{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T23:22:02Z","timestamp":1777332122619,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"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>This article is devoted to study sustainability of entropy generation in an incompressible thermal flow of Newtonian fluids over a thin needle that is moving in a parallel stream. Two types of Newtonian fluids (water and air) are considered in this work. The energy dissipation term is included in the energy equation. Here, it is presumed that u\u221e (the free stream velocity) is in the positive axial direction (x-axis) and the motion of the thin needle is in the opposite or similar direction as the free stream velocity. The reduced self-similar governing equations are solved numerically with the aid of the shooting technique with the fourth-order-Runge-Kutta method. Using similarity transformations, it is possible to obtain the expression for dimensionless form of the volumetric entropy generation rate and the Bejan number. The effects of Prandtl number, Eckert number and dimensionless temperature parameter are discussed graphically in details for water and air taken as Newtonian fluids.<\/jats:p>","DOI":"10.3390\/e21010074","type":"journal-article","created":{"date-parts":[[2019,1,18]],"date-time":"2019-01-18T02:22:23Z","timestamp":1547778143000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Thermodynamic Analysis of Entropy Generation Minimization in Thermally Dissipating Flow Over a Thin Needle Moving in a Parallel Free Stream of Two Newtonian Fluids"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700,000, Vietnam"}]},{"given":"Waqar A.","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6516-9809","authenticated-orcid":false,"given":"Muhammad","family":"Qasim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad (CUI), Park Road, Tarlai Kalan, Islamabad-455000, Pakistan"}]},{"given":"Idrees","family":"Afridi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad (CUI), Park Road, Tarlai Kalan, Islamabad-455000, Pakistan"}]},{"given":"Sayer O.","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1115\/1.3451063","article-title":"A study of entropy generation in fundamental convective heat transfer","volume":"101","author":"Bejan","year":"1979","journal-title":"J. Heat Transf."},{"key":"ref_2","unstructured":"Bejan, A. (1982). Entropy Generation through Heat and Fluid Flow, John Wiley and Sons."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/S1164-0235(02)00062-6","article-title":"Thermodynamics analysis of flow and heat transfer inside channel with two parallel plates","volume":"2","author":"Mahmud","year":"2002","journal-title":"Exergy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1088\/0031-8949\/74\/6\/007","article-title":"Irreversibility analysis for a gravity driven non-Newtonian liquid film along an inclined isothermal plate","volume":"74","author":"Makinde","year":"2006","journal-title":"Phys. Scr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0031-8949\/78\/01\/015402","article-title":"Thermal criticality and entropy analysis for a variable viscosity Couette flow","volume":"78","author":"Makinde","year":"2008","journal-title":"Phys. Scr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1446","DOI":"10.3390\/e13081446","article-title":"Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating","volume":"13","author":"Makinde","year":"2011","journal-title":"Entropy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1002\/htj.20404","article-title":"Entropy Generation in an Asymmetrically Cooled Slab with Temperature-Dependent Internal Heat Generation","volume":"41","author":"Aziz","year":"2012","journal-title":"Heat Transf.-Asian Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.crme.2014.09.002","article-title":"Entropy generation in a variable viscosity channel flow of nanofluids with convective cooling","volume":"343","author":"Mkwizu","year":"2015","journal-title":"Compt. Rendus Mecanique"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1504\/IJEX.2013.056131","article-title":"On inherent irreversibility in Sakiadis flow of nanofluids","volume":"13","author":"Makinde","year":"2013","journal-title":"Int. J. Exergy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.energy.2013.01.036","article-title":"Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm","volume":"55","author":"Rashidi","year":"2013","journal-title":"Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s40430-014-0163-x","article-title":"Investigation of entropy generation effects in magnetohydrodynamic three-dimensional flow and heat transfer of viscous fluid over a stretching surface","volume":"37","author":"Butt","year":"2015","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_12","first-page":"36","article-title":"Entropy Generation in MHD free convection boundary layer flow past an inclined flat plat embedded in a porous medium with hall currents","volume":"8","author":"Das","year":"2013","journal-title":"Int. J. Comput. Appl."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"753","DOI":"10.18869\/acadpub.jafm.67.223.22916","article-title":"Entropy generation analysis for stagnation point flow in a porous medium over a permeable stretching surface","volume":"8","author":"Rashidi","year":"2015","journal-title":"J. Appl. Fluid Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.cma.2018.09.044","article-title":"New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media","volume":"344","author":"Sheikholeslami","year":"2019","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_16","first-page":"1524","article-title":"Second law analysis for radiative MHD slip flow of a nanofluid over a stretching sheet with non-uniform heat source effect","volume":"23","author":"Hakeem","year":"2016","journal-title":"Sci. Iran."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.energy.2016.01.067","article-title":"Numerical investigation of magnetic field effects on entropy generation in viscous flow over a stretching cylinder embedded in a porous medium","volume":"99","author":"Butt","year":"2016","journal-title":"Energy"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Afridi, M.I., Qasim, M., Khan, I., Shafie, S., and Alshomrani, A.S. (2016). Entropy Generation in Magnetohydrodynamic Mixed Convection Flow over an Inclined Stretching Sheet. Entropy, 19.","DOI":"10.3390\/e19010010"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1063\/1.1762194","article-title":"Boundary Layer over a thin needle","volume":"10","author":"Lee","year":"1967","journal-title":"Phys. Fluids"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.3450809","article-title":"Forced confection heat transfer from non-isothermal thin needles","volume":"100","author":"Chen","year":"1978","journal-title":"J. Heat Transf. Trans. ASME"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2895","DOI":"10.1088\/0256-307X\/24\/10\/051","article-title":"Boundary layer flow over a continuously moving thin needle in a parallel free stream","volume":"24","author":"Ishaq","year":"2007","journal-title":"Chin. Phys. Lett."},{"key":"ref_22","first-page":"054503-1","article-title":"Forced convection boundary layer flow past non isothermal thin needles in nanofluids","volume":"113","author":"Grosan","year":"2011","journal-title":"J. Heat Transf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.applthermaleng.2016.11.165","article-title":"Boundary layer flow past a continuously moving thin needle","volume":"114","author":"Soid","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ijthermalsci.2017.09.014","article-title":"Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation","volume":"123","author":"Afridi","year":"2018","journal-title":"Int. J. Ther. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:26Z","timestamp":1760185586000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["e21010074"],"URL":"https:\/\/doi.org\/10.3390\/e21010074","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}