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