Research Article
Generalized Thermal Flux Flow for Jeffrey Fluid with Fourier
Law over an Infinite Plate
Muhammad Imran Asjad,
1
Abdul Basit ,
1
Ali Akg¨ ul ,
2
and Taseer Muhammad
3
1
Department of Mathematics, University of Management and Technology Lahore, Lahore 54770, Pakistan
2
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
3
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
CorrespondenceshouldbeaddressedtoAliAkg¨ ul;aliakgul@siirt.edu.tr
Received 30 June 2021; Accepted 28 August 2021; Published 13 September 2021
AcademicEditor:FahdJarad
Copyright © 2021 Muhammad Imran Asjad et al. is is an open access article distributed under the Creative Commons
AttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkis
properly cited.
eunsteadyflowofJeffreyfluidalongwithaverticalplateisstudiedinthispaper.eequationsofmomentum,energy,and
generalizedFourier’slawofthermalfluxaretransformedtonon-dimensionalformfortheproperdimensionlessparameters.e
Prabhakarfractionaloperatorisappliedtoacquirethefractionalmodelusingtheconstitutiveequations.Toobtainthegeneralized
resultsforvelocityandtemperaturedistribution,Laplacetransformisperformed.einfluencesoffractionalparameters α, β, c,
thermalGrashofnumberGr,andnon-dimensionalPrandtlnumberPruponvelocityandtemperaturedistributionarepresented
graphically.eresultsareimprovedintheformofdecayofenergyandmomentumequations,respectively.enewfractional
parametercontainstheMittag-Lefflerkernelwiththreefractionalparameterswhichareresponsibleforbettermemoryofthefluid
properties rather than the exponential kernel appearing in the Caputo–Fabrizio fractional operator. e Prabhakar fractional
operator has advantage over Caputo–Fabrizio in the real data fitting where needed.
1. Introduction
Non-Newtonian fluids have recently become more appro-
priate for technical and scientific applications than New-
tonianfluids.Becausethehighlynon-linearbehaviorofnon-
Newtonian fluid has a complex character, the use of non-
Newtonian fluids in industries is more complicated. e
studyofnon-Newtonianfluidhasgotmuchattentioninthe
disciplineofscienceandengineeringduetotheirvastrange
ofindustrialapplications,productionofpolymers,chemical
industry, lubricant performance, food processing, and bi-
ologicalfluidmovement.Todescribetheviscousbehaviorof
thesefluids,variousapproacheswerepresented.Asubclass
of these fluids, namely, Jeffrey fluid, has attracted a lot of
attention in the last few years. Because its constitutive
equationcanbereducedtothatoftheNewtonianmodelasa
specificcase,theJeffreymodelisconsideredasanextension
ofthewidelyusedNewtonianfluidmodel.eJeffreyfluid
model can represent the stress relaxation property of non-
Newtonian fluids, but the viscous fluid model is unable to
describethisphenomenon.einfluencesofrelaxationand
retardation are demonstrated through the Jeffrey fluid.
HayatandMustafa[1]examinedtheimpactofheattransfer
on free convective flow of Jeffrey fluid through porous
verticalstretchingsheet.Maqbooletal.[2]investigatedthe
behavior of velocity and temperature profiles in a natural
convection heat transfer of MHD Jeffrey fluid with a flat
plate containing porous material using the Laplace trans-
form. Aleem et al. [3] studied the MHD free convection
transportofJeffreyfluidbetweentwowarmedverticalplates
mountedinporousmediumundertheinfluenceofelectric
field.
Jeffrey fluid is not just a basic theoretical concept, but
thisisalsousedtosolveavarietyofpracticaldifficulties,such
as clay rotational motion and heart vessel pumping. Also,
manyscientistsandresearcherslookedathowporosityand
magnetic fields affected flow behavior in many forms of
Jeffrey fluid. e Jeffrey model is a linear model that uses
Hindawi
Mathematical Problems in Engineering
Volume 2021, Article ID 5403879, 9 pages
https://doi.org/10.1155/2021/5403879