Research Article Finite Element Least Square Technique for Newtonian Fluid Flow through a Semicircular Cylinder of Recirculating Region via COMSOL Multiphysics Ilyas Khan , 1 Abid A. Memon, 2 M. Asif Memon, 2 Kaleemullah Bhatti, 2 Gul M. Shaikh, 2 Dumitru Baleanu , 3,4,5 and Ziyad A. Alhussain 1 1 Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia 2 Department of Mathematics, Sukkur IBA University, Sukkur, Sindh, Pakistan 3 Department of Mathematics, Cankaya University, Ankara 06790, Turkey 4 Institute of Space Sciences, Magurele 077125, Romania 5 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan Correspondence should be addressed to Ilyas Khan; i.said@mu.edu.sa and Dumitru Baleanu; baleanu@mail.cmuh.org.tw Received 26 August 2020; Revised 23 September 2020; Accepted 19 October 2020; Published 4 November 2020 Academic Editor: Hijaz Ahmad Copyright©2020IlyasKhanetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is article aims to study Newtonian fluid flow modeling and simulation through a rectangular channel embedded in a semicircularcylinderwiththerangeofReynoldsnumberfrom100to1500.efluidisconsideredaslaminarandNewtonian,and the problem is time independent. A numerical procedure of finite element’s least Square technique is implemented through COMSOL multiphysics 5.4. e problem is validated through asymptotic solution governed through the screen boundary condition. e vortex length of the recirculating region formed at the back of the cylinder and orientation of velocity field and pressurewillbediscussedbythreehorizontalandfourverticallinesalongtherecirculatingregionintermsofReynoldsnumber.It was found that the two vortices of unequal size have appeared and the lengths of these vortices are increased with the increase Reynoldsnumber.Also,theempiricalequationsthroughthelinearregressionprocedureweredeterminedforthosevortices.e orientationofthevelocitymagnitudeaswellaspressurealongthelinespassingthroughthecenterofupperandlowervorticesare the same. 1. Introduction In the engineering sciences, the Navier–Stokes equations governed through Newton’s law of motion possess the paramount importance and describe the physical phe- nomenonofflowintheformofnonlinearpartialdifferential equations in the vector form. ey help to model so many physical problems such as blood flow in the human or animal body, manufacturing designs, manufacturing car, andaircraftdesigns,calculatingdragforceofairflowaround wings, removal of pollutions, weather conditions, rivers, flow of oceans, etc. e literature studies reveal that when the fluid enters theregionwithinasufficientvelocitymagnitudeandcomes intocontactwiththebluffbodiesofanyshape,theformation of vortex shedding and recirculating flow is taken place at the back of the observed body. e size of this recirculating region or increasing with the increase in the velocity magnitude by which the fluid comes into the strike with these bluff bodies. ese vortices are attached as well as detached periodically and creating a von Karman vortex region.efluidwhichpassesthroughthebodiescreatedthe vortices with the negative pressure, which means that, any object presented in the region might be attracted by these vortices.Withtherangeofratios1.6to4totheheightofthe rectangularchannelwithadiameterofthecircleandranging up to 5 the Stuart number, the vortex structure and its incrementwasstudiedbyRashidetal.[1].Itwasderivedthat Hindawi Journal of Mathematics Volume 2020, Article ID 8869308, 11 pages https://doi.org/10.1155/2020/8869308