric pipes with a convective cooling at the surface","volume":"6","author":"Tshehla","year":"2011","journal-title":"Int. J. Phys. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.proeng.2015.11.405","article-title":"Analysis of slip MHD nanofluid flow on entropy generation in a stretching sheet","volume":"127","author":"Govindaraju","year":"2015","journal-title":"Procedia Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s12206-018-1245-y","article-title":"Entropy generation analysis for multi-walled carbon nanotube (MWCNT) suspended nanofluid flow over wedge with thermal radiation and convective boundary condition","volume":"33","author":"Berrehal","year":"2019","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1016\/j.aej.2013.09.002","article-title":"An analytical study on entropy generation of nanofluids over a flat plate","volume":"52","author":"Malvandi","year":"2013","journal-title":"Alexandria Eng. J."},{"key":"ref_10","first-page":"739","article-title":"On the heat transport mechanism and entropy generation in a nozzle of liquid rocket engine using ferrofluid: A computational framework","volume":"6","author":"Acharya","year":"2019","journal-title":"J. Comput. Des. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.jtice.2013.09.018","article-title":"Magnetic field effect on nanofluid flow and heat transfer using KKL model","volume":"45","author":"Sheikholeslami","year":"2014","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.jtice.2013.04.006","article-title":"Numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nanoparticles","volume":"45","author":"Nadeem","year":"2014","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1016\/0020-7225(94)00120-9","article-title":"Effect of a magnetic field on free convection in a rectangular enclosure","volume":"33","author":"Rudraiah","year":"1995","journal-title":"Int. J. Eng. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.jtice.2010.02.002","article-title":"Unsteady MHD flow and heat transfer on a stretching sheet in a rotating fluid","volume":"41","author":"Abbas","year":"2010","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_15","unstructured":"Choi, S.U.S., and Eastman, A. (1995, January 12\u201317). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the International Mechanical Engineering Congress and Exhibition, San Francisco, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"135","DOI":"10.4028\/www.scientific.net\/MSF.802.135","article-title":"Synthesis and characterization of silver nanoparticles","volume":"802","author":"Aguiar","year":"2014","journal-title":"Mater. Sci. Forum"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4277","DOI":"10.1016\/j.aej.2017.07.016","article-title":"Effects of Ag-water nanofluid on hydrodynamics and thermal behaviors of three-dimensional separated step flow","volume":"57","author":"Atashafrooz","year":"2018","journal-title":"Alexandria Eng. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1016\/j.aej.2017.03.018","article-title":"MHD flow of Ag-water nanofluid over a flat porous plate with viscous-Ohmic dissipation, suction\/injection and heat generation\/absorption","volume":"57","author":"Upreti","year":"2018","journal-title":"Alexandria Eng. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Suleman, M., Ramzan, M., Ahmad, S., Lu, D., Muhammad, T., and Chung, J.D. (2019). A numerical simulation of silver-water nanofluid flow with impacts of Newtonian heating and homogeneous-heterogeneous reactions past a nonlinear stretched cylinder. Symmetry.","DOI":"10.3390\/sym11020295"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4236\/anp.2020.91002","article-title":"Impacts of nanoparticle shape on Al2O3-water nanofluid flow and heat transfer over a non-linear radically stretching sheet","volume":"09","author":"Rashid","year":"2020","journal-title":"Adv. Nanopart."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1002\/zamm.19890691115","article-title":"Free Convection on a Vertical Stretching Surface","volume":"69","author":"Wang","year":"1989","journal-title":"ZAMM Z. Angew. Math. Mech."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:23:19Z","timestamp":1760178199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,18]]},"references-count":21,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["e22101171"],"URL":"https:\/\/doi.org\/10.3390\/e22101171","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,18]]}}}